Question

the table shows the number of pages in the books in box a and the number of pages in the books in box b.
number of pages in each book
box a 32 32 28 28 28 28 25 25 35 32
box b 48 20 32 20 32 32 40 20 21 28
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 the mean of Box A

Sum of values in Box A: $32 + 32+28 + 28+28 + 28+25 + 25+35 + 32=293$. There are $n = 10$ values. Mean of Box A, $\bar{x}_A=\frac{293}{10}=29.3$.

Step2: Calculate the mean of Box B

Sum of values in Box B: $48+20 + 32+20+32+32+40+20+21+28 = 293$. There are $n = 10$ values. Mean of Box B, $\bar{x}_B=\frac{293}{10}=29.3$.

Step3: Calculate the median of Box A

Arrange values in Box A in ascending - order: $25,25,28,28,28,28,32,32,32,35$. Since $n = 10$ (even), median of Box A, $M_A=\frac{28 + 28}{2}=28$.

Step4: Calculate the median of Box B

Arrange values in Box B in ascending - order: $20,20,20,21,28,32,32,32,40,48$. Since $n = 10$ (even), median of Box B, $M_B=\frac{28 + 32}{2}=30$.

Answer:

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