Question

molly is doing a project on family size for social studies class. she collected data on the number of first cousins the kids in her neighborhood have. this histogram shows the data she collected.
number of cousins
histogram with x - axis: number of cousins (0 - 4, 5 - 9, 10 - 14, 15 - 19, 20 - 24, 25 - 29) and y - axis: number of kids (0 to 10). bars: 0 - 4: ~3, 5 - 9: ~7, 10 - 14: 10, 15 - 19: ~9, 20 - 24: ~6, 25 - 29: ~3
based on the histogram, which of these statements are true?

• on average, kids in her neighborhood have about 15 cousins.
• the data is nearly symmetrical.
• the mean and median are equal or nearly equal.
• most kids in her neighborhood have more than 20 cousins.

Explanation:

1. "On average, kids in her neighborhood have about 15 cousins": To find the mean, we can estimate using midpoints. The midpoints are 2, 7, 12, 17, 22, 27. The frequencies (from the histogram) are approximately 3, 7, 10, 9, 6, 3. Calculating the weighted mean: $\frac{(2×3)+(7×7)+(12×10)+(17×9)+(22×6)+(27×3)}{3 + 7 + 10 + 9 + 6 + 3}=\frac{6 + 49 + 120 + 153 + 132 + 81}{38}=\frac{541}{38}\approx14.24$, which is near 15. So this is true.
2. "The data is nearly symmetrical": The histogram has a peak around 10 - 14, and the left and right sides (when mirrored) are roughly balanced. The frequencies on the left (0 - 4: 3, 5 - 9: 7, 10 - 14: 10) and right (15 - 19: 9, 20 - 24: 6, 25 - 29: 3) show a symmetric - like distribution. So this is true.
3. "The mean and median are equal or nearly equal": For a nearly symmetrical distribution, the mean and median are close. Since we saw the distribution is nearly symmetrical and the mean is ~14.24, the median (middle value of ordered data) will also be near 15. So this is true.
4. "Most kids in her neighborhood have more than 20 cousins": The frequency for 20 - 24 is 6 and 25 - 29 is 3, total 9. The total number of kids is 38. The highest frequency is 10 (for 10 - 14), so most kids have between 10 - 14 cousins, not more than 20. So this is false.

Answer:

• On average, kids in her neighborhood have about 15 cousins. (True)
• The data is nearly symmetrical. (True)
• The mean and median are equal or nearly equal. (True)
• Most kids in her neighborhood have more than 20 cousins. (False)

The true statements are: "On average, kids in her neighborhood have about 15 cousins", "The data is nearly symmetrical", "The mean and median are equal or nearly equal".