Why is the median line not in the exact middle of the box?

If the median is closer to one side of the box, it means your data is skewed. The data points on the smaller side of the box are more tightly packed together, while the points on the larger side are more spread out.

Can a box plot tell me the mean (average) of the data?

Usually, no. Standard box plots are built entirely around the median and quartiles. Sometimes software will add a small star or 'X' to mark the mean, but you cannot calculate the exact mean just by looking at a standard box plot.

What does it mean if one whisker is much longer than the other?

A longer whisker indicates that the 25% of the data on that side is much more spread out than the 25% on the other side. The data has a wider range in that direction.

How do you read a box plot?

A box plot, or box-and-whisker plot, is a visual snapshot of a dataset's distribution. It answers the question of how to read a dataset's spread by highlighting five specific summary numbers, showing you where most values are concentrated and where the extremes lie. Think of it like reading the summary of a long book: instead of reading every single page, you get the beginning, the middle, the end, and the major twists. In statistics, this summary includes the minimum, first quartile, median, third quartile, and maximum, giving you a complete picture of the data at a glance.

The Box and the Median

The main rectangular box in the middle of the plot represents the middle 50% of your data, also known as the interquartile range (IQR). The line drawn inside this box is the median, which is the exact middle value of your entire dataset. If you lined up all your numbers from smallest to largest, the median is the one right in the center. The edges of the box tell you where the 25th percentile and 75th percentile lie.

The Whiskers and the Ends

The lines extending from the ends of the box are called whiskers. They stretch out to the smallest and largest values in your dataset that are not considered outliers. The ends of the whiskers give you a sense of the overall range of your typical data, showing how far the bottom 25% and top 25% of your data stretch out from the middle box.

Spotting Outliers

Sometimes you will see individual dots or asterisks floating past the ends of the whiskers. These represent outliers, which are unusual data points that fall exceptionally far from the rest of the group. A standard mathematical rule is used to flag these: any point further than 1.5 times the length of the box away from the edge of the box is plotted as an individual outlier.

Worked through

You are looking at a box plot of student test scores. The bottom whisker ends at 55. The box starts at 65, has a vertical line inside at 75, and ends at 85. The top whisker ends at 95. There is a single dot at 30. Identify the median, the middle 50% range, and any outliers.

First, find the median by looking at the line inside the box, which is 75. Next, look at the edges of the box to find the middle 50% of the data; the box starts at 65 and ends at 85, so the middle half of the students scored between 65 and 85. Finally, look beyond the whiskers for any dots. There is a dot at 30, which means 30 is an outlier. This represents a student who scored unusually low compared to the rest of the class.

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Where this comes from: OpenStax Introductory Statistics, Chapter 2: Descriptive Statistics · Khan Academy: Summarizing quantitative data (Box plots)