In Exercises 21–24, find the mean and median for each of the two samples, then compare

the two sets of results.

Pulse Rates Listed below are pulse rates (beats per minute) from samples of adult males and females (from Data Set 1 “Body Data”in Appendix B). Does there appear to be a difference?

Male: 86 72 64 72 72 54 66 56 80 72 64 64 96 58 66

Female: 64 84 82 70 74 86 90 88 90 90 94 68 90 82 80

The pulse rates recorded for adult males and females were as follows:

The formula for the mean value is:

$\overline{x}=\frac{\sum x}{n}$, where xrepresents the observations and ndenotes the count of the observations.

Substitute the values for males.

$$\begin{gathered} \backslash {\overline{x}}_M=\frac{86+72+64+...+66}{15} \\ =\frac{1042}{15} \\ \approx 69.467 \end{gathered}$$

Substitute the values for females.

$$\begin{gathered} {\overline{x}}_D=\frac{64+84+82+...+80}{15} \\ =\frac{1232}{15} \\ \approx 82.133 \end{gathered}$$

Thus, the mean pulse rates for males and females are 69.5 beats per minute and 82.1beats per minute, respectively.

The median is computed in the following steps.

• Sort all the observations.
• n: even; the median is the average of the two middle values.
• n: odd; the median is the middle value.

Compute the median pulse rates for males.

Arrange the observations in ascending order.

The middlemost observation for males is 66.

The median is given as:

$M_M=66$

Thus, the median the pulse rate for males is 66.0beats per minute.

Compute the median for females.

The number of observations is15.

Arrange the observations in ascending order.

The middlemost observation is 84.

The median is given as:

$M_F=84$

Thus, the median pulse rate for females is 84.0beats per minute.

The mean and the median pulse rates(measured in beats per minute) in males are lower than those of females.

As both measures show an almost similar difference between the values, it can be concluded that the population of females has higher pulse rates in general than the population of males.