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Question
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?
Solution
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 the original unit of the series and they 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 a 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.
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A measure of dispersion is a good supplement to the central value in understanding a frequency distribution. Comment.
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If in the previous question, each worker is given a hike of 10 % in wages, how are the mean and standard deviation values affected?
The 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 are the new average daily wage and standard deviation? Have the wages become more or less uniform?
The 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 |
| Wheat |
12 |
10 |
15 |
19 |
21 |
16 |
18 |
9 |
25 |
10 |
| Rice |
22 |
29 |
12 |
23 |
18 |
15 |
12 |
34 |
18 |
12 |
Calculate for each crop,
Range
The 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 |
| Wheat |
12 |
10 |
15 |
19 |
21 |
16 |
18 |
9 |
25 |
10 |
| Rice |
22 |
29 |
12 |
23 |
18 |
15 |
12 |
34 |
18 |
12 |
Calculate for each crop,
Compare the values of different measures for each crop.
The 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 |
| Wheat |
12 |
10 |
15 |
19 |
21 |
16 |
18 |
9 |
25 |
10 |
| Rice |
22 |
29 |
12 |
23 |
18 |
15 |
12 |
34 |
18 |
12 |
Calculate for each crop,
Q.D.
The 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 |
| Wheat |
12 |
10 |
15 |
19 |
21 |
16 |
18 |
9 |
25 |
10 |
| Rice |
22 |
29 |
12 |
23 |
18 |
15 |
12 |
34 |
18 |
12 |
Calculate for each crop,
Mean deviation about Mean
The 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 |
| Wheat |
12 |
10 |
15 |
19 |
21 |
16 |
18 |
9 |
25 |
10 |
| Rice |
22 |
29 |
12 |
23 |
18 |
15 |
12 |
34 |
18 |
12 |
Calculate for each crop,
Mean deviation about Median
The 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 |
| Wheat |
12 |
10 |
15 |
19 |
21 |
16 |
18 |
9 |
25 |
10 |
| Rice |
22 |
29 |
12 |
23 |
18 |
15 |
12 |
34 |
18 |
12 |
Calculate for each crop,
Standard deviation
Calculate the mean deviation using mean and Standard Deviation for the following distribution.
|
Classes |
Frequencies |
|
20 - 40 |
3 |
|
40 - 80 |
6 |
|
80 - 100 |
20 |
|
100 - 120 |
12 |
|
120 - 140 |
9 |
|
|
50 |
