Question

13. Calculate standard deviation, given the following data:
10, 12, 14, 16, 18, 22, 24, 26, 28
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Answer 1

Answer:

This is solution of this question

Answer 2

Standard deviation= 6.07

The standard deviation calculates the square root of the variance. It evaluates the distribution of a dataset according to its mean.

Given x values

10, 12, 14, 16, 18, 22, 24, 26, 28

To find:

Standard deviation

Formula, σ = $\sqrt{{\frac{\sum X^{2} }{n}}-(\frac{\sum X }{n})^{2}$

= 100, 144, 196, 256, 324, 484, 576, 676, 784

n = number of items = 9

Sum of X values = 170

Sum of values = 3540

Substituting in the formula,

σ = $\sqrt{{\frac{3540 }{9}}-{({\frac{170 }{9}})^{2}$

  = $\sqrt{{{393.33}-{(18.88)^{2}$

  = $\sqrt{{{393.33}-{356.45}$

  = $\sqrt{36.88}$

σ = 6.07