Impacts of Changes in Data Practice

Question

Complete this assessment to review what you've learned. It will not count toward your grade.
5 of 55 of 5 Items

Question
Use the table to answer the question.

Number of Pairs of Shoes Number of 6th Graders
2 4
3 3
4 1
5 1
6 3
7 7
8 2
10 1
Michael wants to know how many pairs of shoes 6th graders 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.

Determine the interquartile range (IQR) of the original dataset and the interquartile range of the new dataset with the data point for Michael’s 4 pairs of shoes added.

(1 point)
The interquartile range of the original dataset is
.

The interquartile range of the new dataset after another “4” is added is
.

Answer 1

To find the interquartile range (IQR), we first need to find the first quartile (Q1) and the third quartile (Q3).

For the original dataset:
- Q1 = median of the lower half of the data = median of 2, 3, 4, 5 = (3+4)/2 = 3.5
- Q3 = median of the upper half of the data = median of 6, 7, 8, 10 = (7+8)/2 = 7.5

IQR = Q3 - Q1
IQR = 7.5 - 3.5
IQR = 4

Therefore, the interquartile range of the original dataset is 4.

For the new dataset with Michael's data point added (considering 4 pairs of shoes):
- New data: 2, 3, 1, 1, 3, 7, 2, 1, 4

Now let's find the new Q1 and Q3:
- Q1 = median of 1, 1, 2, 2 = (1+2)/2 = 1.5
- Q3 = median of 3, 4, 7, 7 = (4+7)/2 = 5.5

IQR = Q3 - Q1
IQR = 5.5 - 1.5
IQR = 4

Therefore, the interquartile range of the new dataset with Michael's data point added is also 4.