Question

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?
male: 70, 84, 64, 77, 83, 89, 61, 75, 53, 62, 59, 52, 61, 54, 76
female: 67, 73, 95, 88, 91, 63, 90, 77, 96, 69, 88, 94, 81, 72, 71
find the means.
(the mean for males is 71.1 beats per minute and the mean for females is 80.3 beats per minute. (type integers or decimals rounded to one decimal place as needed.))
find the medians.
(the median for males is 70 beats per minute and the median for females is 81 beats per minute. (type integers or decimals rounded to one decimal place as needed.))
compare the results. choose the correct answer below.
a. the mean is lower for males, but the median is lower for females.
b. the mean and the median for males are both lower than the mean and the median for females.
c. the mean and the median for females are both lower than the mean and the median for males.
d. the mean and median appear to be roughly the same for both genders.
e. the median is lower for males, but the mean is lower for females.

Explanation:

We are given the mean and median for males and females:

• Mean for males: \(74.1\) beats per minute, Median for males: \(70\) beats per minute.
• Mean for females: \(80.3\) beats per minute, Median for females: \(81\) beats per minute.

Now we compare the mean and median values:

• Mean comparison: \(74.1<80.3\) (mean for males is lower than mean for females).
• Median comparison: \(70 < 81\) (median for males is lower than median for females).

So we check the options:

• Option A: Says mean is lower for males but median is lower for females. But we saw median for males is also lower. So A is incorrect.
• Option B: Says mean and median for males are both lower than mean and median for females. This matches our comparison (\(74.1<80.3\) and \(70 < 81\)).
• Option C: Says mean and median for females are lower than for males. Which is opposite of what we found. So C is incorrect.
• Option D: Says mean and median are roughly same. But we have clear differences. So D is incorrect.
• Option E: Says median is lower for males but mean is lower for females. Which is opposite of what we found. So E is incorrect.

Answer:

B. The mean and the median for males are both lower than the mean and the median for females.