Question

Aziz wonders how many pieces of pizza people tend to eat at a pizza party. He surveys 11 people at the end of a pizza party and asks them how many pieces of pizza they ate. A list of his results follows. Aziz uses his results to calculate that the range for number of pieces of pizza eaten is 6, and the interquartile range is 4.
Number of Pieces of Pizza Eaten: 6, 2, 1, 2, 4, 5, 2, 2, 4, 6, 7

After calculating the range and the interquartile range, Aziz realizes he forgot to include himself! He ate 3 pieces of pizza.
Determine the range and interquartile range after a "3" is added to the dataset. Describe how adding a "3" to the dataset impacts the range and the interquartile range.

A. The range is still 6, and the interquartile is still 4. Both range and interquartile range stayed the same.

B. The range is now 7, and the interquartile range is now 3.5. Both the range and the interquartile range changed slightly.

C. The range is now 7, but the interquartile range is still 4. The range increases slightly, but the interquartile range stayed the same.

D. The range is still 6, but the interquartile range is now 3.5. The range stayed the same, but the interquartile range changed slightly.

Answer 1

Sorted data with the 3 added: 1, 2, 2, 2, 2, 3, 4, 4, 5, 6, 6, 7.

Range = 7 − 1 = 6 (unchanged).

Because n = 12 (even), split into lower half (first 6) and upper half (last 6):
- Lower half: 1, 2, 2, 2, 2, 3 → Q1 = median of these = (2 + 2)/2 = 2.
- Upper half: 4, 4, 5, 6, 6, 7 → Q3 = (5 + 6)/2 = 5.5.

IQR = Q3 − Q1 = 5.5 − 2 = 3.5 (changed from 4).

Answer: D. The range stayed the same (6) but the IQR decreased to 3.5.