The yield of wheat per acre for 10 districts of a state is given below. Find the mean deviation and standard deviation.
District
1
2
3
4
5
6
7
8
9
10
Wheat
12
10
15
19
21
16
18
9
25
10
Answers
Explanation:
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The value of range is 16 and the value of mean is 4.3
Explanation:
Question statement:
Calculate for each crop,
(i) Range
(ii) Q.D.
(iii) Mean Deviation about Mean
Solution:
The formula of range:
Range (R ) = H - L
Out the value of H and L.
- H = 25, L = 9
- R = 25 - 9 = 16
(ii) Q1 = Size of (N + 1 / 4) th item
= Size of (10+1 / 4)th item
= Size of 2.75th item
= Size of 2nd item + 3 / 4 (Size of 3rd item − Size of 2nd item)
= 10 + 3 / 4 (10 − 10) = 10 + 0 = 10
Q3 = Size of 3(N + 1 / 4)th item
= Size of 3 (10 + 1 / 4) th item = Size of 8.25th item
= Size of 8th item + 1 / 4 (Size of 9th item − Size of 8th item)
= 19 + 1 / 4 (21 − 19) = 19 + 2 / 4 = 19.5
Quartile Deviation = Q3 − Q1 / 2 = 19.5 − 10 / 2 = 9.52 = 4.75
(iii) Mean (X¯) = ∑X / N = 155 / 10 = 15.5
Mean Deviation from Mean (MDX¯) = ∑|dx| / N = 43 / 10 = 4.3