Measures of Dispersion
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This document discusses quantitative techniques as part of a B.Com program. It covers measures of central tendency and dispersion, including the mean, median, mode, range, mean deviation, and standard deviation. The learning objectives are to understand different measures of central tendency and dispersion. The learning outcomes are to differentiate, determine, and identify relationships between averages, and apply measures of dispersion to data by comparing standard deviation to mean deviation. The document also provides examples and practice questions on these topics.
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This document outlines the key topics and objectives of a Quantitative Techniques course for a B.Com program. The learning objectives are to understand measures of central tendency and dispersion such as mean, median, mode, range, mean deviation, standard deviation, and quartile deviation. Example problems are provided to calculate range, quartile deviation, and the coefficient of quartile deviation from wage distribution data. Multiple choice questions are also included as a review of the concepts taught.
graphical representation 1
This document discusses graphical representation of quantitative data. It explains that graphs are better suited than diagrams for statistical analysis as they allow interpolation, extrapolation and locating values like the median and quartiles. Diagrams are only for comparison. The document then contrasts key differences between diagrams and graphs. Finally, it provides general rules for creating graphs and examples of questions to test comprehension.
KPC skewness 2
This document discusses Karl Pearson's Coefficient of Skewness. It provides the formula for Karl Pearson's Coefficient of Skewness as SK= Mean - Mode/ S.D. An example calculation is shown to demonstrate computing the coefficient from sample data. Multiple choice questions are also provided to test understanding. The learning objectives are to understand measures of skewness including Karl Pearson's Coefficient of Skewness and how to apply it to sample data to analyze the normalcy and skewness of distributions.
graphical representation 4
This document discusses constructing cumulative frequency (ogive) curves from data. It begins by recapping how to create histograms, frequency polygons, and pie charts. Then it provides learning objectives and outcomes around analyzing and presenting data graphically using these visualizations. The main content explains how to calculate less than and more than cumulative frequencies and draw the corresponding ogive curves. It gives examples of drawing less than ogive curves for two data sets listing number of workers by daily wage and number of pensioners by age group. Finally, it presents multiple choice questions to test understanding of ogive curves.
graphical representation 5
This document discusses cumulative frequency curves or ogives. It provides examples of how to construct more than ogive curves using data from frequency distributions. Specifically, it discusses how the more than cumulative frequency is plotted against the lower limit of each class to form the curve. Two example problems are worked through demonstrating how to draw the more than ogive curve from data on test marks and pensioner ages. Multiple choice questions are also provided to assess understanding of key concepts like the different types of ogive curves and how cumulative frequency polygons are used.
graphical representation 2
The document discusses different methods of graphically representing frequency distributions: histograms, frequency polygons, and frequency curves. It provides examples of how to construct each type of graph using sample data on times taken to travel to school, net worth over years, and ages of pensioners. Students will learn how to analyze and interpret these graphs as well as how to present data using histograms, frequency polygons, frequency curves, and pie charts. The document concludes with sample multiple choice questions to test comprehension.
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Measures of Dispersion
- 1. PROGRAMME B.COM SUBJECT QUANTITATIVE TECHNIQUE – I SEMESTER III UNIVERSITY VIJAYANAGAR SRI KRISHNADEVARAYA UNIVERSITY, BALLARI SESSION 41
- 2. RECAP • Merits & Demerits of Mean, Median and Mode
- 3. LEARNING OBJECTIVES • After reading this chapter, a student will be understand different measures of central tendency and Dispersion, i.e., Arithmetic Mean,Mean,Mode, Geometric and Harmonic mean & Range, Mean Deviation, Standard Deviation, Quartile Deviation, Co efficient of variation
- 4. LEARNING OUTCOMES • After the Chapter, The Students Shall be able to Differentiate, Determine, and Identify the relationships among Averages under Different Series of Data and too State the Merits and Demerits of Three Measures. The Students will apply Measures of Dispersion to Sample Population Data by Contrasting the Values of Standard Deviation & The Mean Deviation, Synthesizing the Mean,Standard,and Quartile Deviations into a Useful Description of a Set of Data
- 5. SESSION - 41 • Measures of Dispersion, Meaning, Definition, Concept, Purposes and Methods
- 6. Meaning and Concept of dispersion Dispersion is the extent to which values in a distribution differ from the average of the distribution. Or dispersion helps to understand the distribution of the data. Concept A measure of dispersion indicates the scattering of data. It explains the disparity of data from one another, delivering a precise view of their distribution. The measure of dispersion displays and gives us an idea about the variation and the central value of an individual item
- 7. Definition and Purposes of Dispersion MEANING A.L Bowley defines dispersion is the measure of the variation of the items. Purposes of Dispersion (1) Comparative study (2) Reliability of an average (3) Control the variability (4) Basis for further statistical analysis
- 8. Types of Dispersion I. Absolute Measure of Dispersion • Range • Quartile deviation • Standard deviation • Mean deviation II. Relative Measure of Dispersion • Co-efficient of Range • Co-efficient of Variation • Co-efficient of Standard Deviation • Co-efficient of Quartile Deviation • Co-efficient of Mean Deviation
- 9. MCQs I. The scatter in a series of values about the average is called: (a) Central tendency (b) Dispersion (c) Skewness (d) Symmetry II. The measurements of spread or scatter of the individual values around the central point is called: (a) Measures of dispersion (b) Measures of central tendency (c) Measures of skewness (d) Measures of kurtosis
- 10. MCQs III. The measures used to calculate the variation present among the observations in the unit of the variable is called: (a) Relative measures of dispersion (b) Coefficient of skewness (c) Absolute measures of dispersion (d) Coefficient of variation IV. The degree to which numerical data tend to spread about an average value called: (a) Constant (b) Flatness (c) Variation (d) Skewness
- 11. MCQs V. The measures used to calculate the variation present among the observations relative to their average is called: (a) Coefficient of kurtosis (b) Absolute measures of dispersion (c) Quartile deviation (d) Relative measures of dispersion
- 12. CONTD ANSWERS I. B II. A III. C IV. C V. D
- 13. REFERENCES • S.P. Gupta, Sultan Chand and Sons Publications, 2017 • S. C. Gupta, Himalaya Publishing House, Fundamentals of Statistics, 2018 • R.S.N Pillai and Bagavathi, S.Chand publications, 2010
- 14. THANK YOU