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 values of the different measures for each crop.
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Start your 14-day free trial to unlock the full solution →Wheat: Range 16, Q.D. 4.75, M.D.(mean) 4.3, M.D.(median) 4.3, S.D. 5.04. Rice: Range 22, Q.D. 6.25, M.D.(mean) 6.0, M.D.(median) 5.7, S.D. 7.16. Rice varies more.
WHEAT — sorted: 9, 10, 10, 12, 15, 16, 18, 19, 21, 25 (n = 10, sum = 155, mean = 15.5, median = (15+16)/2 = 15.5).
- (i) Range .
- (ii) Q.D. — is the value ; is the value . .
- (iii) M.D. about mean (15.5) — ; .
- (iv) M.D. about median (15.5) — the median equals the mean here, so .
- (v) S.D. — ; .
RICE — sorted: 12, 12, 12, 15, 18, 18, 22, 23, 29, 34 (n = 10, sum = 195, mean = 19.5, median = (18+18)/2 = 18).
- (i) Range .
- (ii) Q.D. — is the 2.75th value ; is the 8.25th value . .
- (iii) M.D. about mean (19.5) — ; .
- (iv) M.D. about median (18) — ; .
- (v) S.D. — ; . …
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