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Question

Mathematics Question on Variance and Standard Deviation

The standard deviation of the data 6,7,8,9,106, 7, 8, 9, 10 is

A

2\sqrt{2}

B

10\sqrt{10}

C

2

D

10

Answer

2\sqrt{2}

Explanation

Solution

Mean, xˉ=6+7+8+9+105=405=8\bar{x} = \frac{6+7+8+9+10}{5} = \frac{40}{5} = 8 Standard deviation, σ=15(4+1+0+1+4)\sigma = \sqrt{\frac{1}{5}(4+1+0+1+4)} Because, σ=1n∑(xi−xˉ)2\sigma = \sqrt{\frac{1}{n} \sum(x_i - \bar{x})^2} ⇒σ=105=2\Rightarrow \sigma = \sqrt{\frac{10}{5}} = \sqrt{2}