Question

You might need:
Calculator
Problem
Chucky grabbed
\[12\] items in the grocery store that each had a different price and had a mean cost of about
\[\$7.41\]. One of the items was an entire wheel of cheese that cost
\[\$39.99\].
Chucky then decided to put the wheel of cheese back and only buy the other
\[11\] items.
How will removing the wheel of cheese affect the mean and median?
Choose 1 answer:
A
Both the mean and median will decrease, but the median will decrease by more than the mean.
B
Both the mean and median will decrease, but the mean will decrease by more than the median.
C
Both the mean and median will increase, but the median will increase by more than the mean.
D
Both the mean and median will increase, but the mean will increase by more than the median.
Related content

Answer 1

B

Explanation: The total cost was 12(7.41) = 88.92. Removing the $39.99 cheese leaves total 88.92 − 39.99 = 48.93, so the new mean is 48.93/11 ≈ 4.45. The mean therefore decreases by about 7.41 − 4.45 ≈ 2.96.

The median of 12 items is (6th + 7th)/2; after removing the largest item the median becomes the 6th item, so the median decreases by (7th − 6th)/2 (a comparatively small shift). Thus both decrease, and the mean decreases by more than the median.