Question

The shoe sizes of a group of middle school girls are shown.

5.5 6 7 8.5 6.5
6.5 8 7.5 8 5
LO
If a shoe size of 7 is added to the data, how does the IQR change?
O The IQR becomes a 2.5.
O The IQR becomes a 1.5.
The IQR remains a 3.
O The IQR remains a 2.

Answer 1

Explanation:

Adding a shoe size of 7 to the data does not change the IQR.

To calculate the IQR, we first need to find the median of the dataset, which is 7. Then, we find the median of the lower half of the dataset (5.5, 6, 6.5, 7) and the median of the upper half of the dataset (7.5, 8, 8.5).

Lower half: 5.5, 6, 6.5, 7

Upper half: 7.5, 8, 8.5

The median of the lower half is 6.25 and the median of the upper half is 8.

To find the IQR, we subtract the median of the lower half from the median of the upper half:

8 - 6.25 = 1.75

Therefore, the IQR is 1.75 for the given dataset. Adding a shoe size of 7 does not change the values of the dataset that fall above and below the median, so the median, lower half, and upper half of the dataset remain the same. Thus, the IQR remains 1.75.

Therefore, the answer is: The IQR remains a 3.