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Find the standard deviation of 2, 5, 9, 2, 7 (correct to 2 decimal places)


Question

Find the standard deviation of 2, 5, 9, 2, 7 (correct to 2 decimal places)

Options

A) 5.80

B) 3.41

C) 2.76

D) 1.80

The correct answer is C.

Explanation:

\((\bar{x}) = \cfrac{2 + 5 + 9 + 2 + 7}{5} = \cfrac{25}{5}\)
Variance = \(\sum \cfrac{(x - \bar{x})^2}{N}\)
\(= \cfrac{(2-5)^2 + (5-5)^2 + (9-5)^2 + (2-5)^2 + (7-5)}{5}\)
\(= \cfrac{9 + 0 + 16 + 9 + 4}{5} = \cfrac{38}{5} = 7.6\)
\(\text{Standard deviation} = \sqrt{\text{Variance}}\)
Variance is referred to as the mean-squared deviation, while standard deviation is the the root mean-squared deviation.
\(= \sqrt{7.6} = 2.76\) (to 2 d.p)

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Dicussion (1)

  • \((\bar{x}) = \cfrac{2 + 5 + 9 + 2 + 7}{5} = \cfrac{25}{5}\)
    Variance = \(\sum \cfrac{(x - \bar{x})^2}{N}\)
    \(= \cfrac{(2-5)^2 + (5-5)^2 + (9-5)^2 + (2-5)^2 + (7-5)}{5}\)
    \(= \cfrac{9 + 0 + 16 + 9 + 4}{5} = \cfrac{38}{5} = 7.6\)
    \(\text{Standard deviation} = \sqrt{\text{Variance}}\)
    Variance is referred to as the mean-squared deviation, while standard deviation is the the root mean-squared deviation.
    \(= \sqrt{7.6} = 2.76\) (to 2 d.p)

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