Question

adriana is a nurse who measures patients heart rates as part of their annual checkups. these tables show the heart rates of the men and women she saw recently. mens heart rates (beats per minute) 62 70 68 110 75 72 80 75 86 78 womens heart rates (beats per minute) 76 68 80 78 64 82 78 72 66 80 complete the sentences. the median heart rate for the men is the median heart rate for the women. if the outlier were removed, the median heart rate for the men would, and the median heart rate for the women would

Explanation:

Step1: Arrange men's heart - rates in ascending order

62, 68, 70, 72, 75, 75, 78, 80, 86, 110. There are \(n = 10\) data - points. The median for an even number of data - points is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered values. So, the median of men's heart - rates is \(\frac{75 + 75}{2}=75\).

Step2: Arrange women's heart - rates in ascending order

64, 66, 68, 72, 76, 78, 78, 80, 80, 82. There are \(n = 10\) data - points. The median of women's heart - rates is \(\frac{76+78}{2}=77\).

Step3: Analyze the effect of removing the outlier for men

The outlier in men's data is 110. After removing 110, we have 9 data - points: 62, 68, 70, 72, 75, 75, 78, 80, 86. The median (for \(n = 9\), the \(\frac{n + 1}{2}=5\)th ordered value) is 75. So, the median does not change.

Step4: Analyze the effect of removing the outlier for women

Since there is no outlier in women's data (no value that is extremely different from the rest), removing an outlier has no effect on the median. The median remains 77.

Answer:

The median heart rate for the men is less than the median heart rate for the women.
If the outlier were removed, the median heart rate for the men would stay the same, and the median heart rate for the women would stay the same.