Question

The given double box and whisker plot represents random samples of points won by two teams in the last $100$ matches. Which of the following statements about the plot is correct?

• A. Cannot be determined
• B. The points won by Team B are significantly more than the points won by Team A.
• C. The points won by Team A are significantly more than the points won by Team B.
• D. The points won by Team A are not significantly more than the points won by Team B.

Answer 1

The correct option is D The points won by Team A are not significantly more than the points won by Team B.

Team A:
Median $=50$
IQR $=$ third quartile $-$ first quartile $=55-45=10$
Team 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 medians $=55-50=5$
$\frac{\text{Difference in medians}}{\text{IQR}}=\frac{5}{10}=0.5<2$
Because the quotient is less than $2$, there is no significant difference between the given data sets.
Hence, points won by Team A are not significantly more than the points won by Team B.