Question

number of pages in each book
box a 32 32 28 28 28 28 25 25 35
box b 48 20 32 20 32 32 40 20 21
which statement is true about the data?
the mean of box a is greater than the mean of box b.
the mean of box b is greater than the mean of box a.
the median of box a is greater than the median of box b.
the median of box b is greater than the median of box a.

Explanation:

Step1: Calculate mean of Box A

The sum of data in Box A is $32 + 32+28+28+28+28+25+25+35=251$. There are 9 data - points. The mean of Box A, $\bar{x}_A=\frac{251}{9}\approx27.89$.

Step2: Calculate mean of Box B

The sum of data in Box B is $48 + 20+32+20+32+32+40+20+21 = 255$. There are 9 data - points. The mean of Box B, $\bar{x}_B=\frac{255}{9}\approx28.33$.

Step3: Arrange data of Box A in ascending order

$25,25,28,28,28,28,32,32,35$. The median of Box A (9 data - points, middle value is the 5th one) is 28.

Step4: Arrange data of Box B in ascending order

$20,20,20,21,32,32,32,40,48$. The median of Box B (9 data - points, middle value is the 5th one) is 32.

Answer:

The median of Box B is greater than the median of Box A.