AP Stats 1.5: Graphs for Quantitative Data

Three graphs for a quantitative variable

Topic 1.5 covers three graphs for the distribution of one quantitative variable: the histogram, the stem-and-leaf plot, and the dotplot. All three show the frequency or relative frequency of the values, and all three keep the natural ordering of the variable from smallest to largest. Unlike a bar chart for categories, these graphs sit on a numeric axis, so distance along the axis carries meaning. Each graph can show raw frequency or relative frequency on its count axis, which changes the axis labels but not the shape you see.

How each graph is built

Each graph organizes the same values a little differently.

• A histogram groups the values into ordered intervals, or bins, along the horizontal axis. Each bar covers one bin, and its height is the frequency or relative frequency of values in that bin. Changing the bin width changes the shape you see, so the same data can look smooth or jagged depending on the bins.
• A stem-and-leaf plot splits each value into a stem (the leading digit or digits) and a leaf (usually the last digit). For 27, the stem is 2 and the leaf is 7. Stems and leaves are both ordered, and every original value is preserved.
• A dotplot places one dot for each value above its position on the axis, stacking equal values. It works well for small data sets and shows every observation.

A histogram is not a bar chart; its bars touch because the axis is numeric. See histogram vs bar graph.

Choosing and reading these graphs

Which graph fits depends on the data set. A dotplot or stem-and-leaf plot works well for small data sets because it shows every value, and a stem-and-leaf plot keeps the digits so you can recover the exact numbers. A histogram suits larger data sets, since binning summarizes many values into a readable shape.

All three graphs are read the same way, by looking at where the values pile up and how far they spread out. Because they keep the natural ordering of the variable, they set up the descriptions of shape, center, and spread in topic 1.6. When you sketch one, label the axis with the variable and its units so the graph is self-contained.