Chapter 8, Problem T8.2SPT

To determine

To find: The standard error of the mean for the provided data set.

Answer to Problem T8.2SPT

The standard error of the mean is 16.07

Explanation of Solution

Given:

The weights of 3 males are 160, 195 and 215.

Formula used:

The formula to compute the standard error of mean is:

  $S{E}_{\overline{x}}=\frac{s}{\sqrt{n}}$

Where,

s is the sample standard deviation

The formula to compute the sample standard deviation is:

  $s=\sqrt{\frac{{\displaystyle \sum {\left(x-\overline{x}\right)}^2}}{n-1}}$

Calculation:

Here, mean can be calculated as:

  $\begin{array}{c}\overline{x}=\frac{160+215+195}{3}\\ =190\end{array}$

Standard deviation can be calculated as:

  $\begin{array}{c}s=\sqrt{\frac{{\left(160-190\right)}^2+{\left(215-190\right)}^2+{\left(195-190\right)}^{}}{3}}\\ =27.839\end{array}$

Now, the standard error of the mean can be calculated as:

  $\begin{array}{c}S{E}_{\overline{x}}=\frac{s}{\sqrt{n}}\\ =\frac{27.839}{\sqrt{3}}\\ =16.07\end{array}$

The standard error of the mean is 16.07.

Hence, the correct option is (d).