IB Mathematics Analysis and Approaches Question Type 4: Interpretating Information from Box and Whisker Plots Exercises

In a box plot the lower quartile is 7, the median is 10 and the upper quartile is 15. A data value of 12 is observed. Between which percentiles does this value lie?

A box plot of a data set is noticeably skewed to the right. Without numerical values, state whether the mean is greater than, less than, or equal to the median, and explain why.

Two distributions have the following box-and-whisker summaries:

Distribution A: $\min =2$, $Q_1=5$, $\text{median}=9$, $Q_3=14$, $\max =20$. Distribution B: $\min =0$, $Q_1=6$, $\text{median}=11$, $Q_3=13$, $\max =18$.

Which distribution is more variable? Describe the skewness of each distribution.

A box plot shows: $\text{minimum}=4$, $Q_1=9$, $\text{median}=13$, $Q_3=19$, $\text{maximum}=28$. Calculate the interquartile range and determine whether the value $30$ is an outlier.

A box plot displays the five-number summary of a data set as follows: minimum = 4, lower quartile = 7, median = 10, upper quartile = 15, maximum = 20. Calculate the interquartile range (IQR).

A box plot has minimum = 1, $Q_1=3$, median = 5, $Q_3=8$, maximum = 12. Describe the skewness of the distribution and justify your answer based on the box plot structure.

The lifetimes (in hours) of two brands of light bulbs are summarized by box plots:

Brand X: min = 50, $Q_1=60$, median = 70, $Q_3=80$, max = 100.
Brand Y: min = 55, $Q_1=65$, median = 75, $Q_3=85$, max = 95.

Which brand shows more consistent performance? Which brand has the higher typical lifetime?

For the box plot with minimum = 4, $Q_1=7$, median = 10, $Q_3=15$, maximum = 20, calculate the lower and upper fences for outlier detection using the $1.5\times \text{IQR}$ rule. Then determine if the value 22 would be considered an outlier.

A box plot of exam scores shows $Q_1=60$, median = 75 and $Q_3=85$. What fraction of students scored above 85? Explain your reasoning. [2 marks]

Two classes have the following box plot summaries of test scores:

Class A: $\text{median}=70$, $\text{IQR}=20$. Class B: $\text{median}=75$, $\text{IQR}=15$.

Which class shows greater consistency? Which class has the higher central tendency?

Consider a box plot with the following statistics: minimum = 4, $Q_1=7$, median = 10, $Q_3=15$, and maximum = 20.

Find the range of the data set.

Given the box plot summary (minimum = 4, $Q_1=7$, median = 10, $Q_3=15$, maximum = 20), what percentage of the data values lie between the median and the maximum?