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Marcus Estes · Answer 1 · 2023-03-28T08:07:35+0000

The formula to calculate the standard deviation is:

$s=\sqrt[]{\frac{\sum ^n_(i\mathop=1)(x_i-\bar{x})^2}{n-1}}$

first, calculate the mean of the data sample

$\begin{gathered} \bar{x}=(19.83+20.14+19.28+19.75+19.39+19.86+19.02+19.71)/(8) \\ \bar{x}=19.6225 \end{gathered}$

then, apply the standard deviation formula

$\begin{gathered} s=\sqrt[]{((19.83-19.6225)^2+(20.14-19.6225)^2+(19.28-19.6225)^2+(19.75-19.6225)^2+(19.39-19.6225)^2+(19.86-19.6225)^2+(19.02-19.6225)^2+(19.71-19.6225)^2)/(7)} \\ \end{gathered}$
$s\approx0.36262$

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