Question

Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data. 22.6 16.1 36.1 36.0 23.8 20.3

Answer 1

8.35

Explanation:

Mean=(22.6+16.1+36.1+36+23.8+20.3)/6

Mean=25.82

Subtract the mean from each data point and add their squared values

∑(x-mean)²

=(22.6-25.82)²+(16.1-25.82)²+(36.1-25.82)²+(36-25.82)²+(23.8-25.82)²+(20.3-25.82)²

=348.71

N = Number of observations = 6

`Standard\ Deviation=\sqrt{(\sum _(i=1)^(N)(x_i-mean))/(N-1)}`

∴ Standard deviation=√(348.71/6-1)

∴ Standard deviation=8.35