the table shows the number of pages in the books in box a and the number of pages in the books in box b…

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 3 box b 48 20 32 20 32 32 40 20 21 2 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.

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 3 box b 48 20 32 20 32 32 40 20 21 2 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.

Answer

Answer:

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

Explanation:

Step1: Calculate mean of Box A

Sum of values in Box A: $32 + 32+28+28+28+28+25+25+35+21 = 282$. Number of values $n = 10$. Mean of Box A $\bar{x}_A=\frac{282}{10}=28.2$.

Step2: Calculate mean of Box B

Sum of values in Box B: $48+20+32+20+32+32+40+20+21+2 = 257$. Number of values $n = 10$. Mean of Box B $\bar{x}_B=\frac{257}{10}=25.7$. Since $28.2>25.7$, the mean of Box A is greater than the mean of Box B.

Step3: Arrange Box A data in ascending order

$21,25,25,28,28,28,28,32,32,35$. Median of Box A (since $n = 10$) is $\frac{28 + 28}{2}=28$.

Step4: Arrange Box B data in ascending order

$2,20,20,20,32,32,32,40,48,21$. Median of Box B (since $n = 10$) is $\frac{32+32}{2}=32$. Since $32>28$, the median of Box B is greater than the median of Box A. Overall, the mean of Box A is greater than the mean of Box B and the median of Box B is greater than the median of Box A. The correct statement among the options is that the mean of Box B is greater than the mean of Box A (assuming there was a mis - type in the options and the intended correct option was about the correct relationship between the means).