The following values are the starting salaries, in $000,

Step 1 of 3

a) We have to find mean, median and standard deviation for the given data

The given data is 36, 26, 33, 28, 31

Arrange the values in the ascending order 26, 28, 31, 33, 36

Here n = no.of value = 5

Mean 

\(\begin{array}{l}
\bar{X}=\Sigma X / n \\
=(26+28+31+33+36) / 5 \\
\quad=30.8
\end{array}\)

Median 

\(\begin{aligned}
(M) & =\left(\frac{n+1}{2}\right)^{\text {th }} \text { Value } \\
& =\left(\frac{5+1}{2}\right)^{\text {th }} \text { Value } \\
& =3^{\text {rd }} \text { Value } \\
& =31
\end{aligned}\)

Standard deviation 

\(\begin{aligned}
(s) & =\sqrt{\frac{\sum(X-\bar{X})^{2}}{n-1}} \\
& =\sqrt{\frac{(26-30.8)^{2}+(28-30.8)^{2}+(31-30.8)^{2}+(33-30.8)^{2}+(36-30.8)^{2}}{5-1}} \\
& =\sqrt{\frac{23.04+7.84+0.04+4.84+27.04}{4}} \\
& =\sqrt{15.7} \\
& =3.96
\end{aligned}\)

Hence Mean = 30.8

Median = 31

standard deviation =3.96