Question

The weights (in pounds) of three adult males are$160$,$215$and$195$. What is the standard error of the mean for these data?

a. $190$

b. $27.84$

c. $22.73$

d. $16.07$

e.$13.13$

Short answer

The standard error of the mean is$16.07$

Step-by-step solution

Given information

The weights of $3$males are$160,195,215$

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 sample standard deviation can be calculated using the following formula:

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

The objective is to find out the standard error of the mean for the provided data set

The mean can be calculated as follows:

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

The standard deviation can be calculated as follows:

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

The standard error of the mean can now be calculated as follows:

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

The standard error of the mean is $16.07$

Therefore, the correct option is$\left(d\right)$