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 mode shows that Karl has 3 friends who live 3 blocks from him. The mean distance to his friends’ houses is between 2 and 3 blocks. 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.
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 mode shows that Karl has 3 friends who live 3 blocks from him. The mean distance to his friends’ houses is between 2 and 3 blocks. 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 Correct Answer and Explanation is:
Correct Answer:
The mean distance to his friends’ houses is between 2 and 3 blocks.
Explanation
Karl has recorded the distances from his house to eight of his friends’ houses in city blocks:
1, 2, 5, 3, 2, 2, 5, 3
Let’s evaluate the given choices one by one using this data:
1. “The mode shows that Karl has 3 friends who live 3 blocks from him.”
The mode is the number that appears most frequently in a data set.
- Frequencies:
- 1 occurs once
- 2 occurs three times
- 3 occurs two times
- 5 occurs two times
So, the mode is 2, not 3.
✅ This statement is not supported by the data.
2. “The mean distance to his friends’ houses is between 2 and 3 blocks.”
To find the mean, add all the numbers and divide by how many there are.
Sum: 1 + 2 + 5 + 3 + 2 + 2 + 5 + 3 = 23
Number of data points: 8
Mean = 23 ÷ 8 = 2.875
Since 2.875 is between 2 and 3,
✅ This statement is correct and supported by the data.
3. “The minimum distance from Karl’s house to a friend’s is 2 blocks.”
Check the smallest number in the list: 1
✅ This statement is not supported by the data.
4. “The maximum number of blocks the friends live from each other is 4.”
This seems to be referring to the range:
Max: 5, Min: 1 → 5 – 1 = 4
So, technically this statement is true, but it’s confusingly worded, as it sounds like it’s comparing friends’ distances from each other, not from Karl.
Because the most clearly accurate and well-stated choice is about the mean,
✅ the correct and best-supported answer is:
“The mean distance to his friends’ houses is between 2 and 3 blocks.”
