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WhoKnows · Answer 1 · 2023-03-24T10:57:32+0000

The number of observations in the data is n = 10.

Determine the mean of the data.

$\begin{gathered} \mu=(514+508+502+497+495+507+458+477+464+515)/(10) \\ =(4937)/(10) \\ =493.7 \end{gathered}$

So mean of the data is 493.7.

Determine the sum of square difference between observation and mean.

$\begin{gathered} \sum ^n_(i\mathop=1)(x_i-\mu)^2=(514-493.7)^2+(508-493.7)^2+(502-493.7)^2+(497-493.7)^2 \\ +(495-493.7)^2+(507-493.7)^2+(458-493.7)^2+(477-493.7)^2+(464-493.7)^2+(515-493.7)^2 \end{gathered}$
=412.09+204.49+68.89+10.89+1.69+176.89+1274.49+278.89+882.09+453.69

=412.09+204.49+68.89+10.89+1.69+176.89+1274.49+278.89+882.09+453.69

The formula for the standard deviation is,

$\sigma=\sqrt[]{(\sum ^n_(i=1)(x_i-\mu)^2)/(n-1)}$

Substitute the value in the formula to determine the standard deviation of the data.

$\begin{gathered} \sigma=\sqrt[]{(3764.1)/(10-1)} \\ =\sqrt[]{(3764.1)/(9)} \\ =20.4507 \\ \approx20.45 \end{gathered}$

Answer:

Mean: 493.7

Standard deviation: 20.45

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