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Find the standard deviation of the numbers 6, 9, 10, 8 and 7

Mathematics
NECO 2005

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
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Correct Answer: Option A
Explanation

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

 


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