Stemplots (aka, Stem and Leaf Plots)

Although a histogram shows how observations are distributed across groups, it does not show the exact values of individual observations. A different kind of graphical display, called a stemplot or a stem and leaf plot, does show exact values of individual observations.

Stemplots

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

Stems
150
140
130
120
110
100
90
80

Key: 110

Leaves
1

2 6
4 5 7 9
1 2 2 2 5 7 9 9
0 2 3 4 4 5 7 8 9 9
1 1 4 7 8

7 represents an IQ score of 117

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 (80 and 90) and hundreds (100 through 140). However, they could be other units - millions, thousands, ones, tenths, etc. In the example above, the stems and leaves are explicitly labeled for educational purposes. In the real world, however, stemplots usually do not include explicit labels for the stems and leaves.

Some stemplots include a key to help the user interpret the display correctly. The key in the stemplot above indicates that a stem of 110 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.

Test Your Understanding of This Lesson

Problem 1

The stemplot below shows the number of hot dogs eaten by contestants in a recent hot dog eating contest.

80
70
60
50
40
30
20
10

1

4 7
2 2 6
0 2 5 7 9 9
5 7 9
7 9
1

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 data set 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.