Karl records the number of city blocks from his house to each of his friends’ houses. Which statement is supported by the data? Number of City Blocks to Eight Friends’ Houses 1, 2, 5, 3, 2, 2, 5, 3 The minimum distance from Karl’s house to a friend’s is 2 blocks. The maximum number of blocks the friends live from each other is 4. The mean distance to his friends’ houses is between 2 and 3 blocks. The mode shows that Karl has 3 friends who live 3 blocks from him.
The Correct Answer and Explanation is:
Correct Answer:
The mean distance to his friends’ houses is between 2 and 3 blocks.
Explanation (300 words):
To determine which statement is best supported by the data, let’s analyze the distances Karl recorded:
Given distances to eight friends’ houses:
1, 2, 5, 3, 2, 2, 5, 3
Step 1: Minimum Distance
- The smallest number is 1, so the minimum distance is 1 block, not 2.
🔴 So, the first statement is incorrect.
Step 2: Maximum Distance Between Friends
- The maximum distance between any two friends is the difference between the largest and smallest distances:
5−1=45 – 1 = 45−1=4
✅ So, the second statement is technically correct, but let’s compare it with the third option.
Step 3: Mean (Average) Distance
To calculate the mean:Mean=1+2+5+3+2+2+5+38=238=2.875\text{Mean} = \frac{1 + 2 + 5 + 3 + 2 + 2 + 5 + 3}{8} = \frac{23}{8} = 2.875Mean=81+2+5+3+2+2+5+3=823=2.875
- Since 2.875 is between 2 and 3,
✅ the third statement is also correct and more informative than the second.
Step 4: Mode
- The number 2 appears 3 times,
- 3 appears 2 times,
🔴 So, the mode is 2, not 3, and Karl has 3 friends living 2 blocks away, not 3 blocks away.
The fourth statement is incorrect.
Final Evaluation:
Although both the second and third statements are technically correct, the third statement is more directly supported by the data and provides a more meaningful summary of the overall distribution. The mean gives a reliable measure of central tendency, and it is clearly calculated to be between 2 and 3 blocks.
✅ Thus, the best-supported statement is:
“The mean distance to his friends’ houses is between 2 and 3 blocks.”
