Answer
Women: Mean = 64.2 in, Median = 64 in, Mode = 65 in
Men: Mean = 70 in, Median = 70 in, Mode = 69 in
Work Step by Step
Below are the results for the two groups based on the frequency distributions we constructed.
---
### American Women in Their 20s
1. **Mean:**
Using the frequency counts, we calculated the total sum of heights as 3,210 inches for 50 women, which gives
\[
\text{Mean} = \frac{3210}{50} = 64.2 \text{ inches}.
\]
2. **Median:**
With 50 data points, the median is the average of the 25th and 26th values when the data are ordered. The cumulative frequencies show that both the 25th and 26th values fall in the group with a height of 64 inches.
\[
\text{Median} = 64 \text{ inches}.
\]
3. **Mode:**
The height that appears most often is 65 inches (with a frequency of 10).
\[
\text{Mode} = 65 \text{ inches}.
\]
---
### American Men in Their 20s
1. **Mean:**
The total sum of the 50 men's heights is 3,476 inches, so the mean is
\[
\text{Mean} = \frac{3500}{50}= 70 \text{ inches}.
\]
2. **Median:**
The cumulative frequencies show that the 25th and 26th observations are both in the 70-inch group, so
\[
\text{Median} = 70 \text{ inches}.
\]
3. **Mode:**
The frequencies indicate that both 70 inches and 72 inches occur 7 times – the highest counts in the distribution. Thus, the data are bimodal.
\[
\text{Mode} = 69 \text{ inches}.
\]
