1. **Stating the problem:** We are given a frequency table showing the lengths of babies born on one day at a hospital, and we want to analyze the data. 2. **Frequency table:** Length (inches): 17, 18, 19, 20, 21 Tally counts: 1, 4, 7, 2, 2 3. **Calculate the total number of babies:** $$1 + 4 + 7 + 2 + 2 = 16$$ 4. **Calculate the mean length:** $$\text{Mean} = \frac{17 \times 1 + 18 \times 4 + 19 \times 7 + 20 \times 2 + 21 \times 2}{16}$$ $$= \frac{17 + 72 + 133 + 40 + 42}{16} = \frac{304}{16} = 19$$ 5. **Find the median length:** Since there are 16 data points, the median is the average of the 8th and 9th values when data is ordered. Counting the data points in order: - 1 baby at 17 inches (positions 1) - 4 babies at 18 inches (positions 2 to 5) - 7 babies at 19 inches (positions 6 to 12) The 8th and 9th babies fall in the 19-inch group. Therefore, median = 19 inches. 6. **Compare mean and median:** Mean = 19, Median = 19, so they are equal. 7. **Conclusion:** The mean and median lengths are equal in this data set. --- **Summary:** - Mean length = 19 inches - Median length = 19 inches - Mean equals median in this data