Question

The box plots show male and females grades in mathematics class: Which of the following best describes the information about the interquartile ranges?

Answer 1

I think the answer is "The interquartile range for females should be higher because the overall mean is higher". 

Answer 2

The interquartile ranges are quite close in value.

Explanation:

We have been given two box-plots and we are asked to choose the correct statement about the interquartile ranges.

Since we know that interquartile range is difference between upper and lower quartile.

`IQR=Q_3-Q_1`

Let us find IQR for the female grades in math.

We can see from box-plot representing female grades that upper quartile is about 90 and lower quartile is about 75.

`\text{IQR of female grades}=90-75`

`\text{IQR of female grades}=15`

Now let us find IQR for the male grades in math.

`\text{IQR of male grades}=85-70`

`\text{IQR of male grades}=15`

We can see IQR values for males and females are same, therefore, last statement is true.