Question Type 4: Interpretating information from box and whisker plots Bootcamps

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).

Using the same box plot (minimum = 4, $Q_1 = 7$, median = 10, $Q_3 = 15$, maximum = 20), find the range of the data set.

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.

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×IQR rule. Then determine if the value 22 would be considered an outlier.

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.

A box plot shows: minimum = 4, $Q_1 = 9$, median = 13, $Q_3 = 19$, maximum = 28. Calculate the lower and upper quartiles and determine whether the value 30 is an outlier.

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.

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

Class A: median = 70, IQR = 20.
Class B: median = 75, IQR = 15.

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

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?

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

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

Which distribution is more variable? Which distribution is more skewed, and in what direction?

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?