The double box and whisker plot represents random samples of points won by two teams in the last 100 matches played. Based on this, which one of these is the correct statement?

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Solution

Park A:
Median $= 50$
IQR $=$ Third quartile $-$ First quartile $= 55 - 45 = 10$

Park B:
Median $= 55$
IQR $=$ Third quartile $-$ First quartile $= 60 - 50 = 10$

Since the variabilities are the same, we can describe the visual overlap by expressing the difference in the medians as a multiple of the IQR.
Difference in median $= 55 - 50 = 5$
$\frac{Difference in medians}{IQR} = \frac{5}{10} = 0.5 < 2$
Because the quotient is less than $2$ , the difference in the medians is not significant.
Hence, points won by team $A$ are not significantly more than that of team $B$ .

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