Types of Graphs

Box plot

The figure below is a "box plot." It shows the distribution of a single variable. The box plot below is from some survey data. It shows the same data as shown on the "histogram" page of this website. Both the "histogram" and the "box plot" are designed to visually portray a distribution.

The box plot shows five values, from left to right: the minimum value observed in the data, the first quartile, the median, the third quartile, and the maximum value.

Minimum value

The smallest value of the observed variable.

First quartile

If you were to sort all the observed values from smallest to largest, the first quartile would be 25% "down the list." Said differently, 25% of the observations are smaller than the first quartile value. Very loosely speaking, it's the value where the observations start to "get commonplace."

Median (i.e., second quartile)

If you were to sort all the observed values from smallest to largest, the median would be 50% "down the list." That is, 50% of the observations are smaller than the median. Obviously, then, 50% of the observations are higher than the median. Loosely speaking, the median is one indication of the "middle" of the variable.

Third quartile

This is similar to the first and second quartile except this is the value that's higher than 75% of the observations. Said differently, only 25% of the observations are higher than this number. Again, very loosely speaking, it's the value where the observations stop being "commonplace."

Maximum value

The highest value of the observed variable.

Overall interpretation

So, the entire length of the box plot shows the full range of values, and the thick boxes in the middle of the plot show the "middle 50%" of the values. If the distribution has a long tail, it will be shown on the box plot as a long thin line. To see that, compare the figure below with the histogram here. Both the box plot below and the histogram on that page portray the same data.

Number of cars purchased in the last 10 years