The document NCERT Solutions - Measures of Dispersion Commerce Notes | EduRev is a part of the Commerce Course Economics Class 11.

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**Page No 89:**

**Question 1: 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.**Question 2: 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 well-defined 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.**Question 3: Some measures of dispersion depend upon the spread of values whereas some calculate 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.**Question 4: 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****Question 5: The yield of wheat and rice per acre for 10 districts of a state is as under:****Calculate for each crop,(i) Range(ii) Q.D.(iii) Mean Deviation about Mean(iv) Mean Deviation about Median(v) Standard Deviation(vi) Which crop has greater variation?(vii) Compare the value of different measures for each crop.**

Highest value of distribution (H) = 25

Lowest value of distribution (L) = 9

Range = H – L

= 25 – 9

=16

Highest value of distribution (H) = 34

Lowest value of distribution (L) = 12

Range = H – L

=34 – 12

= 22

Arranging the production of wheat in increasing order

9, 10, 10, 12, 15, 16, 18, 19, 21, 25

= 2.75th item

=Size of 2th item + 0.75 (size of 3rd item – size of 2nd item)

= 10 + 0.75 (10 – 10)

= 10 + 0.75 × 0

=10

= 8.25th

=Size of 8

= 19 + 0.25 (21 – 19)

= 19 + 0.25 × 2

= 19 + 0.50 = 19.50

= 4.75

Arranging the data of production of rice

12, 12, 12, 15, 18, 18, 22, 23, 29, 34

= 2.75th item

= size of 2

= 12 + 0 .75 (12 – 12)

= 12 + 0.75 × 0

= 12

= 8.25th item

= Size of 8th item + 0.25 (size of 9th item – size of 8th item)

= 23 + 0.25 (29 – 23)

= 23 + 0.25 × 6

= 23 + 1.5

= 24.5

= 6.25

b.

Since

Q1 = 12, Q3 = 24.5

The coefficient of variation is more reliable than all other measures.

(i) a higher run getter, or

(ii) a more reliable batsman in the team?

(i) Average of Batsman X is higher than that of Batsman Y, so he should be selected if we want to score higher run.

(ii) The Batsman X is more reliable than Batsman Y. This is because the coefficient of variation of Batsman X is higher than that of Batsman Y.

**Page No 90:**

**Question 8: 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.****(i) Which brand gives higher life?(ii) Which brand is more dependable?Answer:**

(i) The average life of bulb of Brand B has comparatively higher life than the bulb of Brand A.

(ii) The bulbs of Brand B is more dependable as CV of Brand B is lesser than CV of Brand A.

Answer:

N = 50

= 200

σ = 40

So, Total Wages = 200 × 50

= Rs 10,000

Now, increased wage rate = Rs 20

Total raise = 50 × 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

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 × 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

Answer:

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