Stemplots

A stemplot (aka, stem and leaf plot) is a type of chart that shows how individual values are distributed within a set of data.

Stemplots

A stemplot is used to display quantitative data, generally from small datasets (50 or fewer observations). The stemplot below shows IQ scores for 30 sixth graders.

In a stemplot, the entries on the left are called stems; and the entries on the right are called leaves. In the example above, the stems are tens (8 represents 80, 9 represents 90, 10 represents 100, and so on); and the leaves are ones. However, the stems and leaves could be other units - millions, thousands, ones, tenths, etc.

Some stemplots include a key to help the user interpret the display correctly. The key in the stemplot above indicates that a stem of 11 with a leaf of 7 represents an IQ score of 117.

Looking at the example above, you should be able to quickly describe the distribution of IQ scores. Most of the scores are clustered between 90 and 109, with the center falling in the neighborhood of 100. The scores range from a low of 81 (two students have an IQ of 81) to a high of 151. The high score of 151 might be classified as an outlier.

Note: In the example above, the stems and leaves are explicitly labeled for educational purposes. In the real world, however, stemplots often lack explicit labels for the stems and leaves.

Stemplots vs Histograms

If you drew a continuous line around the leaves of a stemplot, you would have a horizontal histogram. Here, we have a horizontal histogram based on the stemplot shown above.

Note that the histogram mirrors the shape of the stemplot. Like the stemplot, the histogram shows the distribution of IQ scores for 30 sixth-graders; but, unlike the stemplot, the histogram does not show IQ scores for individual students.

Bottom line: The stemplot provides more detail, but the histogram may be easier to read.

Test Your Understanding

Problem 1

The stemplot below shows the number of hot dogs eaten by contestants in a recent hot dog eating contest. Assume that the stems represents tens and the leaves represent ones.

Which of the following statements is true?

I. The range is 70.
II. The median is 46.

(A) I only
(B) II only
(C) I and II
(D) Neither is true.
(E) There is insufficient information to answer this question.

Solution

The correct answer is (C). The range is equal to the biggest value minus the smallest value. The biggest value is 81, and the smallest value is 11; so the range is equal to 81 -11 or 70. Since the dataset has an even number of values, the median is the average of the middle two values - 45 and 47. That is, the median is (45 + 47)/2 or 46.