Question

5. A shoe store employee sets up a display by placing shoeboxes in 10 stacks. The numbers of boxes in each stack are 5, 7, 9, 11, 13, 10, 9, 8, 7, and 5. a. What is the mean of the number of boxes in a stack? T b. Find the median of the number of boxes in a stack. c. If one box is removed from each stack, how will the mean and median be affected?

Answer 1

a) 8.4

b) 8.5

c) The mean and median will be one less (7.4 and 7.5).

Explanation:

Given number of boxes in each stack:

• 5, 7, 9, 11, 13, 10, 9, 8, 7, 5

Part (a)

To find the mean of the number of boxes in a stack, divide the total number of boxes by the number of stacks:

`\implies \sf Mean=(5+7+9+ 11+13+ 10+9+ 8+ 7+5)/(10)=(84)/(10)=8.4`

Part (b)

The median is the middle value when all data values are placed in order of size.

To find the median of the number of boxes in a stack, first place the numbers in order of size:

• 5, 5, 7, 7, 8, 9, 9, 10, 11, 13

As there is an even number of boxes (10), the median is the mean of the two middle values:

`\implies \sf Median=(8+9)/(2)=(17)/(2)=8.5`

Part (c)

If one box is removed from each stack, the total number of boxes is 10 less than before. Therefore:

`\implies \sf Mean=(84-10)/(10)=(74)/(10)=7.4`

The number of boxes in each stack will be (in order of size):

• 4, 4, 6, 6, 7, 8, 8, 9, 10, 12

Therefore, the median is 7.5.

So, if one box is removed from each stack:

• The mean decreases by 1.
• The median decreases by 1.