Question

The following box plot shows the rating of contestants in two different chess tournaments. Are the skills of the players significantly different? Explain.

• A. Yes, because the ratio of the difference in the medians to the IQR is greater than 2.
• B. Yes, because the ratio of the difference in the medians to the IQR is equal to 2.
• C. The data sets cannot be compared, as they have different IQR.
• D. No, because the ratio of the difference in the medians to the IQR is less than 2.

Answer 1

The correct option is A Yes, because the ratio of the difference in the medians to the IQR is greater than 2.

State Chess Tournament
Median rating $=2410$
Lower quartile $=2400$
Upper quartile $=2440$
Interquartile range $=2440-2400=40$

National Chess Tournament
Median rating $=2570$
Lower quartile $=2560$
Upper quartile $=2600$
Interquartile range $=2600-2560=40$

IQRs are the same. Therefore, we can compare the skill level of the players by calculating the ratio of the difference of the medians to the IQR.

Difference of the median ratings $=2570-2410=160$
Ratio of the difference in medians to IQR $=\frac{160}{40}=4>2$

As this ratio is greater than 2, the difference in the players skill level is significant.