The document is a statistics survey report that was prepared by three students - Muhammad Saeed, Muhammad Aamir Riaz, and Muhammad Imran. It discusses conducting a survey on the essentiality of mathematics in professional life. The purpose of the study was to find students' opinions on how important mathematics is for their fields. The report defines key statistical terms and concepts used in the survey such as population, sample, measures of central tendency, and quartiles.
This document provides an overview of a lesson about further discussing the importance of the mean as a measure of central tendency. It discusses how to determine expected values when targeting a particular mean value. Other types of means are also introduced, such as weighted means, trimmed means, geometric means, and harmonic means. The lesson outline includes introducing the mean, calculating expected values for a targeted mean, and an advanced section on other means. Examples are provided to illustrate calculating expected values and different types of means.
The lesson plan discusses measures of central tendency for ungrouped data. It defines the three measures - mean, median, and mode. The lesson explains how to calculate each measure through examples and formulas. Students will practice finding the mean, median, and mode of various data sets.
This document discusses descriptive statistics and summarizing distributions. It covers measures of central tendency including the mean, median, and mode. It also discusses measures of dispersion such as variance and standard deviation. These measures are used to describe the characteristics of frequency distributions and determine where the center is located and how spread out the data is. The choice between measures depends on whether the distribution is normal or skewed.
Variance and standard deviation are measures of spread used to describe the shape of distributions associated with the mean. While two distributions may have the same mean, their variance and standard deviation can show that they have very different shapes. To calculate variance and standard deviation, you first find the deviation of each value from the mean, square the deviations, and sum them. You then divide the sum by n-1 to get the variance, and take the square root of the variance to find the standard deviation.
Central tendency refers to statistical measures that identify a central or typical value for a data set. The three main measures are the mean, median, and mode. The mean is the average value calculated by dividing the sum of all values by the number of values. The median is the middle value of the data set when sorted. The mode is the most frequently occurring value. Different measures are better suited depending on the type of data and how it is distributed.
Mba i qt unit-2_measures of central tendencyRai University
This document discusses various measures of central tendency, including the arithmetic mean. It defines the arithmetic mean as the total of the values divided by the number of values. It describes direct and short-cut methods for calculating the arithmetic mean for both ungrouped and grouped data. Some key properties of the arithmetic mean are that the sum of deviations from the mean is 0, and the sum of squared deviations is minimized at the mean. Weighted arithmetic mean is also discussed, which assigns weights to values before calculating the average.
The document discusses measures of central tendency, including the mean, median, and mode. It provides an example of monthly family incomes and calculates each measure using the data. The mean is the average, the median is the middle value, and the mode is the most frequent value. Each measure has unique properties that determine when it is most appropriate to use.
Sherborne C of E Primary School is a small, rural school located in Gloucestershire, England. It has 43 students ranging from ages 4 to 11 split across two classes. The school was established in 1868 and is the only school for 10km. It has a headteacher, two teachers, and support staff. The school focuses on monitoring student progress through assessments and setting targets to support lifelong learning.
This document provides an overview of a lesson about further discussing the importance of the mean as a measure of central tendency. It discusses how to determine expected values when targeting a particular mean value. Other types of means are also introduced, such as weighted means, trimmed means, geometric means, and harmonic means. The lesson outline includes introducing the mean, calculating expected values for a targeted mean, and an advanced section on other means. Examples are provided to illustrate calculating expected values and different types of means.
The lesson plan discusses measures of central tendency for ungrouped data. It defines the three measures - mean, median, and mode. The lesson explains how to calculate each measure through examples and formulas. Students will practice finding the mean, median, and mode of various data sets.
This document discusses descriptive statistics and summarizing distributions. It covers measures of central tendency including the mean, median, and mode. It also discusses measures of dispersion such as variance and standard deviation. These measures are used to describe the characteristics of frequency distributions and determine where the center is located and how spread out the data is. The choice between measures depends on whether the distribution is normal or skewed.
Variance and standard deviation are measures of spread used to describe the shape of distributions associated with the mean. While two distributions may have the same mean, their variance and standard deviation can show that they have very different shapes. To calculate variance and standard deviation, you first find the deviation of each value from the mean, square the deviations, and sum them. You then divide the sum by n-1 to get the variance, and take the square root of the variance to find the standard deviation.
Central tendency refers to statistical measures that identify a central or typical value for a data set. The three main measures are the mean, median, and mode. The mean is the average value calculated by dividing the sum of all values by the number of values. The median is the middle value of the data set when sorted. The mode is the most frequently occurring value. Different measures are better suited depending on the type of data and how it is distributed.
Mba i qt unit-2_measures of central tendencyRai University
This document discusses various measures of central tendency, including the arithmetic mean. It defines the arithmetic mean as the total of the values divided by the number of values. It describes direct and short-cut methods for calculating the arithmetic mean for both ungrouped and grouped data. Some key properties of the arithmetic mean are that the sum of deviations from the mean is 0, and the sum of squared deviations is minimized at the mean. Weighted arithmetic mean is also discussed, which assigns weights to values before calculating the average.
The document discusses measures of central tendency, including the mean, median, and mode. It provides an example of monthly family incomes and calculates each measure using the data. The mean is the average, the median is the middle value, and the mode is the most frequent value. Each measure has unique properties that determine when it is most appropriate to use.
Sherborne C of E Primary School is a small, rural school located in Gloucestershire, England. It has 43 students ranging from ages 4 to 11 split across two classes. The school was established in 1868 and is the only school for 10km. It has a headteacher, two teachers, and support staff. The school focuses on monitoring student progress through assessments and setting targets to support lifelong learning.
Here are the solutions to the exercises:
1. The area under the standard normal curve between z=-∞ and z=2 is 0.9772 (using the standard normal table)
2. The probability that a z value will be between -2.55 and +2.55 is 0.9932 (using the standard normal table)
3. The proportion of z values between -2.74 and 1.53 is 0.9950
4. P(z ≥ 2.71) = 1 - 0.9958 = 0.0042
5. P(.84 ≤ z ≤ 2.45) = 0.8036 - 0.1967 = 0.6069
This document discusses various measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. The mean is the average and is calculated by summing all values and dividing by the total number of data points. The median is the middle value when data is arranged in order. The mode is the value that occurs most frequently in the data set. Examples are given to demonstrate calculating each measure. The document also discusses advantages and limitations of each central tendency measure.
This document provides a summary of key concepts in advanced business mathematics and statistics. It defines measures of central tendency including mean, mode, and median. It also discusses measures of dispersion like range and standard deviation. Additionally, it covers topics like regression, hypothesis testing, probability, and different types of statistical analysis.
This document provides an overview of statistics concepts including measures of central tendency (mean, median, mode), calculating these measures, outliers and their effect, trimmed means, weighted means, and percentiles. It includes examples and step-by-step solutions for calculating various statistical measures. Key topics covered are finding the mean, median, and mode of data sets, how outliers impact these measures, calculating trimmed and weighted means, and an introduction to percentiles.
This document provides an overview of statistical estimation and inference. It discusses point estimation, which provides a single value to estimate an unknown population parameter, and interval estimation, which gives a range of plausible values for the parameter. The key aspects of interval estimation are confidence intervals, which provide a probability statement about where the true population parameter lies. The document also covers important concepts like sampling distributions, the central limit theorem, and factors that influence the width of a confidence interval like sample size. Examples are provided to demonstrate calculating point estimates, confidence intervals, and dealing with independent samples.
This study examines the relationship between finger gnosis, the ability to mentally represent one's fingers, and mathematical performance in adults. The researchers hypothesize that better finger gnosis skills will be positively correlated with faster calculation times, higher SAT/ACT math scores, and greater use of memory-based addition strategies. Participants will complete finger gnosis, addition strategy, and calculation fluency tasks. The researchers aim to replicate previous findings linking finger gnosis and math skills, and determine if finger gnosis relates to strategic choice in addition. Understanding this relationship could help improve math instruction by bridging symbolic and non-symbolic number representations.
This document discusses measures of central tendency, specifically mean, median, and mode. It begins by defining measures of central tendency as averages that represent central or typical values within a data set. The document then outlines different methods for calculating the mean, or arithmetic average, of both raw (ungrouped) and grouped data sets. It provides examples of calculating the mean of raw data sets directly using the formula for mean, and through the assumed mean method which uses deviations from an assumed mean to simplify calculations for large data sets. The document emphasizes that the mean is the sum of all values divided by the number of values. It also discusses how mean is calculated for grouped data by assigning values to class intervals based on their midpoints.
Statistics is an important area of mathematics taught from Grades 7 to 10. It involves collecting and organizing data, calculating measures of central tendency and variability, understanding probability, and drawing conclusions. Teachers use experiential learning approaches where students collect their own real-world data and reflect on what it shows. Cooperative activities develop skills like surveying classmates or communities. Discovery-based methods engage students in exploring statistical concepts through hands-on experiments and interviews. The goal is for deep, active learning as students make sense of their own experiences with statistics.
This article provides a brief discussion on several statistical parameters that are most commonly used in any measurement and analysis process. There are a plethora of such parameters but the most important and widely used are briefed in here.
This document discusses measures of central tendency, which provide a single value to represent the center of a data set. There are three main types: mean, median, and mode. The mean is the average and there are different types of means depending on the data, including arithmetic mean and weighted mean. The median is the middle value of the data when sorted. The mode is the most frequently occurring value. Calculating these measures allows analysis and comparison of data sets.
The document discusses different types of averages including mode, mean, and median. It provides definitions and examples of how to calculate each. The mode is the most common value, the mean is the average found by adding all values and dividing by the total count, and the median is the middle value when data is arranged in order. The document shows how to identify the mode, mean, and median in various data sets and discusses when each measure is most appropriate.
The document provides an overview of descriptive statistics and statistical graphs, including measures of center such as mean, median, and mode, measures of variation such as range and standard deviation, and different types of statistical graphs like histograms, boxplots, and normal distributions. It discusses key concepts like outliers, percentiles, quartiles, sampling distributions, and the central limit theorem. The document is intended to describe important statistical tools and concepts for summarizing and describing the characteristics of data sets.
This document provides an overview of statistical inference. It discusses descriptive statistics, which summarize data, and inferential statistics, which are used to generalize from samples to populations. Key concepts covered include estimation, hypothesis testing, parameters, statistics, confidence intervals, significance levels, types of errors. Examples are given of how to calculate confidence intervals for means and proportions and how to perform hypothesis tests using z-tests and t-tests. Steps for conducting hypothesis tests are outlined.
Statistical estimators are functions used to estimate unknown parameters of a theoretical probability distribution based on random variable observations. There are two main types of estimators: point estimators that provide a single value and interval estimators that provide a range of values within which the parameter is estimated to lie. Key properties for ideal estimators include being unbiased, consistent, sufficient, and having minimum variance. Examples are provided to illustrate calculating confidence intervals for population means based on sample statistics.
This document provides an overview of key concepts related to statistical estimation and hypothesis testing, including:
- The difference between point estimation and interval estimation, and examples like confidence intervals for the mean and proportion.
- How to calculate and interpret confidence intervals.
- The roles of the null and alternative hypotheses in hypothesis testing and how to interpret p-values.
- Types I and II errors and how the significance level affects these.
- When to use parametric vs. nonparametric tests and examples of selected nonparametric tests like the chi-square test of goodness of fit.
Mathematics skill development programmeTeam BiZdom
The document provides an overview of a Mathematics Skill Development programme that aims to help children overcome their fear of mathematics and gain confidence in the subject. It does this by introducing problem-solving techniques using real-life examples to build a deeper understanding of mathematical concepts and operations. The programme covers topics like algebra, geometry, measurement, numbers and arithmetic, probability, statistics and mathematical reasoning. It uses interactive booklets and CD-ROMs to explain examples at different levels of difficulty to develop logical and creative thinking skills.
MEASURES OF CENTRAL TENDENCY AND VARIABILITYMariele Brutas
The document introduces focus questions about norms, standards, and how data is analyzed using descriptive statistics. It then provides an overview of different measures used to analyze ungrouped and grouped data, including measures of central tendency (mean, median, mode) and measures of variability (range, standard deviation). Finally, it includes sample pre-assessment questions about these concepts.
The document describes experimental designs and statistical tests used to analyze data from experiments with multiple groups. It discusses paired t-tests, independent t-tests, and analysis of variance (ANOVA). For ANOVA, it provides an example to calculate sum of squares for treatment (SST), sum of squares for error (SSE), and the F-statistic. The example shows applying a one-way ANOVA to compare average incomes of accounting, marketing and finance majors. It finds no significant difference between the groups. A randomized block design is then proposed to account for variability from GPA levels.
Chapter 6 part1- Introduction to Inference-Estimating with Confidence (Introd...nszakir
Introduction to Inference, Estimating with Confidence, Inference, Statistical Confidence, Confidence Intervals, Confidence Interval for a Population Mean, Choosing the Sample Size
This document discusses key concepts in statistical estimation including:
- Estimation involves using sample data to infer properties of the population by calculating point estimates and interval estimates.
- A point estimate is a single value that estimates an unknown population parameter, while an interval estimate provides a range of plausible values for the parameter.
- A confidence interval gives the probability that the interval calculated from the sample data contains the true population parameter. Common confidence intervals are 95% confidence intervals.
- Formulas for confidence intervals depend on whether the population standard deviation is known or unknown, and the sample size.
This document discusses the geometry of card wires used in carding machines. It covers the different types of wires including cylinder, doffer, licker-in, and flat top wires. Important parameters that affect carding quality like tooth depth, pitch, base thickness, front and back angles are explained. Different steel alloys used in manufacturing card wires based on their applications are also outlined. Maintaining optimal wire geometry tailored to fiber characteristics is key to efficient fiber control and high quality carding.
Fibre is any raw material that has a hair-like appearance or elongated shape due to its high ratio of length to thickness. A textile fibre must have suitable length, pliability, fineness and strength for conversion into yarns and fabrics. Yarn is a continuous strand composed of natural or manmade fibres or filaments used for weaving and knitting. Spinning is the process of converting fibres into yarn, which can be done through wet, dry or melt spinning depending on the fibre properties. Fibre properties like staple length, fineness and strength influence spinning and the properties of the final yarn.
Here are the solutions to the exercises:
1. The area under the standard normal curve between z=-∞ and z=2 is 0.9772 (using the standard normal table)
2. The probability that a z value will be between -2.55 and +2.55 is 0.9932 (using the standard normal table)
3. The proportion of z values between -2.74 and 1.53 is 0.9950
4. P(z ≥ 2.71) = 1 - 0.9958 = 0.0042
5. P(.84 ≤ z ≤ 2.45) = 0.8036 - 0.1967 = 0.6069
This document discusses various measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. The mean is the average and is calculated by summing all values and dividing by the total number of data points. The median is the middle value when data is arranged in order. The mode is the value that occurs most frequently in the data set. Examples are given to demonstrate calculating each measure. The document also discusses advantages and limitations of each central tendency measure.
This document provides a summary of key concepts in advanced business mathematics and statistics. It defines measures of central tendency including mean, mode, and median. It also discusses measures of dispersion like range and standard deviation. Additionally, it covers topics like regression, hypothesis testing, probability, and different types of statistical analysis.
This document provides an overview of statistics concepts including measures of central tendency (mean, median, mode), calculating these measures, outliers and their effect, trimmed means, weighted means, and percentiles. It includes examples and step-by-step solutions for calculating various statistical measures. Key topics covered are finding the mean, median, and mode of data sets, how outliers impact these measures, calculating trimmed and weighted means, and an introduction to percentiles.
This document provides an overview of statistical estimation and inference. It discusses point estimation, which provides a single value to estimate an unknown population parameter, and interval estimation, which gives a range of plausible values for the parameter. The key aspects of interval estimation are confidence intervals, which provide a probability statement about where the true population parameter lies. The document also covers important concepts like sampling distributions, the central limit theorem, and factors that influence the width of a confidence interval like sample size. Examples are provided to demonstrate calculating point estimates, confidence intervals, and dealing with independent samples.
This study examines the relationship between finger gnosis, the ability to mentally represent one's fingers, and mathematical performance in adults. The researchers hypothesize that better finger gnosis skills will be positively correlated with faster calculation times, higher SAT/ACT math scores, and greater use of memory-based addition strategies. Participants will complete finger gnosis, addition strategy, and calculation fluency tasks. The researchers aim to replicate previous findings linking finger gnosis and math skills, and determine if finger gnosis relates to strategic choice in addition. Understanding this relationship could help improve math instruction by bridging symbolic and non-symbolic number representations.
This document discusses measures of central tendency, specifically mean, median, and mode. It begins by defining measures of central tendency as averages that represent central or typical values within a data set. The document then outlines different methods for calculating the mean, or arithmetic average, of both raw (ungrouped) and grouped data sets. It provides examples of calculating the mean of raw data sets directly using the formula for mean, and through the assumed mean method which uses deviations from an assumed mean to simplify calculations for large data sets. The document emphasizes that the mean is the sum of all values divided by the number of values. It also discusses how mean is calculated for grouped data by assigning values to class intervals based on their midpoints.
Statistics is an important area of mathematics taught from Grades 7 to 10. It involves collecting and organizing data, calculating measures of central tendency and variability, understanding probability, and drawing conclusions. Teachers use experiential learning approaches where students collect their own real-world data and reflect on what it shows. Cooperative activities develop skills like surveying classmates or communities. Discovery-based methods engage students in exploring statistical concepts through hands-on experiments and interviews. The goal is for deep, active learning as students make sense of their own experiences with statistics.
This article provides a brief discussion on several statistical parameters that are most commonly used in any measurement and analysis process. There are a plethora of such parameters but the most important and widely used are briefed in here.
This document discusses measures of central tendency, which provide a single value to represent the center of a data set. There are three main types: mean, median, and mode. The mean is the average and there are different types of means depending on the data, including arithmetic mean and weighted mean. The median is the middle value of the data when sorted. The mode is the most frequently occurring value. Calculating these measures allows analysis and comparison of data sets.
The document discusses different types of averages including mode, mean, and median. It provides definitions and examples of how to calculate each. The mode is the most common value, the mean is the average found by adding all values and dividing by the total count, and the median is the middle value when data is arranged in order. The document shows how to identify the mode, mean, and median in various data sets and discusses when each measure is most appropriate.
The document provides an overview of descriptive statistics and statistical graphs, including measures of center such as mean, median, and mode, measures of variation such as range and standard deviation, and different types of statistical graphs like histograms, boxplots, and normal distributions. It discusses key concepts like outliers, percentiles, quartiles, sampling distributions, and the central limit theorem. The document is intended to describe important statistical tools and concepts for summarizing and describing the characteristics of data sets.
This document provides an overview of statistical inference. It discusses descriptive statistics, which summarize data, and inferential statistics, which are used to generalize from samples to populations. Key concepts covered include estimation, hypothesis testing, parameters, statistics, confidence intervals, significance levels, types of errors. Examples are given of how to calculate confidence intervals for means and proportions and how to perform hypothesis tests using z-tests and t-tests. Steps for conducting hypothesis tests are outlined.
Statistical estimators are functions used to estimate unknown parameters of a theoretical probability distribution based on random variable observations. There are two main types of estimators: point estimators that provide a single value and interval estimators that provide a range of values within which the parameter is estimated to lie. Key properties for ideal estimators include being unbiased, consistent, sufficient, and having minimum variance. Examples are provided to illustrate calculating confidence intervals for population means based on sample statistics.
This document provides an overview of key concepts related to statistical estimation and hypothesis testing, including:
- The difference between point estimation and interval estimation, and examples like confidence intervals for the mean and proportion.
- How to calculate and interpret confidence intervals.
- The roles of the null and alternative hypotheses in hypothesis testing and how to interpret p-values.
- Types I and II errors and how the significance level affects these.
- When to use parametric vs. nonparametric tests and examples of selected nonparametric tests like the chi-square test of goodness of fit.
Mathematics skill development programmeTeam BiZdom
The document provides an overview of a Mathematics Skill Development programme that aims to help children overcome their fear of mathematics and gain confidence in the subject. It does this by introducing problem-solving techniques using real-life examples to build a deeper understanding of mathematical concepts and operations. The programme covers topics like algebra, geometry, measurement, numbers and arithmetic, probability, statistics and mathematical reasoning. It uses interactive booklets and CD-ROMs to explain examples at different levels of difficulty to develop logical and creative thinking skills.
MEASURES OF CENTRAL TENDENCY AND VARIABILITYMariele Brutas
The document introduces focus questions about norms, standards, and how data is analyzed using descriptive statistics. It then provides an overview of different measures used to analyze ungrouped and grouped data, including measures of central tendency (mean, median, mode) and measures of variability (range, standard deviation). Finally, it includes sample pre-assessment questions about these concepts.
The document describes experimental designs and statistical tests used to analyze data from experiments with multiple groups. It discusses paired t-tests, independent t-tests, and analysis of variance (ANOVA). For ANOVA, it provides an example to calculate sum of squares for treatment (SST), sum of squares for error (SSE), and the F-statistic. The example shows applying a one-way ANOVA to compare average incomes of accounting, marketing and finance majors. It finds no significant difference between the groups. A randomized block design is then proposed to account for variability from GPA levels.
Chapter 6 part1- Introduction to Inference-Estimating with Confidence (Introd...nszakir
Introduction to Inference, Estimating with Confidence, Inference, Statistical Confidence, Confidence Intervals, Confidence Interval for a Population Mean, Choosing the Sample Size
This document discusses key concepts in statistical estimation including:
- Estimation involves using sample data to infer properties of the population by calculating point estimates and interval estimates.
- A point estimate is a single value that estimates an unknown population parameter, while an interval estimate provides a range of plausible values for the parameter.
- A confidence interval gives the probability that the interval calculated from the sample data contains the true population parameter. Common confidence intervals are 95% confidence intervals.
- Formulas for confidence intervals depend on whether the population standard deviation is known or unknown, and the sample size.
This document discusses the geometry of card wires used in carding machines. It covers the different types of wires including cylinder, doffer, licker-in, and flat top wires. Important parameters that affect carding quality like tooth depth, pitch, base thickness, front and back angles are explained. Different steel alloys used in manufacturing card wires based on their applications are also outlined. Maintaining optimal wire geometry tailored to fiber characteristics is key to efficient fiber control and high quality carding.
Fibre is any raw material that has a hair-like appearance or elongated shape due to its high ratio of length to thickness. A textile fibre must have suitable length, pliability, fineness and strength for conversion into yarns and fabrics. Yarn is a continuous strand composed of natural or manmade fibres or filaments used for weaving and knitting. Spinning is the process of converting fibres into yarn, which can be done through wet, dry or melt spinning depending on the fibre properties. Fibre properties like staple length, fineness and strength influence spinning and the properties of the final yarn.
There are three main systems used for measuring yarn count: fixed weight, fixed length, and Tex. The fixed weight system uses British and American units, fixed length uses metric units, and Tex is an internationally agreed upon standard. Yarn count can be measured directly by weight per unit length or indirectly by length per unit weight. Direct systems include Tex, Denier, pounds per spindle, militex, and kilotex. Indirect systems include English, French, metric, and worsted counts. It is important in the textile industry to have standardized yarn counting systems to distinguish thickness and facilitate calculations involving weight.
Dezyne E'cole College student portfolio made after her 1year duration of study at the college. B.sc. Fashion Technology student are given technical inputs to make them industry ready. Presenting her work just after 9 months of her period of study at Dezyne E'cole College , Ajmer.
LATEST DEVELOPMENT IN YARN EVENNESS TESTING MACHINE ...Praveen Rams
This document provides an overview of yarn evenness testing and the latest developments in yarn evenness testing machines. It discusses what yarn evenness testing is, the different types of variations that can occur, and how the Uster evenness tester works. The Uster tester uses a capacitance principle to measure mass variations as yarn passes through an electric field, and can test yarn, roving, and sliver at speeds from 2-400 meters per minute. It provides measurements of parameters like unevenness percentage, neps, and thickness variations that can help evaluate yarn quality.
This document provides information about the operating principles and components of a ring frame spinning machine. The key points are:
- Roving bobbins are fed into the drafting system where they are attenuated to the final yarn count. The drafting system plays an important role in yarn uniformity.
- After drafting, the spindle imparts twist to the thin ribbon of fibers to provide strength. Each rotation of the ring traveler produces a twist in the yarn as it is wound onto the tube on the spindle.
- The ring traveler, guided by the spinning ring, moves around the high-speed spindle to wind the yarn without a drive of its own. This converts the roving into a twisted
Importance, Effect & Testing of Yarn EvennessAmirul Eahsan
This document discusses irregularity or unevenness of fiber, which refers to variations in mass per unit length of a fiber assembly. It describes two common methods for measuring irregularity - the irregularity U% and the coefficient of variation C.V%. Several methods for measuring fiber irregularity are outlined, including visual inspection, cutting and weighing, and various testing machines like the Uster Evenness Tester and photoelectric testers. Irregular fibers can affect yarn strength, fabric appearance, and dyeing/finishing. Maintaining low irregularity is important for quality control in textile production.
Sewing thread is a smooth, hard twisted yarn that undergoes a special finishing process to make it resistant to stresses when passing through needles and during sewing operations. It is spun evenly and used for seaming and stitching fabrics.
This document discusses yarn count and twisting. It defines yarn count as the weight per unit length or length per unit weight of yarn. There are two main systems for determining yarn count - direct and indirect. The direct system measures weight of a fixed length, while the indirect measures length of a fixed weight. Twist is also discussed, including its effects on appearance, durability and fabric properties. The document outlines how to determine twist direction and twists per inch in piled yarns. Count variation is defined as well.
The document provides information on the physical properties of raw cotton including fiber length, fineness, strength, cleanliness, and chemical deposits. It then discusses the components and processes of a blow room line. The key goals of the blow room are to open compressed cotton fibers with minimal damage, remove impurities, and create an evenly blended sliver. Common blow room machines include bale openers, mixers, cleaners, and scutchers which use beaters, grids, and air flow to open, clean, and blend the fibers into a uniform lap for input to the carding process.
Yarn count expresses the coarseness or fineness of yarn and is measured using various systems. There are indirect and direct count systems, with indirect systems like cotton using length per unit weight and direct systems like jute using weight per unit length. Various instruments can measure count, including the quadrant balance for short lengths, warp reel and balance method for longer lengths, and Beesley's balance for small fabric samples. Count affects properties like thickness and strength and is an important consideration in textile manufacturing.
This document provides information for a workshop on yarn and textile sculpture. It discusses identifying artists who wrap objects and the techniques they use. Participants will learn how to manipulate yarn in different ways and apply that knowledge by wrapping a chosen object with yarn and other textiles. The document lists various wrapping and knotting techniques and instructs participants to choose an object, gather materials, wrap it creatively, and document their work.
The document discusses textile spinning and quality control processes. It describes the key steps in textile spinning which include: yarn production from staple fibers using drawing and twisting; filament yarn production by forcing fiber-forming substances through spinnerets. The main processes are: blowroom preparation, carding, drawing, roving and ring spinning. Quality is ensured through testing of raw materials and processes. Fiber properties like length, strength and uniformity are evaluated. Machines are also tested to minimize count variations and improve yarn evenness and strength in the final product.
This document summarizes the process of yarn manufacturing from fibers through spinning. It describes how fibers are opened, cleaned and formed into laps in the blowroom. The laps then go through carding to be further cleaned and formed into slivers. Combing is used to straighten and parallelize fibers. Drawing drafts and blends slivers. Roving/Simplex frames draft and add twist to form rovings. Ring frames further draft and twist rovings to produce yarn, which is then wound onto bobbins. The key steps are blowroom, carding, combing or drawing, roving/Simplex frame, and ring frame spinning.
Textile yarn manufacturing involves several key steps. Fibers are first opened and cleaned through blowroom and carding processes. Drawing further arranges fibers into parallel strands called slivers. Roving attenuates slivers and adds twist. Ring frames then spin roving into yarn using drafts and twist. Combing upgrades raw materials by removing short fibers. The processes work to arrange, draft, and twist fibers into consistent yarns for weaving or other uses.
Fibers are converted into yarns through several processes to prepare them for fabric construction. Fibers are first opened, blended, and cleaned. They then undergo either carding or combing to further clean and align the fibers into slivers. The slivers are drawn and spun into yarns, which can be done through ring spinning, rotor spinning, or air jet spinning. Ring spinning produces the highest quality yarns while rotor and air jet spinning have higher production rates. The yarns are then wound onto packages or cones and are ready to be used to create fabrics through weaving or knitting.
Here are the steps to find the quartiles for this data set:
1. Order the data from lowest to highest: 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7
2. The number of observations is 16. To find the quartiles, we split the data into 4 equal parts.
3. n/4 = 16/4 = 4
4. Q1 is the median of the lower half of the data, which is the 4th observation: 2
5. Q2 is the median of all the data, which is also the 8th observation: 3
6. Q3 is the median of the upper half
The document discusses different measures of central tendency (mean, median, mode) and how to determine which is most appropriate based on the type of data. It also covers measures of dispersion like range, standard deviation, and variance which provide information about how spread out values are from the central point. The mean is the most commonly used measure of central tendency but the median is less affected by outliers, while the mode represents the most frequent value.
This document discusses measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating the arithmetic mean, geometric mean, harmonic mean, median, and mode. Examples are given for calculating each measure. The merits and demerits of each measure are outlined. In conclusion, the mean is affected by outliers while the median and mode are robust to outliers, and the mode is easiest to calculate by counting frequencies.
measures of central tendency in statistics which is essential for business ma...SoujanyaLk1
This document discusses various measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. The mean is the sum of all values divided by the total number of values and is the most widely used measure. The median is the middle value when data is arranged from lowest to highest. The mode is the most frequently occurring value. The document gives examples of calculating each measure and discusses their relative strengths and weaknesses for different data distributions.
This document discusses various measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. The mean is the sum of all values divided by the number of values and is the most widely used measure. The median is the middle value when data is arranged from lowest to highest. The mode is the value that occurs most frequently. Examples are given demonstrating how to calculate each measure for both individual values and grouped data.
The document discusses various measures of central tendency used in statistics. The three most common measures are the mean, median, and mode. The mean is the sum of all values divided by the number of values and is affected by outliers. The median is the middle value when data is arranged from lowest to highest. The mode is the most frequently occurring value in a data set. Each measure has advantages and disadvantages depending on the type of data distribution. The mean is the most reliable while the mode can be undefined. In symmetrical distributions, the mean, median and mode are equal, but the mean is higher than the median for positively skewed data and lower for negatively skewed data.
Slideshare notes about measures of central tendancy(mean,median and mode)IRADUKUNDA Fiston
This presentation discusses various measures of central tendency including the mean, median, mode, harmonic mean and geometric mean. It provides definitions and formulas for calculating each measure along with their merits and demerits. The mean is the sum of all values divided by the number of values and can be affected by outliers. The median is the middle value when values are arranged from lowest to highest. The mode is the most frequent value. Harmonic and geometric means are other types of averages.
This document provides an overview of key concepts in statistics including measures of central tendency (mean, median, mode), measures of dispersion (variance, standard deviation), and central moments (skewness, kurtosis). It discusses calculating and comparing the mean, median, mode, and how they each describe the central position of a data distribution. It also explains how variance and standard deviation measure how spread out the data is from the mean. The document is intended as a textbook for students and general readers to learn basic statistical concepts.
The document discusses various measures of central tendency (averages) and dispersion that are used to summarize and describe data in statistics. It defines common averages like the arithmetic mean, median, mode, harmonic mean, and geometric mean. It also covers measures of dispersion such as the range, quartile deviation, mean deviation, and standard deviation. As an example, it analyzes test score data from 5 students using the arithmetic mean to find the average score.
This document outlines the syllabus for a statistics and probabilities course, which covers topics such as descriptive statistics like measures of central tendency and dispersion, probability distributions, hypothesis testing, regression, and experimental design. It provides definitions and examples of key statistical concepts like populations, samples, variables, measures of central tendency including mean, median and mode, and measures of dispersion like range, mean deviation, variance and standard deviation. The course aims to teach students how to make informed judgments and decisions using statistical methods.
Answer the questions in one paragraph 4-5 sentences. · Why did t.docxboyfieldhouse
Answer the questions in one paragraph 4-5 sentences.
· Why did the class collectively sign a blank check? Was this a wise decision; why or why not? we took a decision all the class without hesitation
· What is something that I said individuals should always do; what is it; why wasn't it done this time? Which mitigation strategies were used; what other strategies could have been used/considered? individuals should always participate in one group and take one decision
SAMPLING MEAN:
DEFINITION:
The term sampling mean is a statistical term used to describe the properties of statistical distributions. In statistical terms, the sample meanfrom a group of observations is an estimate of the population mean. Given a sample of size n, consider n independent random variables X1, X2... Xn, each corresponding to one randomly selected observation. Each of these variables has the distribution of the population, with mean and standard deviation. The sample mean is defined to be
WHAT IT IS USED FOR:
It is also used to measure central tendency of the numbers in a database. It can also be said that it is nothing more than a balance point between the number and the low numbers.
HOW TO CALCULATE IT:
To calculate this, just add up all the numbers, then divide by how many numbers there are.
Example: what is the mean of 2, 7, and 9?
Add the numbers: 2 + 7 + 9 = 18
Divide by how many numbers (i.e., we added 3 numbers): 18 ÷ 3 = 6
So the Mean is 6
SAMPLE VARIANCE:
DEFINITION:
The sample variance, s2, is used to calculate how varied a sample is. A sample is a select number of items taken from a population. For example, if you are measuring American people’s weights, it wouldn’t be feasible (from either a time or a monetary standpoint) for you to measure the weights of every person in the population. The solution is to take a sample of the population, say 1000 people, and use that sample size to estimate the actual weights of the whole population.
WHAT IT IS USED FOR:
The sample variance helps you to figure out the spread out in the data you have collected or are going to analyze. In statistical terminology, it can be defined as the average of the squared differences from the mean.
HOW TO CALCULATE IT:
Given below are steps of how a sample variance is calculated:
· Determine the mean
· Then for each number: subtract the Mean and square the result
· Then work out the mean of those squared differences.
To work out the mean, add up all the values then divide by the number of data points.
First add up all the values from the previous step.
But how do we say "add them all up" in mathematics? We use the Roman letter Sigma: Σ
The handy Sigma Notation says to sum up as many terms as we want.
· Next we need to divide by the number of data points, which is simply done by multiplying by "1/N":
Statistically it can be stated by the following:
·
· This value is the variance
EXAMPLE:
Sam has 20 Rose Bushes.
The number of flowers on each b.
This document discusses measures of central tendency including the mean, median, and mode. It defines each measure and provides examples of how to calculate them. The mean is the sum of all values divided by the number of values and is the most widely used measure. The median is the middle value when data is arranged from lowest to highest. The mode is the most frequently occurring value in a data set. The document also compares the properties of each measure and how they relate to different data distributions.
This document discusses measures of central tendency including the mean, median, and mode. It defines each measure and provides examples of how to calculate them using data sets. The mean is the average value obtained by dividing the sum of all values by the number of values. The median is the middle value when values are arranged in order. The mode is the most frequent value in the data set. The document outlines advantages and disadvantages of each measure and concludes that measures of central tendency describe the typical or central value in a data set.
Unit 1 - Mean Median Mode - 18MAB303T - PPT - Part 1.pdfAravindS199
Sir Francis Galton was a prominent English statistician, anthropologist, eugenicist, and psychometrician in the 19th century. He produced over 340 papers and books, and created the statistical concepts of correlation and regression. As a pioneer in meteorology and differential psychology, he devised early weather maps, proposed theories of weather patterns, and developed questionnaires to study human communities and intelligence. The document discusses Galton's background and contributions to statistics, anthropology, meteorology, and psychometrics.
This document provides an agenda and overview for a week 1 lecture on applied managerial statistics. The agenda includes discussing terminal course objectives, essential questions, important statistical concepts, getting started with Minitab software, and descriptive statistics. Key concepts covered are measures of central tendency (mean, median, mode) and dispersion (range, standard deviation, interquartile range). The document aims to complement textbook materials and provide a bridge to the first course module through live demonstration of descriptive statistics in Minitab.
The modal rating is the rating value that occurs most frequently in the dataset. To find the mode, we would need to analyze the rating frequencies and identify which rating has the highest count. Without access to the actual dataset values and frequencies, I cannot determine the modal rating directly. The mode is a measure of central tendency that is best for identifying the most common or typical value in a dataset.
This document discusses various measures of central tendency including the mean, median, and mode. It defines each measure and provides examples of how to calculate them for both grouped and ungrouped data. The mean is the sum of all values divided by the number of values and is the most widely used measure. The median is the middle value when data is ordered from lowest to highest. The mode is the most frequently occurring value. The document compares the properties of each measure and how they are affected by outliers. It also discusses when each measure is most appropriate to use.
This document provides definitions and descriptions of various defects that can occur in fabrics, along with their possible causes. It discusses defects such as abrasion marks, bows, broken ends, coarse ends or picks, crease marks, holes, knots, mixed weft, neps, oil stains, reediness, slack ends, smash, and starting marks. For each defect, a brief definition is given as well as potential reasons for why the defect may occur, such as issues with loom machinery, yarn preparation, or the weaving process. The document is compiled by Rauf Electronic Equipment Service to inform readers about common fabric defects.
This document provides information about car financing options, including a 16% financing rate, requiring a minimum 20% down payment, and the ability to finance between Rs. 150,000 to Rs. 1.5m over 3 to 5 years. It includes installment factors for different financing periods and provides examples of monthly installments and total costs for 5-year and 3-year financing terms on a Rs. 500,000 car with a 20% down payment of Rs. 100,000.
The document provides information about financing a Suzuki Baleno 1300 CC car over different durations with various financing companies. It includes the car price, down payment amount and percentage, financing duration, monthly installment amount, total amount to be paid, and total interest for periods of 5 years, 2 years, 3 years and 4 years with different companies like SONERI, CITI, MCB, KASB, Faysal Bank and Alfalah Bank.
The document discusses two laws: the Law of Duality and the Law of Sacrifice. The Law of Duality states that in mature markets, there will generally only be two dominant competitors that share most of the market. It provides several examples of dual competitor markets. The Law of Sacrifice states that to gain something, one must give something up - there is no getting something for nothing. It notes that focus requires deciding what not to do, and that learning to say "no" often requires experiencing the pain of saying "yes" too often.
The floods in Pakistan in 2010 caused widespread damage that severely impacted the country's economy. Agriculture, which accounts for 20% of GDP, was hit hardest with over 1.9 million acres of crops damaged. This economic blow, combined with infrastructure destruction and rising inflation, threatened to reduce Pakistan's GDP growth rate from a projected 4.5% to around 3.5%. The floods also exacerbated Pakistan's fiscal issues by increasing government spending needs while reducing tax revenue, potentially widening the budget deficit to 6-7% of GDP.
Post flood impact on pakistan economy newAzhar Hussain
The document summarizes the economic impacts of massive flooding in Pakistan in 2010. It notes that over 20 million people were affected across 78 districts, with major damage to infrastructure, crops, housing and industry. The agriculture sector suffered over $429 billion in losses, while overall economic costs were estimated at over $43 billion. This was expected to significantly slow GDP growth, worsen the fiscal deficit, increase inflation and poverty, and negatively impact the balance of payments. Recovery was expected to be difficult due to ongoing issues around inflation, fiscal management, energy shortages, and damage to supply chains.
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How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
Essentiality of mathematics
1. STATISTICS SURVEY REPORT 1
PREPARED BY:
1. Muhammad Saeed
2. MUHAMMAD AAMIR RIAZ
3. Muhammad Imran
FACILITATOR:
1 MA’AM RAKHSHANDA SHAH
TOPIC: “ESSENTIALITY OF MATHEMATICS”
COURSE: BUSSINESS MATHEMATICS
DATE : 30TH MAY 2003
2. STATISTICS SURVEY REPORT 2
ACKNOWLEDGEMENT:
We, Muhammad Imran, Muhammad Aamir Riaz,
Muhammad Saeed, worked in a group, to carry out a
survey on “Essentiality Of Mathematics In Our
Professional Life” which is also the requirement of this
course, as this survey and the arrangement of data of
this survey both are very time consuming &
overshadowing effort but we thanks Almighty Allah
who empowered us to complete these practical and
report.
We would also like to say coordinal thanks and
appreciate the memorable behaviour and loving
attitudes of all the students of TIP to whom we have
given the survey forms and in this regard their
cooperation was beyond our expectations and this,
helped us a lot in gratifying the data &
accomplishment of this report.
We wish to elegantly and heartily thank to the
instructor of our course, Ma’am Rakshanda Shah for his
complete collaboration and assistance.
Responsibility for any sort of errors and exclusions
is certainly our.
3. STATISTICS SURVEY REPORT 3
TOPIC:
“Evolutionary study for the ignorance and fear of mathematics
in designing, management and textile science students.”
As it is a very famous saying;
“Math is a way for lazy people to learn how to do thing
quickly and well.”
“It’s a way to have a well organized mind and it will help you
to solve all kinds of problems later on in your age”.
PURPOSE OF STUDY:
Our objective is to find the opinion of students about the essentiality of
mathematics for professional field.
My report is concerned with the feed back of students about the
essentiality and the interest of mathematics in their professional field.
The foremost objective is to compare the interest in mathematics
between designing, management and textile science and also
comparison between those students who likes and those who dislike
the mathematics and their marks in exams.
QUESTIONNAIRES:
Questionnaires can be most simply defined as apprises of collecting
such information, from desired individuals groups or organizations,
which cannot be easily obtained from direct sources.
“OR”
The word questionnaires are used most often to describe a method of
gathering information from a sample of individuals. This sample is
usually just a fraction of the population being studied.
4. STATISTICS SURVEY REPORT 4
Assignment of statistics
Evaluate yourself as a mathematician
Name: ________________________
Sex: __________________________ class: __________
Age: _________________________ year: ___________
Discipline: Textile science Designing
Management
1 Your marks in math’s in intermediate
Less then 60
60-70
70-80
80-90
Above 90
2 Is mathematics is essential for your professional field?
Yes NO
3 Do you like mathematics?
Yes NO
4 What do you think that what is your level of mathematics?
Low High Moderate
5 Is mathematics hard for you?
YES NO
6 Your knowledge in maths is enough for daily life concerned.
YES NO
7 You want to learn more maths.
YES NO
(if yes than tick Q#8) (If no than tick Q#9)
8 You like math’s due to
You found good teachers your parent’s guidance
Your natural ability you don’t know
9 You fear by math’s due to
You found not good teachers your don’t want to learn yourself
You don’t find help from parents you don’t know
10 Regarding your ability in maths can you provide help to some one else?
YES NO
Respondent signature:__________
5. STATISTICS SURVEY REPORT 5
“SOME IMPORTANT DEFINITIONS”
DEFINITION OF STATISTICS:
Statistics are numerical facts in any field of study.
“OR”
Statistic deals with techniques or methods for collecting
analyzing and drawing conclusions from data.
Statistics methods are divided into two categories namely descriptive
and inferential.
2 Descriptive statistics
3 Inferential statistics
DESCRIPTIVE STATISTICS:
It deals with the collections classifications summarization and
presentation of data.
INFERENTIAL STATISTICS:
It deals with the conclusions drawn about a population using the data
of a sample taken from the same population.
POPULATION:
Population consists of the totality of the observations with which we
are concerned.
SAMPLE:
A sample is a subset of a population.
SIMPLE RANDOM SAMPLE:
A simple random sample of “n” observations is a sample that is chosen
in such a way that very subset of n observations of the population has
the same probability of being selected.
PROBABILITY:
A probability is a numeric measure of the likelihood or chance that a
particular event will occur.
Symbolically it is written as;
6. STATISTICS SURVEY REPORT 6
n( A)
P( A) =
n(S )
It is further distributed into following ones;
1. Binomial 2. Poisson
3. Hyper geometric 4. Normal
MEASUREMENT OF TENDENCY:
Generally we have two types of tendencies;
1. Measures of central tendency
2. Measures of dispersion
1. MEASURES OF CENTRAL TENDENCY:
It is defined as a single value of the data, which truly represents the
whole data.
It is further classified into;
i. Arithmetic Mean
ii. Geometric Mean
iii. Harmonic Mean
iv. Median
v. Mode
ARITHMETIC MEAN:
It is the most commonly used measure and usually termed as simple
mean.
“It is defined as the sum of the values divided by the number
of values in the raw data.”
Here the mean of a sample of n values, is known as sample mean and
is denoted by x .
n
∑x i
x= i =1
n
Whereas, if the data is not a sample but the entire population of N
values, it is termed as population mean and is denoted by µ.
N
∑x i
µ= i =1
N
WEIGHTED ARITHMETIC MEAN:
The mean of a data gives equal importance or weights to each of the
values of raw data. In some general cases all values in the raw data
7. STATISTICS SURVEY REPORT 7
don’t have the same importance. A weighted mean is used to assign
any degree of importance to each value of the data by choosing
appropriate weights for these values.
xw =
∑ w.x
∑w
Here, “w” are the weights assigned to the values of data.
GEOMETRIC MEAN:
Geometric mean is defined only for non-zero positive values. It is the
nth root of the product of n values in the data.
G = n x1 x2...xK
WEIGHTED GEOMETRIC MEAN;
If weights are assigned to the values of the data, in this regard we can
calculate the geometric mean.
G.M . = Anti log[
∑ w.log x ]
∑w
HARMONIC MEAN:
Harmonic mean is defined only for non-zero positive values; it is the
reciprocal of mean of reciprocal of values.
K
H = K
1
∑i = 1 xi
WEIGHTED HARMONIC MEAN:
If all values of the data are not equally important, a weighted
harmonic mean is calculated after assigning appropriate weights to
the values of the data.
H .M . =
∑w
w
∑( x )
MEDIAN:
Median is defined as the middle value of the data when the values are
arranged in ascending or descending order.
~
µ=λ+ h ( n − c. f )
f 2
8. STATISTICS SURVEY REPORT 8
MEDIAN OF A FREQUENCY DISTRIBUTION:
Values of the data in an interval are evenly or uniformly spread in
that interval is known as the median of the frequency distribution.
Width of the interval
No. of values in the interval
PARTITION VALUES OR QUARTILES:
QUARTILES:
There are three values, which can divide the arranged data in four
equal parts or quarters. These values are called quartiles.
h n
Qi = l + ( i − c. f )
f 4
DECILES:
There are nine values, which can divide the arranged data in ten equal
parts.
h n
Di = l + ( i − c. f )
f 10
PERCENTILES:
Similarly, the 99 values, which divide the arranged data in 100 equal
parts, are called percentiles.
h n
Pi = l + ( i − c. f )
f 100
MODE:
Mode is a measure of central tendency generally used when the data is
of qualitative nature where the addition (for mean) or arrangement
(for median) of values is not possible.
It is defined as that category of the attribute, which repeats maximum
number of times in the data.
fm − f 1
Mode = x = l + (
ˆ )×h
2 fm − f 1 − f 2
MODE OF A FREQUENCY DISTRIBUTION:
In a frequency distribution mode is that value of the variable for
which the frequency curve takes maximum height.
9. STATISTICS SURVEY REPORT 9
A frequency distribution with one mode is called unimodal and with
two modes is called a bimodal frequency distribution.
2. MEASURES OF DISPERSION:
The dispersion is defined as the scatter or spread of the values from
one another or from some common values. The method to compute the
amount of dispersion present in any data is called “Measures of
Dispersion” or “Measures of Variation”.
The measures of dispersion are further classified into;
i. Range
ii. Quartile Deviation
iii. Mean Deviation
iv. Standard Deviation
RANGE:
Range is the simple measure of dispersion and is defined as the
differences between the maximum and minimum values of the data.
R = Xmax− Xmin
Range is generally rough and crude measurement as it ignores the
variation among all the values.
QUARTILE DEVIATION:
The difference between the third and first quartiles is called the
interquartile range and quartile deviation is the half of the
interquartile range and is also known as the semi-interquartile range.
Q3 − Q1
Q.D. =
2
MEAN DEVIATION:
Dispersion can be measured in terms of the quantities that each value
of the data deviates from average value.
Mean deviation for ungrouped data;
M .D. =
∑| x − x |
n
Mean deviation for grouped data;
K
∑f i | xi − x |
M .D . = i =1
K
∑f
i =1
i
10. STATISTICS SURVEY REPORT 10
Hence in this regard it is defined as, sum of absolute deviations from
mean divided by the number of values.
STANDARD DEVIATION:
Standard Deviation is the most widely used measure of dispersion and
is defined as the positive square root of a quantity called variance.
Standard deviation for sample-ungrouped data;
n
∑ (x − x)i
2
s= i =1
n −1
Standard deviation for population-ungrouped data;
N
∑(x − µ) i
2
σ = i =1
N
Standard deviation for sample-grouped data;
K K
n∑ f x − (∑ fi xi )2 2
i i
s= i =1 i =1
n(n −1)
Standard deviation for population-grouped data;
K K
N∑ f x − (∑ fi xi )2 2
i i
σ= i =1 i =1
N
11. STATISTICS SURVEY REPORT 11
SAMPLING OF THE DATA:
POPULATION SAMPLE
DEPARTMENT TOTAL TOTAL
M F M F
Designing 12 39 51 8 25 33
Management 38 14 52 21 12 33
Science 130 3 133 31 2 34
Total 180 56 236 60 40 100
Here at TIP, after conducting this survey, we analyze
that male in Science department are more proficient
of learning Mathematics while in the Designing
department female-heads are more engrossed and
interested to learn mathematics as compare to the
males.
12. STATISTICS SURVEY REPORT 12
Q#1: Your Marks In Mathematics In Intermediate?
GENERAL DATA:
This data is regarding to all the departments and on
the ratio of the marks which the students got during
their A levels or in their Intermediate.
MARKS IN
MATH SCIENCE DESIGNING MANAGEMENT
50-60 6 12 6
60-70 10 8 11
70-80 12 7 9
80-90 3 4 3
90-100 3 2 4
Total 34 33 33
SCIENCE DESIGNING MANAGEMENT
14
12
No. of students
10
8
6
4
2
0
50-60 60-70 70-80 80-90 90-100
Marks
13. STATISTICS SURVEY REPORT 13
ANALYZING THE QUESTIONS:
Now we will proceed for calculation of data question no 1;
SCIENCE STUDENTS:
Marks in Mid Frequency
mathematics point “f” C.F fxX f x X2
“x”
50-60 55 6 6 330 18150
60-70 65 10 16 650 42250
70-80 75 12 28 900 67500
80-90 85 3 31 255 21675
90-100 95 3 34 289 27075
∑f = 34 ∑ f .x = 2420 ∑ f .x2 = 176650
Mean = µ = ∑
f .x
∑f
2420
= = 71.176
34
Mean = µ = 71.176
~ h n
Median= µ = λ + ( − c. f )
f 2
Median = n/2 th term
= 34/2
=17th term
L.C.B=70 f=12
Mid point=75 h=10
~ 10
µ = 70 + (17 − 16) = 70.8333
12
~
Median = µ = 70.833
fm − f 1
Mode= l + ( )×h
2 fm − f 1 − f 2
12 − 10
= 70 + ( ) × 10 =70.8181
24 − 10 − 3
Mode = µ = 70.8181
ˆ
14. STATISTICS SURVEY REPORT 14
Quartile;
Q1 = l + h ( n − c. f )
f 4
Q1 = n th term =34/4=8.5th term
4
L.C.B = 60 f = 10 C.F = 6
10
Q1= 60 + (8.5 − 6) = 62.5
10
Standard deviation for sample-grouped data;
K K
n∑ f x − (∑ fi xi )2
2
i i
s= i =1 i =1
n(n −1)
34 × 176650 − (2420) 2
s= = 11.55
34(33)
Standard deviation=11.55
MANAGEMENT STUDENTS:
Marks Mid
Frequency
in point C.F fxX f x X2
“f”
mathematics “x”
50-60 55 6 6 330 18150
60-70 65 11 17 715 46475
70-80 75 9 26 675 50625
80-90 85 3 29 285 21675
90-100 95 4 33 380 36100
∑f = 33 ∑ f .x = 2385 ∑ f .x2 = 183025
Mean = µ = ∑
f .x
∑f
2385
= = 72.27
33
Mean = µ = 72.27
15. STATISTICS SURVEY REPORT 15
~ h n
Median= µ = λ + ( − c. f )
f 2
Median = n/2 th term
= 33/2
=16.5th term
L.C.B=60 f=11 C.F=6
Mid point=65 h=10
~ 10
µ = 60 +(16.5 − 6) = 69.54
11
~
Median = µ = 69.54
fm − f 1
Mode= l + ( )×h
2 fm − f 1 − f 2
11 − 6
= 60 + ( ) × 10 = 67.142
22 − 6 − 9
Mode = µ = 67.142
ˆ
Quartile;
Q1 = l + h ( n − c. f )
f 4
n term =33/4=8.25th term
Q1 = th
4
L.C.B = 60 f = 11 C.F = 6
10
Q1= 60 + (8.25 − 6) = 62.045
11
Q1 = 62.045
Standard deviation for sample-grouped data;
K K
n∑ f x − (∑ fi xi )2
2
i i
s= i =1 i =1
n(n −1)
33 × 183025 − (2385) 2
s= = 18.24
33(32)
Standard deviation=18.24
16. STATISTICS SURVEY REPORT 16
DESIGNING STUDENTS:
Marks in Mid Frequency C.f fxX f x X2
mathematics point “f”
“x”
50-60 55 12 12 660 36300
60-70 65 8 20 520 33800
70-80 75 7 27 525 39375
80-90 85 4 31 340 28900
90-100 95 2 33 190 18050
∑f = 33 ∑ f .x = 2235 ∑ f .x 2
= 156425
Mean = µ = ∑
f .x
∑f
2235
= = 67.72
33
Mean = µ = 67.72
~ h n
Median= µ = λ + ( − c. f )
f 2
Median = n/2 th term
= 33/2
=16.5th term
L.C.B=60 f=8
Mid point=65 h=10
~ 10
µ = 60 + (16.5 − 12) = 65.625
8
~
Median = µ = 65.625
Standard deviation for sample-grouped data;
K K
n∑ f x − (∑ fi xi )2
2
i i
s= i =1 i =1
n(n −1)
33 × 156425 − (2235) 2
s= = 12.56
33(32)
Standard deviation=12.56
17. STATISTICS SURVEY REPORT 17
Q#2: Is Mathematics Essential For Your Profession?
DEPARTMENTS MALE FEMALE TOTAL
Yes No Yes No
Designing 3 5 5 20 33
Management 16 5 9 3 33
Science 24 7 2 1 34
Total 43 17 16 24 100
Designing Management Science
50
No of students
40
30
20
10
0
Yes No Yes No
MALE FEMALE
COMMENTS:
The table shows that the highest number of students who think that
mathematics is essential for their professions are science students but
students of management and designing departs are also agreed on this
point that mathematics have key importance and significant impact on
their professions.
18. STATISTICS SURVEY REPORT 18
Q#3: Do You Like Mathematics?
DEPARTMENTS YES NO TOTAL
Designing 14 19 33
Management 28 5 33
Science 26 8 34
Total 68 32 100
Series1 Series2
30
25
# OF STUDENTS
20
15
10
5
0
Designing Management Science
COMMENTS:
The comments passed on this question are that the management
student’s are much more in the favour to learn mathematics, science
students are also in the favour of this course but in less ratio as
compare to management students because they think that the course
offered hare at our institute don’t influence their professions so they
don’t favour to learn it more.
19. STATISTICS SURVEY REPORT 19
Q#4: What Do You Think About Your Level Of
Mathematics?
LEVELS MALE FEMALE TOTAL
Average 27 19 46
Good 25 16 41
Excellent 8 5 13
Total 60 40 100
30
25
# of Students
20
Average
15 Good
Excellent
10
5
0
MALE FEMALE
Gender
We can also drive the probability from the given data, a random
sample of 100 students are classified above according to the gender
and the level of education.
If a person is chosen randomly from this data, the probability would
be;
A: A person is male and given the person has average level of
mathematics.
So, P (A) = P (Average Level of Mathematics) = 46/100
P (A ∩ B) = P(Average Level of Maths and Male) = 27/100
P( A ∩ B) 27 46 27
So, P (B/A) = = / =
P( A) 100 100 46
B: Person doesn’t have excellent level of mathematics and given that
the person is male.
P (A/B) = 52/87
20. STATISTICS SURVEY REPORT 20
COMMENTS:
Here the graphs and the data values indicate the favour to the level of
mathematics on the basis of gender, generally the male and female are
in average ratio regarding to their interest for mathematics and a very
few male and females in our institute have excellent favour ratio for
mathematics.
21. STATISTICS SURVEY REPORT 21
Q#5: Is Mathematics Hard For You?
Q#7: Do You Want To Learn More Maths?
Departments Hard Not hard Yes No
Designing 13 20 14 19
Management 8 25 28 5
Science 5 29 26 8
Total 26 74 68 32
Designing Management Science
35
30
No of students
25
20
15
10
5
0
Hard Not Hard YES NO
Q.5 Q.7
COMMENTS:
The table shows that the most students who feel maths is not difficult
for them but some students of designing feel that maths is hard for
them but they want to learn mathematics.
22. STATISTICS SURVEY REPORT 22
Q#6: Is Your Knowledge In Mathematics Enough For
Daily Life Concerned?
DEPARTMENTS YES NO TOTAL
Designing 31 2 33
Management 31 2 33
Science 33 1 34
Total 95 5 100
Designing Management Science
35
30
# of students
25
20
15
10
5
0
YES NO
COMMENTS:
These data comments that the mathematics’ course offered here at
TIP provide enough help for their daily life concerned. On the basis of
data, students of all the departments agree on the importance of the
information provided by these courses.
23. STATISTICS SURVEY REPORT 23
Q# 8 and 9: You Like Mathematics Due To?
REASONS LIKE DON'T LIKE TOTAL
Due to teacher 26 12 38
Due to parent's 5 0 5
Your personal interest 33 4 37
You don't know 4 16 20
Total 68 32 100
Due to teacher Due to parent's
Your personal interest You don't know
40
No of students
30
20
10
0
LIKE Reasons DON'T LIKE
COMMENTS:
We can conclude that the majority of students choose to learn
mathematics if they have their own personal interest in it and secondly
they in to it due to their teacher’s recommendations. Parental interest
has a very little effect into it.
24. STATISTICS SURVEY REPORT 24
Q#10: Regarding Your Ability In Mathematics Can You
Provide Help To Some One Else?
GENDER YES NO TOTAL # OF STUDENTS
Male 51 9 60
Female 36 4 40
Total 87 13 100
Male Female
60
50
no of students
40
30
20
10
0
YES NO
COMMENTS:
This question looks upon on the ability of the students good in
mathematics and they can provide help to the other students on the
basis of their ability in mathematics. In this regard, it is constructive
to say that both the males and females in a large ratio encourage
helping others in this subject.
27. STATISTICS SURVEY REPORT 27
CONCLUSION:
By the comparison of Management, Sciences and Designing
faculties, we conclude that all the departments agreed on
the intense importance and inimitable significance of
Mathematics and think it is essential for all of them, which
we think is not expected as our suppositions about Designing
department.
It is a common fact, students having harder field of study
avoid mathematics but here at T.I.P majority of Designing
students think that mathematics is hard but on the other
hand, majority of them has showed their interests to learn
Mathematics and their proportion is slightly higher then the
Sciences students. Here it is interesting thing to discuss is
that majority of Designing students also thinks that
Mathematics is easier as compare to their designing and arts
subject, hence on this basis they are interested to learn
Mathematics. However, al lot of students in all of the
faculties give the response that mathematics is a very
interesting and easy subject but at TIP they are not
interested to learn it more, may be the reason is that they
think it is not compatible to their profession or don’t help
them in their profession.
Here a very remarkable and significant matter of discussion
is that majority of students don’t want to learn the
Mathematics on the teaching methods and teaching criteria
of their Instructors. Some of the students think that they
have good teachers and only on this basis they consider
Mathematics interesting and want to learn it while on he
other student same ratio of students opposed this object.
28. STATISTICS SURVEY REPORT 28
RECOMMENDATIONS:
After getting the results of the analysis of our survey
we recommend that Mathematics should be taken
as “Applied/Associated ” subject in every discipline
of textiles.
For the students of the basic classes of textiles, the
quality teachers should be provided so that they
could develop a good interest in Mathematics in
them.
If the parents have low interest in Mathematics and
they find it hard to study, then they should keep their
views to themselves and should allow their children
to choose their field of interest themselves.
There should be a few courses of “Mathematical
Modeling”.
29. STATISTICS SURVEY REPORT 29
REFERENCES:
Introduction To Statistics
By: Ronalde Walpole
Applied Mathematics For Business, Economics, And
The Social Sciences
By; Frank S. Budnick
Statistics Concepts And Methods
By; S. Khursheed Alam
Elements Of Statistics & Probability
By; Shahid Jamal
SOFTWARE USED:
1) Ms Word
2) Ms Excel
3) Ms Equation Editor 3.0
4) Minitab