Question

Number of Siblings Number of 6th Graders
0 3
1 12
2 5
3 2
4 0
5 2
Kaylen wants to know how many siblings 6th graders have. She surveys the 6th graders on her soccer team. Her results are given in the table. She calculates that the interquartile range for number of siblings is 1. She then realizes that she counted one data value twice by accident. She needs to remove one of the “0 siblings” values from the table.

Determine how removing a “0” from the dataset will impact the interquartile range.

(1 point)
Responses

The new interquartile range is 1. The interquartile range stayed the same.
The new interquartile range is 1. The interquartile range stayed the same.

The new interquartile range is 6.5. The interquartile range increased.
The new interquartile range is 6.5. The interquartile range increased.

The new interquartile range is 1.5. The interquartile range increased.
The new interquartile range is 1.5. The interquartile range increased.

The new interquartile range is 0.5. The interquartile range decreased.
The new interquartile range is 0.5. The interquartile range decreased.

Answer 1

Correct answer: The new interquartile range is 1. The interquartile range stayed the same.

Reason: Originally there are 24 students (0:3, 1:12, 2:5, 3:2, 5:2). Q1 is median of positions 1–12 = 1, Q3 is median of positions 13–24 = 2, so IQR = 2 − 1 = 1.

After removing one 0 there are 23 students (0:2, 1:12, 2:5, 3:2, 5:2). The median is position 12 (value 1); Q1 is median of positions 1–11 = 1; Q3 is median of positions 13–23 = 2. IQR still = 2 − 1 = 1.