# 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.

Stems15 14 13 12 11 10 9 8 Key: 11 |
Leaves1 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 (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 usually do not
include explicit labels for the stems and leaves.

## 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.

8 7 6 5 4 3 2 1 |
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.