Question

Number of Shoes Owned by 6th Graders
Number of Pairs of Shoes Number of 6th Graders
2 5
3 6
4 1
5 1
6 4
7 7
8 2
10 1
Michael wants to know how many pairs of shoes 6th graders typically own. He surveys the 6th graders at his summer camp. His results are given in the table. After Michael creates the table, he realizes that he forgot to include himself. Michael owns 4 pairs of shoes.

Calculate the median of the original dataset and the median of the new dataset with the data point for Michael’s 4 pairs of shoes added.

Answer 1

First dataset:
- Total students = 5+6+1+1+4+7+2+1 = 27 (odd), so median is the 14th value.
- Cumulative positions: 2 (1–5), 3 (6–11), 4 (12), 5 (13), 6 (14–17).
- The 14th value = 6, so median = 6 pairs.

After adding Michael (one more 4):
- Total students = 28 (even), so median is the average of the 14th and 15th values.
- Cumulative positions now: 2 (1–5), 3 (6–11), 4 (12–13), 5 (14), 6 (15–18).
- 14th = 5 and 15th = 6, so median = (5+6)/2 = 5.5 pairs.

Answer: original median = 6; new median = 5.5.