Question

Which answer is the approximate standard deviation of the data set?

(15, 19, 3, 12, 17, 2, 2, 8)
A. 6.5
B. 8.5
C. 4.3
D. 7.0

Answer 1

Answer: A. 6.5

Explanation:

Here, the given set = { 15, 19 3, 12, 17, 2, 2, 8}

Mean,
`\overline{ x} = (15+19+3+12+17+2+2+8)/(8) = (78)/(8) = 9.75`

Number of elements, n = 8

`\frac{\sum (|x-\overline{x}|)^2}{n}=42.4375`

Thus, the standard deviation,
`\sigma =\frac{\sqrt{\sum(|x-\overline{x}|)^2} }{n}=\sqrt{(339.5)/(8)}=√(42.4375) = 6.51440711\approx 6.5`

⇒ Option A is correct.