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NCERT Solution for Class 11 Commerce Statistics for Economics Chapter 6 - Measures of Dispersion

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NCERT Solution for Class 11 Commerce Statistics for Economics Chapter 6 - Measures of Dispersion Page/Excercise 89

Solution 1

Averages give an idea about the representative value of the series around which other items of the series tend to approach. They do not tell us about the variability of the data. To measure the variation of data, measures of dispersion such as range, quartile deviation, mean deviation and standard deviation are calculated. Thus, both averages and measures of dispersion help in understanding the frequency distribution holistically.

Solution 2

Standard deviation is the best measure of dispersion because

  1. Comprehensive measure: It is based on all the items of a series and does not ignore any item of the series.
  2. Unaffected by change in sample: Because the standard deviation is based on all the values, a change in sample has little effect on it.
  3. Easy comparison: It helps in comparing variability among two or more data sets.
  4. Independent of origin: A change of origin does not affect the standard deviation.
  5. Algebraic treatment: It is capable of further algebraic treatment as it does not ignore the signs of deviations in its calculation. 

Solution 3

Yes, I agree that some measures of dispersion depend on the spread of values, whereas some calculate the variation of values from the central value. The measures of dispersion which depend on the spread of values are called absolute measures. These are range, quartile deviation, inter-quartile range, mean deviation, standard deviation and Lorenz curve. These measures show dispersion in the original unit of the series. Thus, such measures cannot be used when comparison is between two or more data sets having different units.

Variation of values from a central value is calculated by relative measures. The relative measures are coefficient of range, coefficient of quartile deviation, coefficient of mean deviation, coefficient of standard deviation and coefficient of variation. Such measures do not have any units. Thus, these are used to compare between two or more data sets.

Solution 4

 

  

Solution 5(i)

  1. Range of Wheat:

Highest value (H) = 25

Lowest value (L) = 9

Range = H - L

Range = 25 - 9

Thus, Range =16

 

  1. Range of Rice:

Highest value (H)= 34

Lowest value (L) = 12

Range = H - L

Range = 34 -12

Thus, Range = 22 

Solution 5(ii)

  1. Q.D. of Wheat:

  1. Q.D of Rice:

  

Solution 5(iii)

  1. MD about mean of wheat:

  1. MD about mean of rice:

  

Solution 5(iv)

  1. MD about median of wheat:

  1. MD about median of rice:

  

NCERT Solution for Class 11 Commerce Statistics for Economics Chapter 6 - Measures of Dispersion Page/Excercise 90

Solution 5(v)

  1. SD of wheat:

  1. SD of rice:

  

Solution 5(vi)

  1. Coefficient of variation of wheat:

  1. Coefficient of variation of Rice:

  

Rice has greater variation because the coefficient of variation for rice is greater than that of wheat.

Solution 5(vii)

Basis

Wheat

Rice

Range

16

22

QD

4.75

6.75

MD about Mean

4.3

6

MD about Median

4.3

5.7

SD

5.04

7.16

CV

32.51

36.71

Solution 6

  1. Coefficient of range of wheat:

  1. Coefficient of QD of wheat:

  

  1. Coefficient of MD of wheat:

  

Solution 7

Batsman X

Batsman Y

  1. If we want a higher run getter, then Batsman X should be selected as the average of Batsman X is more than that of Batsman Y.
  2. If we want a more reliable batsman in the team, then Batsman Y should be chosen as the coefficient of variation of Batsman Y is less than that of Batsman X. 

Solution 8

For Brand A:

  

For Brand B:

 

  

  1. Brand B gives higher life as the average life of Brand B light bulbs is more than that of Brand A light bulbs.
  2. Brand B is more dependable as the coefficient of variation of Brand B is less than that of Brand A. 

Solution 9

Given:

Standard deviation will not change as the given case is of change of origin, and change of origin does not affect standard deviation. Hence, wages show the same uniformity.

Solution 10

Given:

  

Solution 11

Solution 12

  

Text Book Solutions

CBSE XI Commerce - Statistics for Economics

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