Random samples of the test scores of $50$ students of the two classes, Class $A$ and Class $B$ , for a mathematics test are displayed in the following box and whisker plot. Based on this, select the correct statement.

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Solution

Class A dataset:
Median $= 85$
IQR $=$ Third quartile $-$ First quartile $= 90 - 80 = 10$

Class B dataset:
Median $= 95$
IQR $=$ Third quartile $-$ First quartile $= 100 - 85 = 15$

Difference in the medians $= 95 - 85 = 10$
IQR to be considered to find the ratio of difference in the median and IQR $= 15$

So, $\frac{Difference in median}{IQR} = \frac{10}{15} = 0.66 < 2$

Since the ratio is less than $2$ , we can conclude that the scores obtained by the students of a class are not significantly higher than that of the other class.

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Random samples of the test scores of 50 students of the two classes, Class A and Class B, for a mathematics test are displayed in the following box and whisker plot. Based on this, select the correct statement.

Random samples of the test scores of $50$ students of the two classes, Class $A$ and Class $B$ , for a mathematics test are displayed in the following box and whisker plot. Based on this, select the correct statement.