11.2a: Comparing Box Plots with Similar Variability

In this lesson, you will learn about the interquartile range and how to compare box plots with similar variability.

Box plots provide 5 key pieces of information about the data: the least and greatest values, the lower and upper quartiles, and the median. From this data, we can compare the box plot to other plots, comparing the spread or variability and the medians or centers.

Practice:

Least value: Greatest Value:

Find the median and describe what it means for the data:

Find and describe the lower and upper quartiles:

The interquartile range is the difference between the lower and upper quartiles, which is represented by the lengths of the box. The interquartile range measures the spread of the middle 50% of the data. Find the interquartile range:

Why is one-half of the box wider than the other half of the box?

Box Plots with Similar Variability:

You can compare two box plots numerically according to their centers or medians, and their spreads or variability. Range and interquartile range (IQR) are both measures of spread. Box plots with similar variability should have similar boxes and whiskers.

Example:

Compare the shapes of the box plots:

Compare the centers of the box plots:

Compare the spreads by calculating the IQR and comparing the ranges:

Group A IQR: Group B IQR:

Range:

Which group has the greater variability in the bottom 50% of the shopping times? The top 50% of shopping times? Explain.