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Economics · Class 11 Commerce

Ch 16Measures of Dispersion — Class 11 Economics, concept-first.

In the previous chapter of the NCERT Class 11 Statistics for Economics course you studied how to sum up a whole set of data into a single representative value — a measure of central tendency such as the mean, median or mode.

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Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

Introduction

In the previous chapter of the NCERT Class 11 Statistics for Economics course you studied how to sum up a whole set of data into a single representative value — a measure of central tendency such as t…

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Measures Based Upon Spread of Values

The first two measures of dispersion — range and quartile deviation — describe dispersion by measuring the spread within which the values of a distribution lie.

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Measures of Dispersion from Average

Dispersion was defined as the extent to which values differ from their average. Range and quartile deviation, though useful, measure only the spread of values and do not directly measure how far the v…

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Absolute and Relative Measures of Dispersion

All the measures described so far — range, quartile deviation, mean deviation and standard deviation — are absolute measures of dispersion.

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Lorenz Curve

All the measures discussed so far give a numerical value of dispersion. The Lorenz Curve is a graphical measure, used especially for estimating inequalities in a distribution — most familiarly, income…

Key Concepts

The key concepts and terms of this chapter, with brief explanations, are:

Summary

- A measure of dispersion improves our understanding of the behaviour of an economic variable, because an average by itself hides the variability in the data.

Worked Examples

Solved examples, worked out step by step.

+Show 14 questions14 questions
  1. Example 1Calculate the range and quartile deviation (Q.D.) of the following observations: 20, 25, 29, 30, 35, 39, 41, 48, 51, 60 and 70.Free
  2. Example 2For the following distribution of marks scored by a class of 40 students, calculate the range and quartile deviation (Q.D.). | Class interva…Free
  3. Example 3Calculate the mean deviation (from the mean) of the following values: 2, 4, 7, 8 and 9.Free
  4. Example 5Using the values 2, 4, 7, 8 and 9, calculate the mean deviation from the median.Preview
  5. Example 6Calculate the mean deviation from the mean for the following distribution of the profits of companies. | Profits (₹ lakh) | 10–20 | 20–30 |…Preview
  6. Example 7Calculate the mean deviation from the median for the following distribution. | Class interval | 20–30 | 30–40 | 40–60 | 60–80 | 80–90 | | --…Preview
  7. Example 8Calculate the standard deviation of the values 5, 10, 25, 30 and 50 by the actual mean method.Preview
  8. Example 9Calculate the standard deviation of the values 5, 10, 25, 30 and 50 by the assumed mean method, taking the assumed mean as 25.Preview
  9. Example 10Calculate the standard deviation of the values 5, 10, 25, 30 and 50 by the direct method.Preview
  10. Example 11Calculate the standard deviation of the values 5, 10, 25, 30 and 50 by the step-deviation method, dividing the values by the common factor 5…Preview
  11. Example 12Calculate the standard deviation of the values 5, 10, 25, 30 and 50 by the step-deviation method, taking deviations from the arbitrary value…Preview
  12. Example 13Calculate the standard deviation for the following continuous distribution by the actual mean method. | Class interval | 10–20 | 20–30 | 30–…Preview
  13. Example 14For the same continuous distribution (Example 13), calculate the standard deviation by the assumed mean method, taking the assumed mean as 4…Preview
  14. Example 15For the same continuous distribution (Example 13), calculate the standard deviation by the step-deviation method, taking deviations from 40…Preview

Exercises

+Show 12 questions12 questions
  1. Q1A measure of dispersion is a good supplement to the central value in understanding a frequency distribution. Comment.Free
  2. Q2Which measure of dispersion is the best and how?Free
  3. Q3Some measures of dispersion depend upon the spread of values whereas some are estimated on the basis of the variation of values from a centr…Free
  4. Q4In a town, 25% of the persons earned more than ₹45,000 whereas 75% earned more than ₹18,000. Calculate the absolute and relative values of d…Preview
  5. Q5The yield of wheat and rice per acre for 10 districts of a state is as under: | District | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | | --- |…Preview
  6. Q6In the previous question, calculate the relative measures of variation and indicate the value which, in your opinion, is more reliable.Preview
  7. Q7A batsman is to be selected for a cricket team. The choice is between X and Y on the basis of their scores in five previous tests: | | | | |…Preview
  8. Q8To check the quality of two brands of light bulbs, their life in burning hours was estimated for 100 bulbs of each brand: | Life (in hrs) |…Preview
  9. Q9The average daily wage of 50 workers of a factory was ₹200 with a standard deviation of ₹40. Each worker is given a raise of ₹20. What is th…Preview
  10. Q10If, in the previous question, each worker is given a hike of 10% in wages, how are the mean and standard deviation values affected?Preview
  11. Q11Calculate the mean deviation (about the mean) and the standard deviation for the following distribution. | Classes | 20–40 | 40–80 | 80–100…Preview
  12. Q12The sum of 10 values is 100 and the sum of their squares is 1090. Find out the coefficient of variation.Preview