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# Dotplots and Stem-and-Leaf Plots Study Guide (page 2)

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Updated on Oct 5, 2011

#### Hint

When taking differences between treatments when data are paired, it is important to always take the difference in a consistent manner.

We could have taken the number of blinks while playing video games minus the number of blinks during normal conversation. Each difference would have had the same magnitude, but the opposite sign. Create a dotplot and discuss what the display implies about the data.

#### Solution

The dotplot of the 15 values of the differences in the number of blinks during normal conversation and video game playing is shown in Figure 4.3. Every participant blinked more during the two minutes of normal conversation than he or she did during the observed two minutes of playing the video games. (This may be seen because all differences are positive.) The smallest difference in the number of blinks was 13 and the largest was 40.

## Stem-and-Leaf Plots

A stem-and-leaf plot can be used to effectively display numerical data. Each number in the data set is broken into two pieces, a stem and a leaf. The stem is all but the last digit of the number, and the leaf is the last digit. To create a stem-and-leaf plot, do the following:

1. Determine the stem values. The stems should be equally spaced.
2. For each observation in the data set, attach a leaf to the appropriate stem. It is standard, though not mandatory, to put the leaves in increasing order at each stem value.

Look again at the heights of the 62 orchestra members. The stem-and-leaf plot of the data is shown as follows:

As we saw in the dotplot, the orchestra members who are 53.5 and 83.8 inches tall have gaps between themselves and the next shortest and the next tallest members, respectively.

The stem-and-leaf plots of two groups can be compared using back-to-back stem-and-leaf plots. To construct one, a common stem is used. One group has leaves extending to the left of the stem; the other group's leaves extend to the right of the stem. Groups are labeled at the top. To compare the heights of female and male orchestra members, we would obtain the following back-to-back stem-and-leaf plot.

The conclusions are similar to those from the parallel dotplots. The males tend to be taller than the females, though significant overlap exists in the heights of the two genders. One male was more than 7 inches taller than the next tallest orchestra member, and one female was more than 4 inches shorter than the next shortest orchestra member. In the next lesson, we will consider whether these values are unusual enough to be considered outliers.

#### Example

Draw a stem-and-leaf plot of the differences in the numbers of blinks during normal conversation and video game playing. Comment on the plot.

#### Solution

We might begin by using the tens column as the stem. This would result in the following graph:

Suppose now we decide to use seven stem values instead of four. The additional stems are created by making two stems for each of the 1, 2, and 3 stems. The first stem value is associated with the ones digits of 0 through 4; the second stem value is associated with the ones digits of 5 through 9. This stem-and-leaf plot is shown here:

In the second plot, it is obvious that a gap exists in the data; no observations were made between 34 and 40. It appears 40 is an unusual value. With this one exception, in a two-minute period, the participants blinked between 13 and 34 more times during normal conversation than while playing a video game.

## Dotplots and Stem-and-Leaf Plots In Short

Dotplots and stem-and-leaf plots are simple graphical presentations of the data. They provide a good view of the data. However, they are practical only for small- to medium-size data sets.

Find practice problems and solutions for these concepts at Dotplots and Stem-and-Leaf Plots Practice Exercises.

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