Question

Below are boxplots of SAT Critical Reading and Math scores for a randomly selected group of female juniors at a highly competitive suburban school.

Which of the following cannot be justified by the plots shown above?

(a) The maximum Critical Reading score is higher than the maximum Math score.

(b) Critical Reading scores are skewed to the right, whereas Math scores are somewhat skewed to the left.

(c) The median Critical Reading score for females is slightly higher than the median Math score.

(d) There appear to be no outliers in the SAT score distributions.

(e) The mean Critical Reading score and the mean Math score for females are about the same.

Short answer

It is not possible to justify that the mean Critical Reading score and the mean Math score for females are about the same. So, option (e) is correct

Step-by-step solution

Given Information

We are given that the boxplots of SAT Critical Reading and Math scores for a randomly selected group of female juniors at a highly competitive suburban school and we have to find that which following statements can not justified from plot.

Explanation 

Now,

$1$. As the right whisker of top boxplot is more to the right than the right whisker of bottom boxplot so option (a) is correct.

$2$. As, the right whisker of the top boxplot is longer than the left whisker so option (b) is correct.

$3$. As the line in the middle top boxplot is more to the right of the line in middle bottom boxplot.

$4$. As there are no X symbols in the boxplot which represent the outliers.

$5$. As boxplot does not contain any information about mean so , it can not be justified.

Hence, option (e) is the statement which can not be justified from boxplot.