Problem

Listed below are pulse rates (beats per minute) from samples of adult males and females. Find the mean and median for each of the two samples and then compare the two sets of results. Does there appear to be a difference?
$\begin{array}{llllllllllllllll}\text { Male: } & 54 & 88 & 62 & 79 & 87 & 55 & 56 & 63 & 56 & 75 & 56 & 70 & 64 & 60 & 66 \\ \text { Female: } & 65 & 92 & 95 & 91 & 89 & 72 & 87 & 69 & 89 & 86 & 81 & 90 & 88 & 91 & 66\end{array}$
Find the means.
The mean for males is beats per minute and the mean for females is beats per minute. (Type integers or decimals rounded to one decimal place as needed.)
Find the medians.
The median for males is beats per minute and the median for females is beats per minute. (Type integers or decimals rounded to one decimal place as needed.)
Compare the results. Choose the correct answer below.
A. The median is lower for males, but the mean is lower for females.
B. The mean and the median for females are both lower than the mean and the median for males.
C. The mean and the median for males are both lower than the mean and the median for females.
D. The mean and median appear to be roughly the same for both genders.
E. The mean is lower for males, but the median is lower for females.
Does there appear to be a difference?
A. Since the sample size is small, no meaningful information can be gained from analyzing the data.
B. There does not appear to be any difference.
C. The pulse rates for males appear to be higher than the pulse rates for females.

Answer

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Answer

Final Answer: \[\boxed{\text{The mean for males is approximately 66.1 beats per minute and the mean for females is approximately 83.4 beats per minute. The median for males is 63 beats per minute and the median for females is 88 beats per minute.}}\]

Steps

Step 1 :First, we need to calculate the mean and median for both male and female pulse rates. The mean is calculated by summing all the values and dividing by the number of values. The median is the middle value when the values are sorted in ascending order. If there is an even number of values, the median is the average of the two middle values.

Step 2 :Calculate the mean and median for male pulse rates: \[\text{male pulse rates} = [54, 88, 62, 79, 87, 55, 56, 63, 56, 75, 56, 70, 64, 60, 66]\] \[\text{male mean} = \frac{\sum \text{male pulse rates}}{\text{number of male pulse rates}} = 66.1 \text{ beats per minute}\] \[\text{male median} = 63 \text{ beats per minute}\]

Step 3 :Calculate the mean and median for female pulse rates: \[\text{female pulse rates} = [65, 92, 95, 91, 89, 72, 87, 69, 89, 86, 81, 90, 88, 91, 66]\] \[\text{female mean} = \frac{\sum \text{female pulse rates}}{\text{number of female pulse rates}} = 83.4 \text{ beats per minute}\] \[\text{female median} = 88 \text{ beats per minute}\]

Step 4 :Comparing these results, it appears that both the mean and median pulse rates for females are higher than those for males. Therefore, the correct answer is C. The mean and the median for males are both lower than the mean and the median for females.

Step 5 :There does appear to be a difference in pulse rates between males and females, with females having higher pulse rates on average. Therefore, the correct answer to the last question is also C. The pulse rates for males appear to be lower than the pulse rates for females.

Step 6 :Final Answer: \[\boxed{\text{The mean for males is approximately 66.1 beats per minute and the mean for females is approximately 83.4 beats per minute. The median for males is 63 beats per minute and the median for females is 88 beats per minute.}}\]

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