Statistical formulas
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This document provides formulas for various statistical concepts including: - Mean, median, mode, standard deviation, and correlation for individual and grouped data - Skewness measures including Pearson, Bowley, and Kelly skewness - Index number formulas using simple and weighted aggregative methods - Regression analysis using the least squares method and calculating the regression coefficient - Time series analysis using least squares method to calculate the trend line coefficient
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Measures of Dispersion
This document discusses various measures of dispersion used in statistics, including range, standard deviation, and mean deviation. It provides examples of calculating each measure using both individual data series and grouped data series. For range, it calculates the difference between the highest and lowest values. For standard deviation, it shows how to calculate it using the actual mean method and assumed mean method for both individual and grouped data. The key measures discussed are range, which is the difference between the maximum and minimum values, and standard deviation, which measures how far data points are from the mean.
Mean for Grouped Data
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.
Standard deviation quartile deviation
This document discusses measures of dispersion, specifically standard deviation and quartile deviation. It defines standard deviation as a measure of how closely values are clustered around the mean. Standard deviation is calculated by taking the square root of the average of the squared deviations from the mean. Quartile deviation is defined as half the difference between the third quartile (Q3) and first quartile (Q1), which divide a data set into four equal parts. The document provides examples of calculating standard deviation and quartile deviation for both individual and grouped data sets. It also discusses the merits, demerits, and uses of these statistical measures.
Basic statics
The document defines basic statistics and discusses frequency distribution and types of frequency distributions. It provides steps to construct discrete and continuous frequency distributions, including determining class limits and boundaries. Examples are given to demonstrate creating frequency tables from raw data for discrete and continuous variables. Key concepts discussed include tally marks, frequencies, class intervals, midpoints, and cumulative frequencies.
STANDARD DEVIATION (2018) (STATISTICS)
THIS IS A QUICK AND EASY METHOD TO LEARN STANDARD DEVIATION FOR DISCRETE AND GROUPED FREQUENCY DISTRIBUTION.
IT GIVES A STEP BY STEP, SIMPLE EXPLANATION OF PROBLEMS WITH FORMULAE.
SO WATCH THE ENTIRE VIDEO TODAY.
Measures of Central Tendency
This document discusses various measures of central tendency including arithmetic mean, median, and mode. It provides definitions and formulas for calculating each measure along with examples using raw data and grouped data. The three main points covered are:
1. Measures of central tendency (mean, median, mode) calculate the central or typical value in a data set and are used to describe data distributions.
2. The arithmetic mean is the sum of all values divided by the number of values, the median is the middle number when values are arranged in order, and the mode is the most frequent value.
3. Formulas and methods are provided for calculating each measure using both raw ungrouped data as well as grouped frequency distribution data
MEAN DEVIATION
The mean deviation is a measure of how spread out values are from the average. It is calculated by:
1) Finding the mean of all values.
2) Calculating the distance between each value and the mean.
3) Taking the average of those distances. This provides the mean deviation, which tells us how far on average values are from the central mean. Examples show calculating mean deviation for both grouped and ungrouped data sets.
Assessment of Learning 2 (Overview)
The document discusses frequency distributions and their components. A frequency distribution arranges data into categories and shows the number of observations in each category. Key parts include:
- Class limits, which define the groupings by lower and upper limits.
- Class size, which is the width of each interval. It is calculated as the range divided by the number of classes.
- Class boundaries and marks, which separate and indicate the midpoints of categories.
The document provides steps for constructing a frequency distribution, including computing the range, determining class size, setting limits, tallying scores, and counting frequencies. An example uses exam scores to demonstrate these steps.
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This document discusses various measures of dispersion used in statistics, including range, standard deviation, and mean deviation. It provides examples of calculating each measure using both individual data series and grouped data series. For range, it calculates the difference between the highest and lowest values. For standard deviation, it shows how to calculate it using the actual mean method and assumed mean method for both individual and grouped data. The key measures discussed are range, which is the difference between the maximum and minimum values, and standard deviation, which measures how far data points are from the mean.
Mean for Grouped Data
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.
Standard deviation quartile deviation
This document discusses measures of dispersion, specifically standard deviation and quartile deviation. It defines standard deviation as a measure of how closely values are clustered around the mean. Standard deviation is calculated by taking the square root of the average of the squared deviations from the mean. Quartile deviation is defined as half the difference between the third quartile (Q3) and first quartile (Q1), which divide a data set into four equal parts. The document provides examples of calculating standard deviation and quartile deviation for both individual and grouped data sets. It also discusses the merits, demerits, and uses of these statistical measures.
Basic statics
The document defines basic statistics and discusses frequency distribution and types of frequency distributions. It provides steps to construct discrete and continuous frequency distributions, including determining class limits and boundaries. Examples are given to demonstrate creating frequency tables from raw data for discrete and continuous variables. Key concepts discussed include tally marks, frequencies, class intervals, midpoints, and cumulative frequencies.
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THIS IS A QUICK AND EASY METHOD TO LEARN STANDARD DEVIATION FOR DISCRETE AND GROUPED FREQUENCY DISTRIBUTION.
IT GIVES A STEP BY STEP, SIMPLE EXPLANATION OF PROBLEMS WITH FORMULAE.
SO WATCH THE ENTIRE VIDEO TODAY.
Measures of Central Tendency
This document discusses various measures of central tendency including arithmetic mean, median, and mode. It provides definitions and formulas for calculating each measure along with examples using raw data and grouped data. The three main points covered are:
1. Measures of central tendency (mean, median, mode) calculate the central or typical value in a data set and are used to describe data distributions.
2. The arithmetic mean is the sum of all values divided by the number of values, the median is the middle number when values are arranged in order, and the mode is the most frequent value.
3. Formulas and methods are provided for calculating each measure using both raw ungrouped data as well as grouped frequency distribution data
MEAN DEVIATION
The mean deviation is a measure of how spread out values are from the average. It is calculated by:
1) Finding the mean of all values.
2) Calculating the distance between each value and the mean.
3) Taking the average of those distances. This provides the mean deviation, which tells us how far on average values are from the central mean. Examples show calculating mean deviation for both grouped and ungrouped data sets.
Assessment of Learning 2 (Overview)
The document discusses frequency distributions and their components. A frequency distribution arranges data into categories and shows the number of observations in each category. Key parts include:
- Class limits, which define the groupings by lower and upper limits.
- Class size, which is the width of each interval. It is calculated as the range divided by the number of classes.
- Class boundaries and marks, which separate and indicate the midpoints of categories.
The document provides steps for constructing a frequency distribution, including computing the range, determining class size, setting limits, tallying scores, and counting frequencies. An example uses exam scores to demonstrate these steps.
QUARTILE DEVIATION
This document discusses various statistical measures including the coefficient of variation, quartile deviation, and box and whisker plots. It defines the coefficient of variation as the ratio of the standard deviation to the mean. Formulas for calculating the coefficient of variation by hand and in Excel are provided. Quartile deviation is defined as the semi-variation between the upper and lower quartiles, or the interquartile range. Steps for calculating quartile deviation from a data set are outlined. Finally, box and whisker plots are introduced as a way to visually represent the minimum, maximum, median, quartiles and interquartile range of a data set.
Mean of grouped data
This document provides steps for calculating the mean of grouped data:
1. Make a frequency distribution table with class intervals, frequencies, and midpoints.
2. Multiply the midpoint and frequency for each class to calculate the fx value.
3. Use the formula x=fx/n, where f is the frequency, x is the midpoint, and n is the total frequency, to calculate the mean.
For example, given data grouped into classes with frequencies totaling 30, the mean was calculated to be 73.97.
Histograms
Here are definitions for the key terms related to histograms:
- Data set: A collection of data values.
- Frequency: The number of observations (data values) that fall into a particular class interval. Calculated by counting the number of data values within the interval.
- Class interval: A range of values into which individual observations are categorized. Calculated by dividing the range of the data set into equal-sized sections.
- Frequency polygon: A graph that connects the midpoints of the class intervals to the corresponding frequencies using line segments.
- Midpoint: The average value of the class interval. Calculated by taking the average of the lower and upper class interval boundaries.
- Range: The
Frequency distribution of a continuous variable. in Biostatic
This document describes the process of constructing a frequency distribution for a continuous variable using mileage ratings from 30 cars tested by the EPA. It involves 7 steps: 1) Identifying the smallest and largest values, 2) Calculating the range, 3) Choosing the number of classes, 4) Calculating the class width, 5) Determining class limits, 6) Distributing the data and calculating frequencies, 7) Constructing a histogram and frequency polygon to visualize the distribution. The goal is to group continuous data into classes to understand the overall pattern.
Statistics
Here is the completed table:
Marks Frequency Midpoint Upper boundary Cumulative
frequency
60-64 3 62 64.5 3
65-69 2 67 69.5 5
70-74 6 72 74.5 11
Cumulative Frequency
This document discusses cumulative frequency distribution. It defines cumulative frequency as the frequency of occurrence of values less than a reference value. The document outlines how to build a cumulative frequency distribution table from a frequency table or histogram by summing the frequencies in each class. Cumulative frequency analysis is used to understand how often a phenomenon is below a certain value and can help in describing situations or planning interventions.
Measures of variability grouped data
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
Construction of a frequency table
The document provides steps for constructing a frequency table from a set of test score data: 1) Compute the range and class interval size, 2) Set up the table with class intervals, 3) Tally the observations in each interval and compute frequencies, 4) Compute cumulative and relative frequencies. An example is provided using 30 test scores ranging from 76 to 99 grouped into intervals of size 4.
Mean absolute deviation about mean
This document provides examples and formulas for calculating mean absolute deviation and coefficient of dispersion. Mean absolute deviation is a measure of how far data points deviate from the mean. It is calculated by taking the average of the absolute differences between each data point and the mean. Coefficient of dispersion is calculated by dividing the mean absolute deviation by the mean and multiplying by 100 to express it as a percentage. Two examples are provided to demonstrate calculating mean absolute deviation and coefficient of dispersion using data sets and frequency distributions.
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This presentation discusses frequency distribution graphs. It provides examples of constructing frequency distribution tables and calculating class midpoints and cumulative frequencies. The key graphs for representing frequency distributions are described as histograms, frequency polygons, and cumulative frequency curves for continuous or quantitative data. Bar charts, line graphs and pie charts are also introduced as options to display grouped or ungrouped categorical data. Examples of each type of graph are included.
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The document provides information about different types of diagrams used to represent statistical data visually, including pie charts, bar graphs, frequency polygons, histograms, and cumulative frequency curves. It explains how to construct each type of diagram by plotting variables like frequency and class on x and y axes. Examples are given of drawing each diagram based on sample data. The document also discusses concepts like percentiles, quartiles, and deciles for dividing a data set and calculating measures like median and skewness from a cumulative frequency curve.
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The document contains information about measures of variation and distributions, including:
1) A table showing the age distribution of Nigeria's population in 1991, with the lower quartile around 11 years, median around 24 years, and upper quartile around 40.5 years.
2) A table with test marks for 70 students, including constructing a cumulative frequency curve and determining that 28 students passed with a mark over 47.
3) Box and whisker plots are constructed to represent the goals scored in football matches by two teams, comparing their median, quartiles, and range.
4) Standard deviation is defined as a measure of spread from the mean, and the standard deviations of three data sets S1, S2,
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The document discusses frequency distribution tables and how to create them. It defines statistics, frequency distribution tables, and key terms like data, class, range, and class interval. It provides steps to create a frequency distribution table: 1) arrange data in ascending order, 2) find the range, 3) determine the number of classes, 4) form classes based on class interval, and 5) create a table with classes and frequencies. The document uses an example dataset to demonstrate how to apply these steps to create a frequency distribution table.
Measures of central tendency
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.
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This document provides formulas and definitions for various statistical concepts including:
- Mean, median, mode, standard deviation, and correlation for individual, discrete, continuous, and combined data sets.
- Formulas for price indices like Laspeyre's, Paasche's, and Fisher's index.
- Formulas for regression analysis using the least squares method to find the regression coefficients for the line of best fit.
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This Slide was made for my university presentation in "Statistics and probability" course.In this slide ,you will get short statistical calculation on Distance Between Present residence from Daffodil International University(Using to find the distance & take the shortest value of the possible distances).I think that's will help you by giving information about statistical calculation of Statistics and probability.
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The document discusses different methods of presenting data:
1. Textual or descriptive presentation involves describing data within the text when quantities are small.
2. Tabular presentation arranges data in rows and columns for easy comparison.
3. Diagrammatic presentation uses visual diagrams like bar graphs, pie charts, and line graphs. Common types are histograms, frequency polygons, frequency curves and ogives. Diagrams effectively simplify and compare large data volumes.
Standard deviation and standard error
This document discusses standard deviation and related statistical concepts. It defines standard deviation as a measure of variability around the mean and explains how to calculate it from both ungrouped and grouped data. It also defines related terms like variance, standard error of the mean, and confidence limits of the mean. Standard deviation is calculated using the formula that sums the squared deviations from the mean, divided by n-1. Standard error is the standard deviation divided by the square root of the sample size, and confidence limits refer to ranges around the mean within which we can be certain the population mean falls.
Standard deviation
The standard deviation is a measure of the spread of scores within a set of data. Usually, we are interested in the standard deviation of a population.
Calculation of Arithmetic Mean
This document discusses the calculation of arithmetic mean from data in various formats. It defines arithmetic mean as the sum of all values divided by the number of observations. It then provides examples of calculating the arithmetic mean using direct and shortcut methods for individual series, discrete series with frequencies, continuous series with class intervals, and series with open-ended classes. The different methods are demonstrated using example data sets. References on biostatistics are also included.
Arithematic mean
The document discusses different methods to calculate the arithmetic mean of a data set: direct method, indirect method, and step-deviation method. The direct method calculates the mean as the sum of all values divided by the number of values. The indirect method uses an assumed mean and deviation from that mean. The step-deviation method also uses an assumed mean but calculates step-deviations as the difference from the mean divided by the class interval. Formulas for each method are provided along with examples of calculating the arithmetic mean for both ungrouped and grouped data sets using the different techniques.
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This document discusses various statistical measures including the coefficient of variation, quartile deviation, and box and whisker plots. It defines the coefficient of variation as the ratio of the standard deviation to the mean. Formulas for calculating the coefficient of variation by hand and in Excel are provided. Quartile deviation is defined as the semi-variation between the upper and lower quartiles, or the interquartile range. Steps for calculating quartile deviation from a data set are outlined. Finally, box and whisker plots are introduced as a way to visually represent the minimum, maximum, median, quartiles and interquartile range of a data set.
Mean of grouped data
This document provides steps for calculating the mean of grouped data:
1. Make a frequency distribution table with class intervals, frequencies, and midpoints.
2. Multiply the midpoint and frequency for each class to calculate the fx value.
3. Use the formula x=fx/n, where f is the frequency, x is the midpoint, and n is the total frequency, to calculate the mean.
For example, given data grouped into classes with frequencies totaling 30, the mean was calculated to be 73.97.
Histograms
Here are definitions for the key terms related to histograms:
- Data set: A collection of data values.
- Frequency: The number of observations (data values) that fall into a particular class interval. Calculated by counting the number of data values within the interval.
- Class interval: A range of values into which individual observations are categorized. Calculated by dividing the range of the data set into equal-sized sections.
- Frequency polygon: A graph that connects the midpoints of the class intervals to the corresponding frequencies using line segments.
- Midpoint: The average value of the class interval. Calculated by taking the average of the lower and upper class interval boundaries.
- Range: The
Frequency distribution of a continuous variable. in Biostatic
This document describes the process of constructing a frequency distribution for a continuous variable using mileage ratings from 30 cars tested by the EPA. It involves 7 steps: 1) Identifying the smallest and largest values, 2) Calculating the range, 3) Choosing the number of classes, 4) Calculating the class width, 5) Determining class limits, 6) Distributing the data and calculating frequencies, 7) Constructing a histogram and frequency polygon to visualize the distribution. The goal is to group continuous data into classes to understand the overall pattern.
Statistics
Here is the completed table:
Marks Frequency Midpoint Upper boundary Cumulative
frequency
60-64 3 62 64.5 3
65-69 2 67 69.5 5
70-74 6 72 74.5 11
Cumulative Frequency
This document discusses cumulative frequency distribution. It defines cumulative frequency as the frequency of occurrence of values less than a reference value. The document outlines how to build a cumulative frequency distribution table from a frequency table or histogram by summing the frequencies in each class. Cumulative frequency analysis is used to understand how often a phenomenon is below a certain value and can help in describing situations or planning interventions.
Measures of variability grouped data
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
Construction of a frequency table
The document provides steps for constructing a frequency table from a set of test score data: 1) Compute the range and class interval size, 2) Set up the table with class intervals, 3) Tally the observations in each interval and compute frequencies, 4) Compute cumulative and relative frequencies. An example is provided using 30 test scores ranging from 76 to 99 grouped into intervals of size 4.
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This document provides examples and formulas for calculating mean absolute deviation and coefficient of dispersion. Mean absolute deviation is a measure of how far data points deviate from the mean. It is calculated by taking the average of the absolute differences between each data point and the mean. Coefficient of dispersion is calculated by dividing the mean absolute deviation by the mean and multiplying by 100 to express it as a percentage. Two examples are provided to demonstrate calculating mean absolute deviation and coefficient of dispersion using data sets and frequency distributions.
frequency distribution & graphs
This presentation discusses frequency distribution graphs. It provides examples of constructing frequency distribution tables and calculating class midpoints and cumulative frequencies. The key graphs for representing frequency distributions are described as histograms, frequency polygons, and cumulative frequency curves for continuous or quantitative data. Bar charts, line graphs and pie charts are also introduced as options to display grouped or ungrouped categorical data. Examples of each type of graph are included.
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This is a presentation which covers the measures of central tendency and variability for grouped data.
Frequency distribtution curve
The document provides information about different types of diagrams used to represent statistical data visually, including pie charts, bar graphs, frequency polygons, histograms, and cumulative frequency curves. It explains how to construct each type of diagram by plotting variables like frequency and class on x and y axes. Examples are given of drawing each diagram based on sample data. The document also discusses concepts like percentiles, quartiles, and deciles for dividing a data set and calculating measures like median and skewness from a cumulative frequency curve.
Math unit18 measure of variation
The document contains information about measures of variation and distributions, including:
1) A table showing the age distribution of Nigeria's population in 1991, with the lower quartile around 11 years, median around 24 years, and upper quartile around 40.5 years.
2) A table with test marks for 70 students, including constructing a cumulative frequency curve and determining that 28 students passed with a mark over 47.
3) Box and whisker plots are constructed to represent the goals scored in football matches by two teams, comparing their median, quartiles, and range.
4) Standard deviation is defined as a measure of spread from the mean, and the standard deviations of three data sets S1, S2,
Frequency distribution table
The document discusses frequency distribution tables and how to create them. It defines statistics, frequency distribution tables, and key terms like data, class, range, and class interval. It provides steps to create a frequency distribution table: 1) arrange data in ascending order, 2) find the range, 3) determine the number of classes, 4) form classes based on class interval, and 5) create a table with classes and frequencies. The document uses an example dataset to demonstrate how to apply these steps to create a frequency distribution table.
Measures of central tendency
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.
Raj
This document provides formulas and definitions for various statistical concepts including:
- Mean, median, mode, standard deviation, and correlation for individual, discrete, continuous, and combined data sets.
- Formulas for price indices like Laspeyre's, Paasche's, and Fisher's index.
- Formulas for regression analysis using the least squares method to find the regression coefficients for the line of best fit.
Statistics and probability
This Slide was made for my university presentation in "Statistics and probability" course.In this slide ,you will get short statistical calculation on Distance Between Present residence from Daffodil International University(Using to find the distance & take the shortest value of the possible distances).I think that's will help you by giving information about statistical calculation of Statistics and probability.
Presentation of Data
The document discusses different methods of presenting data:
1. Textual or descriptive presentation involves describing data within the text when quantities are small.
2. Tabular presentation arranges data in rows and columns for easy comparison.
3. Diagrammatic presentation uses visual diagrams like bar graphs, pie charts, and line graphs. Common types are histograms, frequency polygons, frequency curves and ogives. Diagrams effectively simplify and compare large data volumes.
Standard deviation and standard error
This document discusses standard deviation and related statistical concepts. It defines standard deviation as a measure of variability around the mean and explains how to calculate it from both ungrouped and grouped data. It also defines related terms like variance, standard error of the mean, and confidence limits of the mean. Standard deviation is calculated using the formula that sums the squared deviations from the mean, divided by n-1. Standard error is the standard deviation divided by the square root of the sample size, and confidence limits refer to ranges around the mean within which we can be certain the population mean falls.
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Frequency distribution of a continuous variable. in Biostatic
Frequency distribution of a continuous variable. in Biostatic
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The standard deviation is a measure of the spread of scores within a set of data. Usually, we are interested in the standard deviation of a population.
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This document discusses the calculation of arithmetic mean from data in various formats. It defines arithmetic mean as the sum of all values divided by the number of observations. It then provides examples of calculating the arithmetic mean using direct and shortcut methods for individual series, discrete series with frequencies, continuous series with class intervals, and series with open-ended classes. The different methods are demonstrated using example data sets. References on biostatistics are also included.
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The document discusses different methods to calculate the arithmetic mean of a data set: direct method, indirect method, and step-deviation method. The direct method calculates the mean as the sum of all values divided by the number of values. The indirect method uses an assumed mean and deviation from that mean. The step-deviation method also uses an assumed mean but calculates step-deviations as the difference from the mean divided by the class interval. Formulas for each method are provided along with examples of calculating the arithmetic mean for both ungrouped and grouped data sets using the different techniques.
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a. Simple Arithmetic Mean
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b) Shortcut Method
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This document provides an introduction and overview of the statistical concept of mode. It defines mode as the value with the highest frequency in a data set. It then discusses different methods for computing the mode of individual data series, discrete series, and grouped series. These include computing by inspection, making discrete/grouped series, and using the formula mode = 3(median) - 2(mean). The document notes advantages of mode include being easy to understand and not being affected by outliers. Disadvantages include mode sometimes being undefined or indeterminate and not using all data. Applications of mode include quick measurement and when data is categorical.
Introduction biostatistics
This document introduces common measures of central tendency (mean, median, mode) and variation (range, variance, standard deviation, coefficient of variation) in biostatistics. It defines each measure and provides examples of calculating and interpreting them. The mean is the most common measure of central tendency but the median is more robust to outliers. The choice of central tendency measure depends on whether the data is skewed. The mode is used for measuring popularity. Measures of variation quantify how spread out the data values are.
Measures of central tendency
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 defined as the sum of all values divided by the total number of observations. It can be calculated using direct or shortcut methods for discrete, continuous, and weighted data. The geometric and harmonic means are also defined. The median is the middle value when data is arranged in order. Formulas are provided for calculating the median from discrete and continuous distributions. Examples are included to demonstrate calculating each measure of central tendency.
To find mode docs
The document discusses the concept of mode in statistics. It defines mode as the value that occurs most frequently in a data set. It provides different methods to calculate the mode for individual data series, discrete series, and grouped series. These include inspection methods, making discrete series, using the mean and median formula, and grouping methods. The document also outlines some merits of using mode, such as being easily understood, as well as some demerits, such as it not being based on all observations. It concludes by discussing some uses of mode and providing a reference.
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Statistical formulas
- 1. Statistical Formulas Gaurav Sharma BUPIN: 17pba015 MBA 1st
- 2. Direct Method: Individual series: X̅ = 𝜮𝑿 𝑵 Discrete Series: X̅ = 𝜮𝒇𝑿 𝑵 Continuous Series: X̅ = 𝜮𝒇𝒎 𝑵 Short-cut Method: Individual Series: X̅ =A+ 𝜮𝒅 𝑵 Discrete Series: X̅ =A+ 𝜮𝒇𝒅 𝑵 Continuous Series: X̅ = A+ 𝜮𝒇𝒅 𝑵 Step-deviation Method: Discrete Series: X̅ = A+ 𝜮𝒇𝒅′ 𝑵 × i Continuous Series: X̅ = A+ 𝜮𝒇𝒅 𝑵 × i Here X̅ = Mean
- 3. Combined Mean: X̅ = 𝑵 𝟏X͞ 𝟏+𝑵 𝟐X͞ 𝟐 𝑵𝟏+𝑵𝟐 Weighted Mean: X̅ = ∑𝑾𝑿 ∑𝑾
- 4. Individual Series: Size of N+1/2th item Continuous Series: Size of N/2th item M= 𝑵 𝟐 −𝒄𝒇 𝒇 × i Here M=median
- 5. Individual Series: The value that has higher frequency in a frequency distribution. Continuous Series: Z= L1 + 𝒇𝟏−𝒇𝟎 𝟐𝒇𝟏−𝒇𝟎−𝒇𝟐 × i Empirical Node Z= 3M - 2X̅ Here Z=Mode
- 6. Individual Series: Q1 = 𝑁+1 4 Q3 = 3 𝑁+1 4 Q.D = 𝑄3−𝑄1 2 Continuous Series: QD = L1 + 𝑁 4 −𝑐𝑓 𝑓 × i Coeff. QD= 𝑄3−𝑄1 𝑄3+𝑄1
- 7. Individual Series: MD = Σ|d| N Discrete Series: MD = Σf|d| N Coefficient: Coeff. MD = MD M orX̅
- 8. Individual Series: Direct Method: σ= ΣX 2 𝑁 Short-cut Method: σ= 𝛴𝑑𝑥2 𝑁 − ( 𝛴𝑑𝑥 𝑁 )² Step- Deviation Method: σ = 𝛴𝑑𝑥2 𝑁 − ( 𝛴𝑑𝑥 𝑁 )²×𝑖 Descrete & Continuous Series: Short-Cut Method : σ= 𝛴𝑓𝑑𝑥² 𝑁 − ( 𝛴𝑓𝑑𝑥 𝑁 )² Step Deviation Method: σ= 𝛴𝑑𝑥′2 𝑁 − ( 𝛴𝑑𝑥′ 𝑁 )²×𝑖
- 9. Coefficient of SD: σ= = ϭ 𝑋 Coefficient of variation : C.Vd = σ 𝑋 ×100 Combined SD = 𝑵 𝟏ϭ 𝟏+𝑵 𝟐ϭ 𝟐+𝑵 𝟏 𝒅 𝟏+𝑵₂𝒅₂ 𝑵 𝟏+𝑵₂
- 10. Karl Pearson Skewness: SKp = X̅ −𝒁 σ Bowley’s Skewnes: SKb = 𝑸𝟑+𝑸𝟏−𝟐𝑴 𝑸𝟑−𝑸𝟏 Kelly’s Skewness: SKk = 𝒅𝟗+𝒅𝟏−𝟐𝑴 𝒅𝟗−𝒅𝟏
- 11. Simple Aggregative Method Simple Relative Method: Price method = Σp1 Σp0 ×100 Quantity Method = Σq1 Σq0 ×100 Price Relative Method: Price Method = Σ p1 p0 ×100 N Quantity Method = Σ q1 q0 ×100 N
- 12. Weighted Aggregative Method Lespeyer’s Method = Σp1q0 Σp0q0 ×100 Pashche’s Method = Σp1q1 Σp0q1 ×100 Fisher’s Method = Σp1q0 Σp0q0 × Σp1q1 Σp0q1 ×100 Dorbish & Bowley’s Method= Σp1q0 Σp0q0 + Σp1q1 Σp0q1 ×100 2 Marshell’s Method = Σp1q0+Σp1q1 p0q0+p0q1 ×100 Time Reversal Test : P01 X P10 = 1 Factor Reversal Test P01 XQ01 = ΣP1q1/ΣP0q0
- 13. Actual Mean: r= 𝛴𝑥𝑦 𝛴𝑥2.𝛴𝑦2 Assumed Mean: r= 𝑁.𝛴𝑑𝑥𝑑𝑦−𝛴𝑑𝑥.𝛴𝑑𝑦 𝑁𝛴𝑑𝑥²− 𝛴𝑑𝑥 2. 𝑁.𝛴𝑑𝑦²−(𝛴𝑑𝑦)²
- 14. 1.Y on X Y=a+ bX ΣY=Na+bΣx ΣXY=aΣX+bΣX² 2.X on Y X=a+ bY ΣX=Na+bΣY ΣXY=aΣY+bΣY² A-Least square method (using normal equation.) 1.Y on X Y-Y̅=byx(X- X̅) byx= 𝑁.𝛴𝑥𝑦−𝛴𝑥.𝛴𝑦 𝑁.𝛴𝑥²−(𝛴𝑥)² 2.X on Y X- X̅=bxy(Y-Y̅) bxy= 𝑁.𝛴𝑥𝑦−𝛴𝑦.𝛴𝑥 𝑁.𝛴𝑦²−(𝛴𝑦)² B-Equation using coefficient (Using Mean)
- 15. 1.Y on X Y-Y̅=byx(X-X̅) byx= 𝑁.𝛴𝑑𝑥𝑑𝑦−𝛴𝑑𝑥.𝛴𝑑𝑦 𝑁.𝛴𝑑𝑥²−(𝛴𝑑𝑥)² 2. X on Y X-X̅=bxy(Y-Y̅) bxy= 𝑁.𝛴𝑑𝑥𝑑𝑦−𝛴𝑑𝑦.𝛴𝑑𝑥 𝑁.𝛴𝑑𝑦²−(𝛴𝑑𝑦)² Assumed mean): Time series Least square method yс = a +bx if x =0 then a = ∑y 𝑁 b = ∑xy ∑x²