CBSE NCERT Class XI (11th)  Economics
Ncert Solutions of Statistics for Economics for Chapter 6 : Measures of Dispersion
Exercise : Solutions of Questions on Page Number
: 89
Q1 :
A measure of dispersion is a good supplement to the
central value in understanding a frequency distribution. Comment.
Answer :
The study of the averages is only one sided distribution
story. In order to understand the frequency distribution fully, it is essential
to study the variability of the observations. The average measures center of
the data whereas the quantum of the variation is measured by the measures of
dispersion like range, quartile deviation, mean deviation and Standard
Deviation. For example, if a country has very high income group people and very
low income group people, then we can say that the country has large income
disparity.
Q2 :
Which measure of dispersion is the best and how?
Answer :
Standard Deviation is the best measure of dispersion as it
satisfies the most essentials of the good measure of dispersion. The following
points make Standard Deviation the best measure of dispersion:
1. Most of the statistical theory is based on Standard
Deviation. It helps to make comparison between variability of two or more sets
of data. Also, Standard Deviation helps in testing the significance of random
samples and in regression and correlation analysis.
2. It is based on the values of all the observations. In
other words, Standard Deviation makes use of every item in a particular
distribution.
3. Standard Deviation has a precise value and is a
welldefined and definite measure of dispersion. That is, it is rigidly
defined.
4. It is independent of the origin.
5. It is widely used measure of dispersion as all data
distribution is nearer to the normal distribution.
6. It enables algebraic treatment. It has correct mathematical
processes in comparison to range, quartile deviation and mean deviation.
Q3 :
Some measures of dispersion depend upon the spread of
values whereas some are estimated on the basis of the variation of values from
a central value. Do you agree?
Answer :
Yes, it is true that some measures of dispersion depend upon
the spread of values, whereas some calculate the variation of values from the
central value. The spread of values is determined by the absolute measures of
dispersion like Range, Quartile Mean Deviation, and Standard Deviation. These
measures express dispersion in terms of original unit of the series and it
cannot be used for the comparison of statistical data having different units.
On the other hand, the relative measures of the dispersion calculate the
variability of the values from a central value. The relative measure includes
coefficient of Range, Mean Deviation and Variation. It is used when the
comparison has to be made between two statistical sets. These measures are free
from any units.
Q4 :
In a town, 25% of the persons earned more than Rs 45,000
whereas 75% earned more than 18,000. Calculate the absolute and relative values
of dispersion.
Answer :
Absolute Value of Dispersion
Relative Value of Dispersion
Q5 :
The yield of wheat and rice per acre for 10 districts of
a state is as under:
District

1

2

3

4

5

Answer :
(i) Range
a. Wheat
Highest value of distribution (H) = 25
Lowest value of distribution (L) = 9
Range = H  L
= 25
 9
=16
b. Rice
Highest value of distribution (H) = 34
Lowest value of distribution (L) = 12
Range = H  L
=34  12
= 22
(ii) Quartile Deviation
a. Wheat
Arranging the production of wheat in increasing order
9, 10, 10, 12, 15, 16, 18, 19, 21, 25
= 2.75^{th} item
=Size of 2th item + 0.75 (size of 3^{rd} item 
size of 2^{nd} item)
= 10 + 0.75 (10  10)
= 10 + 0.75 x 0
=10
= 8.25th
=Size of 8^{th} item + 0.25 (size of 9^{th} item
 size of 8^{th} item)
= 19 + 0.25 (21  19)
= 19 + 0.25 x 2
= 19 + 0.50 = 19.5
Q6 :
In the previous question, calculate the relative measures
of variation and indicate the value which, in your opinion, is more reliable.
Answer :
(i) Coefficient of Range
a) Wheat
b) Rice
(ii) Coefficient of Quartile Deviation
a) Wheat
b) Rice
Q_{1} = 12, Q_{3} =
24.5
(iii) Coefficient of Mean Deviation from mean
a) Wheat
b) Rice
(iv) Coefficient of Variation
a) Wheat
Q7 :
A 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
which are:
X

25

85

40

80

Answer :
Batsman X


X

X  = x
X  70

x^{2}


25

 45

2025


85

+ 15

225


 30

Q8 :
To check the quality of two brands of light bulbs, their
life in burning hours was estimated as under for 100 bulbs of each brand.
Life

No. of bulbs


(in hrs)

Answer :
For Brand A


Life
(in hours)

No. of bulbs

M

A = 125

d'^{2}

fd'

fd'^{2}


Q9 :
Average daily wage of 50 workers of a factory was Rs 200
with a Standard Deviation of Rs 40. Each worker is given a raise of Rs 20. What
is the new average daily wage and Standard Deviation? Have the wages become
more or less uniform?
Answer :
N = 50
= 200
s = 40
So, Total Wages = 200 x 50
= Rs 10,000
Now, increased wage rate = Rs 20
Total raise = 50 x 20 = Rs 1,000
Total Wage after raise = 10,000 + 1,000
=Rs 11,000
= Rs 220
Initial Standard Deviation = Rs 40
So, New Standard Deviation = Rs 40 + Rs 20
= Rs 60
Note: New Standard Deviation will rise by the
same amount as the wage of each worker has increased.
Q10 :
If in the previous question, each worker is given a hike
of 10% in wages, how are the Mean and Standard Deviation values affected?
Answer :
Average wage = Rs 200
Hike in wages = 10% of Rs 200
= Rs 20
Individual raise given to each worker = Rs 20
Total raise in wage = 50 x 20 = Rs 1,000
New Total Wage = Rs 10,000 + Rs 1000
= Rs 11,000
Initial Standard Deviation = Rs 40
So, New Standard Deviation = Rs 40 + 20
= Rs 60
Q11 :
Calculate the Mean Deviation using mean and Standard
Deviation for the following distribution.
Classes

Frequencies

20  40

3

40  80

Answer :
Classes

Frequency

m

A = 90
d = X  A

fd'

d'^{2}

fd'^{2}


20  40

3

30

Q12 :
The sum of 10 values is 100 and the sum of their squares
is 1090. Find out the Coefficient of Variation.
Answer :
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