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Calculate var...

Question

Calculate variance and standard deviation of the following data :
10, 12, 8, 14, 16

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Solution

$A M = ¯ ¯ ¯ x = \frac{10 + 12 + 8 + 14 + 16}{5} = \frac{60}{5} = 12$

$V a r i a n c e = \frac{(10 - 12)^{2} + (12 - 12)^{2} + (8 - 12)^{2} + (14 - 12)^{2} + (16 - 12)^{2}}{5}$

$= \frac{4 + 0 + 16 + 4 + 16}{5} = \frac{40}{5} = 8$

$S D (σ) = \sqrt{V a r i a n c e} = \sqrt{8}$

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