The following are the masses (in kg) of members in a club: 59, 44, 53, 49, 57, 40, 48, and 50. Calculate the variance of the distribution.
A
35
B
36
C
40
D
50
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Variance(s\(^2\)) = \(\frac{\sum{(x - \overline{x})^2}}{n}\)
But mean = 50 (from question 39 same information)
x
x - \(\overline{x}\)
(x - \(\overline{x})^2\)
59
9
81
44
- 6
36
53
3
9
57
7
49
49
- 1
1
40
-10
100
48
- 2
4
50
0
0
\(\sum{(x - \overline{x})^2}\) = 280
Variance(s\(^2\)) = \(\frac{\sum{(x - \overline{x})^2}}{n}\) = \(\frac{280}{8}\) = 35
Source: Myschool Past Questions Archive (Record #71845)