This document provides information about a Business Statistics course including objectives, policies, assessment details, topics, assignments, and formulas. The course aims to teach students how and when to apply statistical techniques to decision making. It will have 57 lectures, 2 class tests, 2 hourly tests, and 3 assignments. Internal assessment will be based on a mid-semester exam, presentation, tests, assignments. Topics will cover data collection, distributions, central tendency measures, dispersion measures, and correlation. Students will complete activities collecting and analyzing preference data, and presenting organizational sales and production data. Formulas taught will include measures of central tendency, dispersion, correlation, and error.
Basic Statistics for Class 11, B.COm, BSW, B.A, BBA, MBAGaurav Rana
The document provides an overview of key concepts in statistics for social work. It discusses topics such as data collection methods, organization and presentation of data, measures of central tendency including mean, median and mode, and measures of dispersion. For example, it explains how to calculate the arithmetic mean for both grouped and ungrouped data using direct, assumed mean and step deviation methods. It also discusses how to calculate the median and mode for discrete and continuous data series.
This document discusses measures of central tendency including mean, median, and mode. It provides definitions and formulas for calculating these measures from individual data series, discrete series, and continuous series. For mean, it describes both direct and shortcut methods for different data types. For median, it explains how to calculate it from individual and discrete series when the number of observations is odd or even. For mode, it gives methods to determine the modal value from individual and discrete series through inspection or tallying frequencies. Examples of calculations are also included.
1. The document provides the scheme of work and lesson notes for Economics for Grade 11 students at Princeton College in Nigeria for the first term of the 2019/2020 school year.
2. It outlines 10 weeks of topics to be covered including basic economic tools, measures of dispersion, economic systems, and key economic indicators.
3. The lessons provide definitions, formulas, examples, and practice problems for students to learn concepts like mean, median, mode, range, variance, and standard deviation.
Here are the steps to solve this problem:
1. Prepare the frequency distribution table with the class intervals, frequencies, and calculate fX.
2. Find the mean (x) using the formula x = fX/f.
3. Calculate the deviations (X - x).
4. Square the deviations to get (X - x)2.
5. Multiply the frequencies and squared deviations to get f(X - x)2.
6. Calculate the variance using the formula σ2 = f(X - x)2 / (f - 1).
7. Take the square root of the variance to get the standard deviation.
8. The range is the difference between the upper
This document provides biographical information about the statistician Ronald Fisher:
- Fisher was born in 1890 in London, England and had a happy childhood until his father lost his business when Fisher was 14.
- He made significant contributions to statistics and developed concepts like maximum likelihood estimation and the analysis of variance.
- Fisher spent time in England and Australia in his career and made groundbreaking advances in the field of statistics.
This document discusses different methods for presenting data graphically. It defines bar charts, histograms, frequency polygons, pie charts, and ogives. Examples of each type of graph are provided using sample data on examination scores of 60 students. Bar charts and histograms use class marks and frequencies to show the distribution. Frequency polygons connect the points on a line graph. Pie charts show the proportion of each class. Ogives use class boundaries and cumulative frequencies to indicate less than and greater than distributions. Students are assigned an activity to practice constructing these various graphs using their own collected data.
This document discusses various statistical measures of dispersion and variation in data, including range, interquartile range, mean deviation, and standard deviation. It provides formulas and examples for calculating each measure. The range is defined as the difference between the highest and lowest values. The interquartile range is the difference between the first and third quartiles. Mean deviation measures the average distance from the mean. Standard deviation uses the differences from the mean to calculate the average deviation and is the most common measure of variation.
The chapter introduces various techniques for summarizing and depicting data through charts and graphs, including frequency distributions, histograms, frequency polygons, ogives, pie charts, stem-and-leaf plots, Pareto charts, and scatter plots. It emphasizes the importance of choosing graphical representations that clearly communicate trends in the data to intended audiences. Sample problems at the end of the chapter provide examples of constructing and interpreting various charts and graphs.
Basic Statistics for Class 11, B.COm, BSW, B.A, BBA, MBAGaurav Rana
The document provides an overview of key concepts in statistics for social work. It discusses topics such as data collection methods, organization and presentation of data, measures of central tendency including mean, median and mode, and measures of dispersion. For example, it explains how to calculate the arithmetic mean for both grouped and ungrouped data using direct, assumed mean and step deviation methods. It also discusses how to calculate the median and mode for discrete and continuous data series.
This document discusses measures of central tendency including mean, median, and mode. It provides definitions and formulas for calculating these measures from individual data series, discrete series, and continuous series. For mean, it describes both direct and shortcut methods for different data types. For median, it explains how to calculate it from individual and discrete series when the number of observations is odd or even. For mode, it gives methods to determine the modal value from individual and discrete series through inspection or tallying frequencies. Examples of calculations are also included.
1. The document provides the scheme of work and lesson notes for Economics for Grade 11 students at Princeton College in Nigeria for the first term of the 2019/2020 school year.
2. It outlines 10 weeks of topics to be covered including basic economic tools, measures of dispersion, economic systems, and key economic indicators.
3. The lessons provide definitions, formulas, examples, and practice problems for students to learn concepts like mean, median, mode, range, variance, and standard deviation.
Here are the steps to solve this problem:
1. Prepare the frequency distribution table with the class intervals, frequencies, and calculate fX.
2. Find the mean (x) using the formula x = fX/f.
3. Calculate the deviations (X - x).
4. Square the deviations to get (X - x)2.
5. Multiply the frequencies and squared deviations to get f(X - x)2.
6. Calculate the variance using the formula σ2 = f(X - x)2 / (f - 1).
7. Take the square root of the variance to get the standard deviation.
8. The range is the difference between the upper
This document provides biographical information about the statistician Ronald Fisher:
- Fisher was born in 1890 in London, England and had a happy childhood until his father lost his business when Fisher was 14.
- He made significant contributions to statistics and developed concepts like maximum likelihood estimation and the analysis of variance.
- Fisher spent time in England and Australia in his career and made groundbreaking advances in the field of statistics.
This document discusses different methods for presenting data graphically. It defines bar charts, histograms, frequency polygons, pie charts, and ogives. Examples of each type of graph are provided using sample data on examination scores of 60 students. Bar charts and histograms use class marks and frequencies to show the distribution. Frequency polygons connect the points on a line graph. Pie charts show the proportion of each class. Ogives use class boundaries and cumulative frequencies to indicate less than and greater than distributions. Students are assigned an activity to practice constructing these various graphs using their own collected data.
This document discusses various statistical measures of dispersion and variation in data, including range, interquartile range, mean deviation, and standard deviation. It provides formulas and examples for calculating each measure. The range is defined as the difference between the highest and lowest values. The interquartile range is the difference between the first and third quartiles. Mean deviation measures the average distance from the mean. Standard deviation uses the differences from the mean to calculate the average deviation and is the most common measure of variation.
The chapter introduces various techniques for summarizing and depicting data through charts and graphs, including frequency distributions, histograms, frequency polygons, ogives, pie charts, stem-and-leaf plots, Pareto charts, and scatter plots. It emphasizes the importance of choosing graphical representations that clearly communicate trends in the data to intended audiences. Sample problems at the end of the chapter provide examples of constructing and interpreting various charts and graphs.
Statistical Analysis using Central TendenciesCelia Santhosh
This document discusses various statistical measures of central tendency, including the mean, median, and mode. It provides definitions and formulas for calculating the arithmetic mean using direct, shortcut, and step deviation methods for individual, discrete, and continuous data series. It also discusses how to calculate the median and weighted mean. The document compares the merits and demerits of the arithmetic mean and provides examples to illustrate the different calculation techniques for central tendencies.
This document discusses various measures of dispersion used in statistics including range, quartile deviation, mean deviation, and standard deviation. It provides definitions and formulas for calculating each measure, as well as examples of calculating the measures for both ungrouped and grouped quantitative data. The key measures discussed are the range, which is the difference between the maximum and minimum values; quartile deviation, which is the difference between the third and first quartiles; mean deviation, which is the mean of the absolute deviations from the mean; and standard deviation, which is the square root of the mean of the squared deviations from the arithmetic mean.
The course will be taught over 54 lectures and include 2 assignments, 2 tests, and a presentation. Students will be assessed internally through a midterm exam, presentation, assignments, and class tests, as well as an external final exam worth 60 marks total.
The course is offered over 54 lectures and covers topics including matrix algebra, determinants, the binomial theorem, sets and relations, trigonometric functions, and statistics. Students will complete 2 assignments and 2 tests. The course aims to refresh foundational mathematics concepts required for computer science courses. Internal assessment includes a midterm test, presentation, assignments, and class tests.
The document discusses various measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating the arithmetic mean, weighted arithmetic mean, harmonic mean, and geometric mean. Examples are given to demonstrate calculating each type of mean from both ungrouped and grouped data. The properties, merits, and limitations of each mean are also outlined. Relationship among the different means are explained.
The document discusses various measures of central tendency and dispersion used in statistics. It defines mean, median, mode, quartiles, percentiles and deciles as measures of central tendency. It also discusses arithmetic mean, weighted mean, geometric mean, harmonic mean and their relationships. Measures of dispersion discussed include range, mean deviation, standard deviation, variance, interquartile range and coefficient of variation. Formulas to calculate these measures from grouped and ungrouped data are also provided.
This document discusses six measures of variation used to determine how values are distributed in a data set: range, quartile deviation, mean deviation, variance, standard deviation, and coefficient of variation. It provides definitions and examples of calculating each measure. The range is defined as the difference between the highest and lowest values. Quartile deviation uses the interquartile range (Q3-Q1). Mean deviation is the average of the absolute deviations from the mean. Variance and standard deviation measure how spread out values are from the mean, with variance using sums of squares and standard deviation taking the square root of variance.
This document discusses measures of central tendency, specifically how to calculate the mean of grouped data. It provides the formula for calculating the mean of grouped data and walks through an example of finding the mean test scores of students. The document demonstrates how to find the midpoint of each score group, multiply by the frequency, sum the results, and divide by the total frequency to determine the mean.
The median is the middle value when values are ordered from lowest to highest. It divides the data set such that half the values are lower than the median and half are higher. For an even number of values, the median is the average of the two middle values. The mode is the most frequently occurring value. It indicates the most common result. Both the median and mode are less influenced by outliers than the mean. They provide a more representative central value for skewed or irregularly distributed data sets.
NIOS STD X Economics Chapter 17 & 18 Collection, Presentation and analysis of...Sajina Nair
1) The document provides information on collecting, presenting, and analyzing data. It discusses the difference between a fact and data, and how to classify, tabulate, and diagrammatically present data.
2) Methods for calculating central tendency like arithmetic mean for individual, discrete, and continuous data series are demonstrated through examples. Both direct and shortcut methods are explained.
3) The importance of data for economic planning, determining national income, and framing government policies is highlighted. Primary and secondary sources of data are also defined.
This document discusses measures of central tendency, specifically the arithmetic mean. It provides formulas and examples for calculating the arithmetic mean using direct, short-cut, and step-deviation methods for both ungrouped and grouped data. It also discusses calculating the weighted mean and combined mean of two or more related groups. Key characteristics of the arithmetic mean are that the sum of deviations from the mean is zero and the sum of squared deviations is minimum.
This document provides information about various statistical measures of central tendency including the median, mode, and quartiles. It defines each measure and provides examples of how to calculate them from both grouped and ungrouped data sets. Formulas are given for calculating the median, quartiles, deciles, and percentiles for grouped data. The mode is defined as the value that occurs most frequently in a data set, and a formula is provided for calculating it from grouped frequency distributions.
Different analytical techniques in managementSohel Rana
This document discusses different analytical techniques used in management, including frequency distribution, measures of central tendency, measures of dispersion, and correlation and regression analysis. It provides an example using real data from an English course given to employees. The data is analyzed to calculate the mean, median, mode, range, mean deviation, variance, standard deviation, and a correlation coefficient and regression equation are determined from a separate age and salary data set. The analysis demonstrates various statistical techniques for summarizing and analyzing data sets.
This document provides an introduction to statistics, including definitions, scope, and measures of central tendency. It defines statistics as the science of collecting, organizing, analyzing, interpreting, and presenting data. Statistics has applications in various fields including social sciences, planning, mathematics, economics, and business management. Common measures of central tendency discussed are the arithmetic mean, geometric mean, harmonic mean, median, and mode. Formulas for calculating the arithmetic mean using individual data, frequency distributions, and class intervals are provided.
This document provides an overview of various statistical measures and methods of analysis. It discusses measures of central tendency including mean, median, and mode. It also covers measures of variability such as range, standard deviation, and correlation. Statistical analysis helps teachers summarize and compare student performance. The steps involved are collecting and organizing data, selecting an appropriate statistical technique, applying the method of analysis, and interpreting the results. Various graphical representations of data are also presented such as histograms, frequency polygons, and ogives.
This document discusses various measures of central tendency and dispersion. It defines the mean, median, mode, harmonic mean and geometric mean as measures of central tendency. It provides formulas and examples for calculating the arithmetic mean using direct and shortcut methods. The document also discusses measures of dispersion such as range, quartile deviation, mean deviation and standard deviation. It provides examples of calculating the mean, median and mode from frequency distribution tables.
This document provides an overview of key concepts in data analysis and statistics. It defines different types of data (categorical, continuous) and variables (nominal, ordinal, interval, ratio). It then covers various steps in data analysis including data preparation, summarization, and descriptive and inferential statistical methods. Graphical representations like pie charts, bar graphs, histograms and scatter plots are also discussed. Hypothesis testing concepts like null/alternative hypotheses, p-values, and choosing test statistics based on data type are summarized.
This document discusses various concepts related to data analysis including types of data, methods of data preparation and summarization, graphical representation of data, descriptive statistics, hypothesis testing, and different statistical tests used for analysis. It provides examples and explanations of key terms like mean, standard deviation, frequency distribution, pie charts, bar graphs, scatter plots, z-test, t-test, F-test, and chi-square test. Various steps involved in hypothesis testing like setting the null and alternate hypotheses, calculating test statistics, and determining whether to reject or accept the null hypothesis are also outlined.
Standard deviation (SD) is a measure of variability or dispersion of data from the mean. It is calculated as the square root of the average of the squared deviations from the mean. The t-test is used to determine if there is a statistically significant difference between the means of two groups, and requires calculation of the standard error of the difference between the means. There are different procedures for the t-test depending on whether the samples are independent or correlated, large or small. The null hypothesis of no difference between means is tested against the alternative hypothesis at a chosen significance level.
This module discusses measures of variability such as range and standard deviation. It provides examples of computing the range of various data sets as the difference between the highest and lowest values. Standard deviation is introduced as a more reliable measure that considers how far all values are from the mean. Students learn to calculate standard deviation by finding the deviation of each value from the mean, squaring the deviations, taking the average of the squared deviations, and extracting the square root. They practice computing and interpreting the range and standard deviation of sample data sets.
1PPTs-Handout One-An Overview of Descriptive Statistics-Chapter 1_2.pptxAbdulHananSheikh1
This document contains an introduction and qualifications for Dr. Abdul Aziz. It states that he has a Ph.D. in Business Administration from University of Sindh and over 15 years of teaching experience. It also lists his areas of expertise, which include statistics, econometrics, quantitative research methods, and financial subjects. The document notes that 17 students have completed their MS degrees under his supervision and he has published 22 research papers in journals.
Statistical Analysis using Central TendenciesCelia Santhosh
This document discusses various statistical measures of central tendency, including the mean, median, and mode. It provides definitions and formulas for calculating the arithmetic mean using direct, shortcut, and step deviation methods for individual, discrete, and continuous data series. It also discusses how to calculate the median and weighted mean. The document compares the merits and demerits of the arithmetic mean and provides examples to illustrate the different calculation techniques for central tendencies.
This document discusses various measures of dispersion used in statistics including range, quartile deviation, mean deviation, and standard deviation. It provides definitions and formulas for calculating each measure, as well as examples of calculating the measures for both ungrouped and grouped quantitative data. The key measures discussed are the range, which is the difference between the maximum and minimum values; quartile deviation, which is the difference between the third and first quartiles; mean deviation, which is the mean of the absolute deviations from the mean; and standard deviation, which is the square root of the mean of the squared deviations from the arithmetic mean.
The course will be taught over 54 lectures and include 2 assignments, 2 tests, and a presentation. Students will be assessed internally through a midterm exam, presentation, assignments, and class tests, as well as an external final exam worth 60 marks total.
The course is offered over 54 lectures and covers topics including matrix algebra, determinants, the binomial theorem, sets and relations, trigonometric functions, and statistics. Students will complete 2 assignments and 2 tests. The course aims to refresh foundational mathematics concepts required for computer science courses. Internal assessment includes a midterm test, presentation, assignments, and class tests.
The document discusses various measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating the arithmetic mean, weighted arithmetic mean, harmonic mean, and geometric mean. Examples are given to demonstrate calculating each type of mean from both ungrouped and grouped data. The properties, merits, and limitations of each mean are also outlined. Relationship among the different means are explained.
The document discusses various measures of central tendency and dispersion used in statistics. It defines mean, median, mode, quartiles, percentiles and deciles as measures of central tendency. It also discusses arithmetic mean, weighted mean, geometric mean, harmonic mean and their relationships. Measures of dispersion discussed include range, mean deviation, standard deviation, variance, interquartile range and coefficient of variation. Formulas to calculate these measures from grouped and ungrouped data are also provided.
This document discusses six measures of variation used to determine how values are distributed in a data set: range, quartile deviation, mean deviation, variance, standard deviation, and coefficient of variation. It provides definitions and examples of calculating each measure. The range is defined as the difference between the highest and lowest values. Quartile deviation uses the interquartile range (Q3-Q1). Mean deviation is the average of the absolute deviations from the mean. Variance and standard deviation measure how spread out values are from the mean, with variance using sums of squares and standard deviation taking the square root of variance.
This document discusses measures of central tendency, specifically how to calculate the mean of grouped data. It provides the formula for calculating the mean of grouped data and walks through an example of finding the mean test scores of students. The document demonstrates how to find the midpoint of each score group, multiply by the frequency, sum the results, and divide by the total frequency to determine the mean.
The median is the middle value when values are ordered from lowest to highest. It divides the data set such that half the values are lower than the median and half are higher. For an even number of values, the median is the average of the two middle values. The mode is the most frequently occurring value. It indicates the most common result. Both the median and mode are less influenced by outliers than the mean. They provide a more representative central value for skewed or irregularly distributed data sets.
NIOS STD X Economics Chapter 17 & 18 Collection, Presentation and analysis of...Sajina Nair
1) The document provides information on collecting, presenting, and analyzing data. It discusses the difference between a fact and data, and how to classify, tabulate, and diagrammatically present data.
2) Methods for calculating central tendency like arithmetic mean for individual, discrete, and continuous data series are demonstrated through examples. Both direct and shortcut methods are explained.
3) The importance of data for economic planning, determining national income, and framing government policies is highlighted. Primary and secondary sources of data are also defined.
This document discusses measures of central tendency, specifically the arithmetic mean. It provides formulas and examples for calculating the arithmetic mean using direct, short-cut, and step-deviation methods for both ungrouped and grouped data. It also discusses calculating the weighted mean and combined mean of two or more related groups. Key characteristics of the arithmetic mean are that the sum of deviations from the mean is zero and the sum of squared deviations is minimum.
This document provides information about various statistical measures of central tendency including the median, mode, and quartiles. It defines each measure and provides examples of how to calculate them from both grouped and ungrouped data sets. Formulas are given for calculating the median, quartiles, deciles, and percentiles for grouped data. The mode is defined as the value that occurs most frequently in a data set, and a formula is provided for calculating it from grouped frequency distributions.
Different analytical techniques in managementSohel Rana
This document discusses different analytical techniques used in management, including frequency distribution, measures of central tendency, measures of dispersion, and correlation and regression analysis. It provides an example using real data from an English course given to employees. The data is analyzed to calculate the mean, median, mode, range, mean deviation, variance, standard deviation, and a correlation coefficient and regression equation are determined from a separate age and salary data set. The analysis demonstrates various statistical techniques for summarizing and analyzing data sets.
This document provides an introduction to statistics, including definitions, scope, and measures of central tendency. It defines statistics as the science of collecting, organizing, analyzing, interpreting, and presenting data. Statistics has applications in various fields including social sciences, planning, mathematics, economics, and business management. Common measures of central tendency discussed are the arithmetic mean, geometric mean, harmonic mean, median, and mode. Formulas for calculating the arithmetic mean using individual data, frequency distributions, and class intervals are provided.
This document provides an overview of various statistical measures and methods of analysis. It discusses measures of central tendency including mean, median, and mode. It also covers measures of variability such as range, standard deviation, and correlation. Statistical analysis helps teachers summarize and compare student performance. The steps involved are collecting and organizing data, selecting an appropriate statistical technique, applying the method of analysis, and interpreting the results. Various graphical representations of data are also presented such as histograms, frequency polygons, and ogives.
This document discusses various measures of central tendency and dispersion. It defines the mean, median, mode, harmonic mean and geometric mean as measures of central tendency. It provides formulas and examples for calculating the arithmetic mean using direct and shortcut methods. The document also discusses measures of dispersion such as range, quartile deviation, mean deviation and standard deviation. It provides examples of calculating the mean, median and mode from frequency distribution tables.
This document provides an overview of key concepts in data analysis and statistics. It defines different types of data (categorical, continuous) and variables (nominal, ordinal, interval, ratio). It then covers various steps in data analysis including data preparation, summarization, and descriptive and inferential statistical methods. Graphical representations like pie charts, bar graphs, histograms and scatter plots are also discussed. Hypothesis testing concepts like null/alternative hypotheses, p-values, and choosing test statistics based on data type are summarized.
This document discusses various concepts related to data analysis including types of data, methods of data preparation and summarization, graphical representation of data, descriptive statistics, hypothesis testing, and different statistical tests used for analysis. It provides examples and explanations of key terms like mean, standard deviation, frequency distribution, pie charts, bar graphs, scatter plots, z-test, t-test, F-test, and chi-square test. Various steps involved in hypothesis testing like setting the null and alternate hypotheses, calculating test statistics, and determining whether to reject or accept the null hypothesis are also outlined.
Standard deviation (SD) is a measure of variability or dispersion of data from the mean. It is calculated as the square root of the average of the squared deviations from the mean. The t-test is used to determine if there is a statistically significant difference between the means of two groups, and requires calculation of the standard error of the difference between the means. There are different procedures for the t-test depending on whether the samples are independent or correlated, large or small. The null hypothesis of no difference between means is tested against the alternative hypothesis at a chosen significance level.
This module discusses measures of variability such as range and standard deviation. It provides examples of computing the range of various data sets as the difference between the highest and lowest values. Standard deviation is introduced as a more reliable measure that considers how far all values are from the mean. Students learn to calculate standard deviation by finding the deviation of each value from the mean, squaring the deviations, taking the average of the squared deviations, and extracting the square root. They practice computing and interpreting the range and standard deviation of sample data sets.
1PPTs-Handout One-An Overview of Descriptive Statistics-Chapter 1_2.pptxAbdulHananSheikh1
This document contains an introduction and qualifications for Dr. Abdul Aziz. It states that he has a Ph.D. in Business Administration from University of Sindh and over 15 years of teaching experience. It also lists his areas of expertise, which include statistics, econometrics, quantitative research methods, and financial subjects. The document notes that 17 students have completed their MS degrees under his supervision and he has published 22 research papers in journals.
The document discusses organizing and presenting data through descriptive statistics. It covers types of data, constructing frequency distribution tables, calculating relative frequencies and percentages, and using graphical methods like bar graphs, pie charts, histograms and polygons to summarize categorical and quantitative data. Examples are provided to demonstrate how to organize data into frequency distributions and calculate relative frequencies to graph the results.
This document discusses various measures of dispersion used to describe how spread out or clustered data values are around a central measure like the mean or median. It defines absolute and relative measures of dispersion and explains key measures like range, interquartile range, quartile deviation, mean deviation, and their coefficients. Examples are provided to demonstrate calculating each measure for both ungrouped and grouped data. The advantages and disadvantages of range, quartile deviation, and mean deviation are also outlined.
This document discusses analyzing and interpreting test data using various statistical measures. It describes desired learning outcomes around measures of central tendency, variability, position, and covariability. Key measures are defined, including:
- Mean, median, and mode as measures of central tendency
- Standard deviation as a measure of variability
- Measures of position like percentiles and z-scores
- Covariability measures the relationship between two variables
Examples are provided to demonstrate calculating and interpreting these different statistical measures from test data distributions. The appropriate use of measures depends on the level of measurement (nominal, ordinal, interval, ratio). Measures reveal properties like skewness and help evaluate teaching and learning.
This document provides information about statistics and probability. It defines statistics as the collection, analysis, and interpretation of data. There are two main categories of statistics: descriptive statistics, which summarizes and describes data, and inferential statistics, which is used to estimate, predict, and generalize results. The document also discusses population and sample, measures of central tendency (mean, median, mode), measures of dispersion (range, variance, standard deviation), qualitative vs. quantitative data, ways of representing quantitative data (numerically and graphically), and examples of organizing data using a stem-and-leaf plot.
This document contains class notes from an empirical research methods course. It outlines key concepts related to sampling, statistics, experimental design, and data analysis techniques including t-tests, analysis of variance (ANOVA), and factorial ANOVA. Examples are provided to illustrate how to conduct statistical tests in SPSS and how to interpret and report results. Key terms are defined throughout to explain assumptions, computations, and interpretations of different statistical analyses.
This document contains class notes from an empirical research methods course. It outlines key concepts related to sampling, statistics, experimental design, and data analysis techniques including t-tests, analysis of variance (ANOVA), and factorial ANOVA. Examples are provided to illustrate how to conduct statistical tests in SPSS and how to interpret and report results. Key terms are defined throughout to explain assumptions, computations, and interpretations of different statistical analyses.
This document discusses analytical representation of data through descriptive statistics. It begins by showing raw, unorganized data on movie genre ratings. It then demonstrates organizing this data into a frequency distribution table and bar graph to better analyze and describe the data. It also calculates averages for each movie genre. The document then discusses additional descriptive statistics measures like the mean, median, mode, and percentiles to further analyze data through measures of central tendency and dispersion.
The document discusses analyzing test item data through item analysis. Item analysis examines student responses to test items and is used to select the best items, identify flaws, detect learning difficulties, and identify student weaknesses. An item's characteristics, difficulty level, discrimination power, and effectiveness of distractors are evaluated. Data is organized and measures like difficulty index, discrimination index, and attractiveness of distractors are calculated to evaluate items. The summary provides an overview of the key aspects and purposes of item analysis.
The document discusses various methods for collecting, organizing, and analyzing quantitative data. It describes data as facts expressed numerically that are useful for decision making. Common data types include individual series, discrete series, and continuous series. Methods for calculating the arithmetic mean or average as a measure of central tendency are provided for each data type, including direct formulas and shortcut methods. The goal of statistical analysis is to summarize collected data and identify trends or conclusions.
This document discusses summary statistics and measures of central tendency and dispersion. It provides examples of how to calculate the mean, mode, median, and geometric mean of data sets. It also discusses how to calculate the standard deviation and variance of data as measures of dispersion. Regression and correlation analysis are introduced as methods to study the relationship between variables and enable prediction. The least squares approach to determining the linear regression line that best fits a data set is demonstrated through an example.
The document provides information about measures of central tendency and dispersion in statistics. It discusses finding the mode, median, and mean of ungrouped and grouped data. It also discusses determining the range and interquartile range of ungrouped and grouped data. Formulas are provided for calculating the mean, median, mode, range, interquartile range, and variance of data sets. Examples are worked through to demonstrate calculating these statistical measures from raw data sets and frequency distribution tables.
Measure of dispersion by Neeraj Bhandari ( Surkhet.Nepal )Neeraj Bhandari
This document discusses measures of dispersion used in statistics. It defines measures such as range, quartile deviation, mean deviation, variance, and standard deviation. It provides formulas to calculate these measures and examples showing how to apply the formulas. The key points are:
- Measures of dispersion quantify how spread out or varied the values in a data set are. They help identify variation, compare data sets, and enable other statistical techniques.
- Common absolute measures include range, quartile deviation, and mean deviation. Common relative measures include coefficient of range, coefficient of quartile deviation, and coefficient of variation.
- Variance and standard deviation are calculated using all data points. Variance is the average of squared deviations
Measure of dispersion by Neeraj Bhandari ( Surkhet.Nepal )
Module stats
1. Punjab College of Technical Education Ludhiana
COURSE MODULE
BUSINESS STATISTICS
Name of Teacher: Asha Sharma (asha_s81@hotmail.com)
Nidhi Juneja (nidhi_juneja30@yahoo.co.in)
Subject Code: BB-304
No. Of lecture: 57
Class Tests: 2
Hourly test: 2
Assignment: 3
Activity: 2
Course Objective:
Business Statistics is helpful in framing suitable policies in a large number of diversified fields
covering natural, physical and social sciences. It will enable the students to know what is
statistics, how and when to apply statistical techniques to decision making situations and how to
interpret the results.
Class Room Policies:
1. Student will be allowed to enter the class till the attendance is going on, after that no one
can enter the class.
2. No student will be given a chance to reappear for MSE.
3. All the tests will be considered for internals.
4. Each assignment will have weightage & assignments are to be submitted by the
scheduled time, failing which no assignment will be accepted.
Internal Marks Distribution:
Mid Semester Examination: 15
Presentation: 6
1st Hourly Tests: 5
2nd Hourly Tests: 5
Class test: 5
Assignment: 4
3. Lecture No. Contents Assignments
1. Introduction to Business Statistics
• Relevance
• Applications
2. Functions of statistics
• Definiteness
• Condensation
• Comparison
• Prediction
• Formulation Of suitable policies
Limitations
• True only on average
• It can be misused
• One method of studying the problem
• Does not deal with individual measurements
3. Data
• Relevance
• Collection of Data
4. Classification of data
5. Collection of chocolate preference (Activity-1)
6. Formation of discrete
Continuous frequency distribution
7. Tabulation of data
• meaning
• Relevance
• Format of table
8. Case study -1(Portfolio management)
9. Graphic presentation: Meaning
Types of diagrams
• Sub-divided bar
• Multiple bars
• Percentage bar
• Pie Chart
10. Graphic presentation (contd.).
• Graphs of frequency distribution
• Frequency Polygon
• Frequency curve
• Ogives
11. Practical Tutorial- 1
Discussion on the problem of students.
12. Measures of central value / Measures of Location Assignment-1
Relevance
Objectives of averaging
Requisites of a good average
13. Arithmetic mean
# Calculation in Individual
14. Calculation of mean in descrete and continuous series
15. Geometric mean
16. Harmonic mean
17. Median
4. REFERNCES
1. Levin & Rubin: Statistics for Management, Prentice Hall India.
2. Srivastava & Rego : Statistics for Management, Tata McGraw Hill
3. S.P.Gupta : Statistical Methods, Sultan Chand & Sons
4. Andersons, Sweeny and Williams : Cengage Learning, Statistics for Business and
Economics
Activity-1
Students will go to 25 children and ask them about their chocolates’ preferences among the
various brands available in the market. They will collect the data about the name and age of the
children along with their preferences. Then, they will convert this raw data into a Bivariate Table
consisting of 2 variables.
1. Chocolate
2. Age
For Example:
X(Chocolate)/Y(Age 3-5 5-7 7-9 9-11 11-13 13-15
)
Dairy Milk
sMilky Bar
Munch
Perk
5. Nestle
5 Star
Bar One
Activity-2
Calculate the relationship between the marks obtained in 10th & +2 of 15 students.
Assignment-1
Draw the Histogram, Frequency Polygon and Frequency Curve:
1.
Variable Frequency Variable Frequency
100-110 11 140-150 33
110-120 28 150-160 20
120-130 36 160-170 8
130-140 49
2.
Salary (p.m.) No. of employees
Less than 3000 100
3000-4000 20
4000-5000 30
5000-6000 60
6000-7000 75
7000 & More 115
Assignment-2
1. Calculate Median & Mode of the data given below. Using them find arithmetic mean.
Marks 10 20 30 40 50 60
Less Than
No. of 8 23 45 65 75 80
students
2. Find the class intervals if arithmetic mean of the following distribution is 33 & assumed mean
35.
Step -3 -2 -1 0 1 2
Deviation
6. Frequency 5 10 25 30 20 10
Assignment-3
1. Calculate Karl Pearson’s Coefficient Of Correlation from the following data:
X 100 200 300 400 500 600 700
Y 30 50 60 80 100 110 130
2. Find Rank Correlation
X 50 55 65 50 55 60 50 65 70 75
Y 110 110 115 125 140 115 130 120 115 160
Presentation Topics
Every group will take up any Organization according to their convenience and will collect the
data relating to its sales and Production (month wise for 4 years) and will show the same for
every year in graphs and will have to find the average sales and production during the year and
the combined mean for all the 4 years.
The students will be divided into the group of 3. Each group will have to present within 20
minutes.
Presentation Assessment Break Up
Presentation Report 3
Communication skills 4
Formals 1
Query handling 2
Formulae Of Statistics In Course
Arithmetic mean
Direct Method
In Individual Series A.M.= ΣX/N
In Discrete & Continuous series A.M.= ΣFX/ΣF
7. Short Cut Method/ Indirect Method A.M.= A+ΣFdx/ΣF
Step-deviation Method A.M.=A+ΣFdx'/ΣF*i
Geometric Mean G.M.=√ab
Harmonic Mean
In Individual Series N/Σ(1/X)
In Discrete & Continuous series N/Σ(f*1/X)
Median
In Individual & Discrete Series M=N+1/2, (Nth term+N+1/2)/2
Continuous series N1=N/2, M=L+ N1-CF/F*i
Mode
In Individual Series Maximum repeated term
In Discrete & Continuous series Groupung Table & Analysis Table, M=
L+D1/(D1+D2)*i
Quartiles
In Individual & Discrete Series Q1=N+1/4, Q2=2(N+1)/4, Q3=3(N+1)/4
Continuous series N1=N/4, Q1=L+(N1-
C.F.)/F*i,N1=3N/4,Q3=L+(N1-C.F.)/F*i
Decile N1=N/10, D1=L+(N1-
C.F.)/F*i,N1=9N/10,D9=L+(N1-C.F.)/F*i
Percentile N1=10(N/100), P10=L+(N1-
C.F.)/F*i,N1=90N/100,P90=L+(N1-C.F.)/
F*i
Measures of dispersion
Range Highest Value-Lowest Value
Quartile Deviation Q3-Q1/2
Coeffcient of quartile deviation Q3-Q1/Q3+Q1
Mean Deviation
In Individual Series Σ[X-A.M.]/N
In Discrete & Continuous series ΣF[X-A.M.]/N
Coefficient Of Mean Deviation M.D./A.M.or M or Z
Standard Deviation
In Individual Series √Σd²/N-(Σd/N)2
In Discrete & Continuous series √Σfd²/N-(Σfd/N)2
Coefficient Of Standard Deviation S.D./A.M.
Variance S.D.²
Coefficient of variation S.D./A.M.*100
Coefficient Of Correlation
Karl Pearson r=NΣXY-(ΣX.ΣY)/√(NΣX²-
{ΣX}²).√(NΣY²-{ΣY}²)
8. Spearman 1-6ΣD²/N³-N When ranks are not
repeated
1-6[ΣD²+1/12{m³-m}]/N³-N, When ranks
are repeated
Concurrent deviation C √n (2C-n/n)
Standard Error 1-r²/√N
Probable Error 0.6745 (1-r²/√N)