Boxplot vs Histogram

Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.

Boxplot

Graphs and displays

A boxplot is a graph of the five-number summary, with a box from Q1 to Q3, a line at the median, and whiskers to the extremes.

A boxplot turns the five-number summary into a picture: a box spans Q1Q_1 (the first quartile) to Q3Q_3 (the third quartile), a line inside marks the median, and whiskers reach the smallest and largest non-outlier values. For example, a longer right whisker signals a right-skewed distribution. Points more than 1.5×IQR1.5 \times \text{IQR} beyond the nearer quartile are drawn separately as outliers. Boxplots make it easy to compare center and spread across several groups side by side.

Full entry for boxplot

Histogram

Graphs and displays

A histogram displays quantitative data by grouping values into equal-width intervals and drawing a bar for the count in each interval.

A histogram divides the number line into bins of equal width and draws a bar whose height is the frequency in that bin. For example, exam scores might be binned as 60 to 70, 70 to 80, and 80 to 90, with bar heights giving how many scores land in each. Unlike a bar graph, the bars touch because the horizontal axis is a continuous number scale. The bin width you choose affects how smooth or jagged the shape looks.

Full entry for histogram

Where each one fits in the course