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,
(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.
(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
= 2.75th 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 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
= 4.75
b. Rice
Arranging the data of production of rice
12, 12, 12, 15, 18, 18, 22, 23, 29, 34
= 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
= 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
(iii) Mean Deviation about Mean
a. Wheat
|
Wheat Production x |
|
|
9 |
6 |
|
10 |
5 |
|
10 |
5 |
|
12 |
3 |
|
15 |
0 |
|
16 |
1 |
|
18 |
3 |
|
19 |
4 |
|
21 |
6 |
|
25 |
10 |
|
|
|
b. Rice
|
Rice Production x |
|
|
12 |
6 |
|
12 |
6 |
|
12 |
6 |
|
15 |
3 |
|
18 |
0 |
|
18 |
0 |
|
22 |
4 |
|
23 |
5 |
|
29 |
11 |
|
34 |
16 |
|
|
|
(iv) Mean Deviation about Median
a. Wheat
|
Production of Wheat x |
|
|
09 |
6 |
|
10 |
5 |
|
10 |
5 |
|
12 |
3 |
|
15 |
0 |
|
16 |
1 |
|
18 |
3 |
|
19 |
4 |
|
21 |
6 |
|
25 |
10 |
|
|
|
b. Rice
|
Production of rice |
d = X–18 |
|
12 |
6 |
|
12 |
6 |
|
12 |
6 |
|
15 |
3 |
|
|
0 |
|
18 |
0 |
|
22 |
4 |
|
23 |
5 |
|
29 |
11 |
|
34 |
16 |
|
|
|
Since n is even
(v) Standard Deviation
a. Wheat
|
Reduction of Wheat x |
Ax = 15 d= x – Ax |
d2 |
|
9 |
–6 |
36 |
|
10 |
–5 |
25 |
|
10 |
–5 |
25 |
|
12 |
–3 |
9 |
|
15 |
0 |
0 |
|
16 |
1 |
1 |
|
18 |
3 |
9 |
|
19 |
4 |
16 |
|
21 |
6 |
36 |
|
25 |
10 |
100 |
|
|
|
|
b. Rice
|
Production of rice x |
Ax = 18 d = x – A x |
d2 |
|
12 |
–6 |
36 |
|
12 |
–6 |
36 |
|
12 |
–6 |
36 |
|
15 |
–3 |
9 |
|
18 |
0 |
0 |
|
22 |
4 |
16 |
|
23 |
5 |
25 |
|
29 |
11 |
121 |
|
34 |
16 |
256 |
|
|
|
|
(vi) Coefficient of Variation
a. Wheat
b. Rice
(vi) Rice crop has greater variation as the coefficient of variation is higher for rice as compared to that of wheat.
(vii) Rice crop has higher Range, Quartile Deviation, Mean Deviation about mean, Mean Deviation about median, Standard Deviation and Coefficient of Variation.