Advertisements
Advertisements
प्रश्न
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.
उत्तर
a. Wheat
Arranging the production of wheat in increasing order
9, 10, 10, 12, 15, 16, 18, 19, 21, 25
`Q_1 = (N + 1)/4`th item
= `(10 + 1)/4`th item
= `11/4`th item
= 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
`Q_3 = (3(N + 1))/4`th item
= `(3(10 + 1))/4`th item
= `33/4`th item
= 8.25th
= Size of 8th item + 0.25 (size of 9th item - size of 8th item)
= 19 + 0.25 (21 - 19)
= 19 + 0.25 × 2
= 19 + 0.50 = 19.50
Quartile Deviation = `(Q_3 - Q_1)/2`
= `(19.50 - 10)/2`
= `9.50/2`
= 4.75
b. Rice
Arranging the data of production of rice
12, 12, 12, 15, 18, 18, 22, 23, 29, 34
`Q_1 = (N + 1)/4`th item
= `((10 + 1)/4)`th item
= 2.75th item
= size of 2nd item + 0.75 (size of 3rd item - size of 2nd item)
= 12 + 0 .75 (12 - 12)
= 12 + 0.75 × 0
= 12
`Q_3 = (3(N + 1))/4`th item
= `(3(10 + 1))/4`th item
= `33/4`th item
= 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
Quartile Deviation = `(Q_3 - Q_1)/2`
= `(24.5 - 12)/2`
= `12.50/2`
= 6.25
APPEARS IN
संबंधित प्रश्न
A measure of dispersion is a good supplement to the central value in understanding a frequency distribution. Comment.
Which measure of dispersion is the best and how?
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?
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,
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 |
