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# 11.7: Stem-and-Leaf Plots and Histograms

Difficulty Level: At Grade Created by: CK-12

## Learning Objectives

At the end of this lesson, students will be able to:

• Make and interpret stem-and-leaf plots.
• Make and interpret histograms.
• Make histograms using a graphing calculator.

## Vocabulary

Terms introduced in this lesson:

visual representation of data
stem-and-leaf plot
stem, leaf
frequency
histogram
bins
continuous data
round
truncate

## Teaching Strategies and Tips

In the previous lesson, students learned that the appropriateness of an average depends on the shape of the distribution of the data.

• Plotting data is essential and should come naturally as a first step in data analysis.
• In this lesson, students learn to group and visualize data using stem-and-leaf plots and histograms. See Examples 1 and 2, respectively.

Emphasize the similarity between histograms and stem-and-leaf plots – a stem-and- leaf plot resembles a histogram on its side.

Teachers are encouraged to present several examples of stem-and-leaf plots consisting of different kinds of data sets, such as: clustered data that comes as three-digit numbers, data spread out coming in three-digits, data consisting of numbers with 1\begin{align*}1\end{align*} or two decimal places, and data sets with decimals between 0\begin{align*}0\end{align*} and 1\begin{align*}1\end{align*}.

Arrange the data into a stem-and-leaf plot.

a. The students in Mr. Peterson’s math class took the AP Statistics exam. Their math scores are:

3,2,2,3,4,4,3,1,2,3,4,5,4,2,2,3,4,3,4,5,4,3\begin{align*}3, 2, 2, 3, 4, 4, 3, 1, 2, 3, 4, 5, 4, 2, 2, 3, 4, 3, 4, 5, 4, 3\end{align*}

b. The weights, in ounces, of several cookies taken from the same package are:

0.95,0.85,0.93,0.90,0.97,0.96,0.87,0.91\begin{align*}0.95, 0.85, 0.93, 0.90, 0.97, 0.96, 0.87, 0.91\end{align*}

c. The precipitation, in mm, for the city of Townville in the month of October is:

142.20,0.02,0.01,12.15,92.72,103.21,138.90,102.92,12.07,1.00,0.00,0.00,12.01,21.02,22.02,87.91,89.60,132.72,120.82,15.20,12.22,0.00,0.00,0.00,0.00,0.02,0.03,0.01,14.16,18.13\begin{align*}142.20, 0.02, 0.01, 12.15, 92.72, 103.21, 138.90, 102.92, 12.07, 1.00, 0.00, 0.00, 12.01, 21.02, 22.02, 87.91, 89.60, 132.72, 120.82, 15.20, 12.22, 0.00, 0.00, 0.00, 0.00, 0.02, 0.03, 0.01, 14.16, 18.13\end{align*}

Teachers are encouraged to show side-by-side histograms for the same data set as patterns can be more or less apparent with different number of bins.

• By increasing or decreasing bin-widths, students see how the shape of the distribution changes for better or worse.
• Some bin-widths can be random-looking or even misleading.

## Error Troubleshooting

Remind students in Review Questions 1 and 4 to construct ordered stem-and-leaf plots, placing the leaves on each branch in ascending order, before correctly determining the median and the mode.

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