Find the standard deviation of the numbers 6, 9, 10, 8 and 7
A
1.4
B
2
C
2.4
D
5
E
8
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
6, 9, 10, 8 and 7
S.D = \(\sqrt{V}\)
S.D = standard deviation, V = variance
V = \(\frac{\sum({x - \overline{x})^2}}{n}\)
Mean(\(\overline{x}\)) = \(\frac{6 + 9 + 10 + 8 + 7}{5}\) = 8
x
x - \(\overline{x}\)
(x - \(\overline{x}\))\(^2\)
6
6 - 8 = -2
4
9
9 - 8 = 1
1
10
10 - 8 = 2
4
8
8 - 8 = 0
0
7
7 - 8 = -1
1
TOTAL = 10
V = \(\frac{\sum({x - \overline{x})^2}}{n}\) = \(\frac{10}{5}\) = 2
S.D = \(\sqrt{V}\) = \(\sqrt{2}\) = 1.414 ≈ 1.4
Source: Myschool Past Questions Archive (Record #42451)