Mrs. Jackson teaches 7 different sections of math. Students can earn raffle tickets for good behavior each day. At the end of the week, she adds all of the tickets earned by students to see which class has earned the most tickets. She has the following totals: 78, 86, 52, 67, 70, 75 and 78. The next week, she asks the students to create a stem-and-leaf plot to organize the data. How would you create this diagram?

In this concept, you will learn how to build a stem-and-leaf plot to organize the data.

### Organizing Data Using Stem-and-Leaf Plots

A **stem-and-leaf** **plot** is a visual diagram where numbers are organized according to place value. The **data** (the numbers) are organized in either ascending or descending order.

To build a stem-and-leaf plot, use place value as your method of organizing data.

If you have a 15 as a number, the stem would be a ten since that is the tens place value. The leaf would be the 5.

Here is how it looks as a stem-and-leaf plot.

\begin{align*}1\ \bigg |\ 5\end{align*}

This means 15.

A stem-and-leaf plot is most useful when looking at a series of data. When you have a series of data, you can organize the data according to place value.

Let's look at an example.

22, 15, 11, 22, 24, 33, 45

First, organize the numbers by the tens place since all of the numbers have tens places as the highest place value.

11, 15, 22, 22, 24, 33, 45

Next, put each stem on the left side of our vertical line.

Notice that the largest of each place is on the left of the lines. Now put the ones or the leaves on the right of the vertical line.

This is the completed stem-and-leaf plot. Each number in the data has been organized and repeated values are listed in the chart. The tens place is on the left for each number and the ones places that go with each ten are on the right side of the vertical bar.

Let's look at another example.

Make a stem-and-leaf plot from the data.

33, 34, 36, 45, 40, 62, 67, 68

Start by organizing the stems separate from the leaves.

Notice that there isn’t a number in the fifties in the list of data, but you still need to include the stem in the stem-and-leaf plot.

Each stem and set of leaves creates an **interval**. The interval is a range of values in each stem.

Let’s look at the intervals for the stem-and-leaf plot you just created.

The interval for the 30’s is 33 - 36.

The interval for the 40’s is 40 - 45.

The interval for the 60’s is 62 - 68.

### Examples

#### Example 1

Earlier, you were given a problem about Mrs. Jackson and her raffle tickets.

Her classes earned the following number of tickets: 78, 86, 52, 67, 70, 75 and 78. How can her students arrange the data on a stem-and-leaf plot?

First, arrange the numbers from least to greatest.

52, 67, 70, 75, 78, 78, 86

Then, use the tens units as the stem and the ones units as the leaves

The above stem-and-leaf plot represents the data.

#### Example 2

Use the stem-and-leaf plot to answer the question.

What is the largest value in the forties?

First, locate the stem.

4

Next, locate the last leaf for that stem.

5

Then, write the number.

45

The answer is 45. The largest value in the forties is 45.

#### Example 3

Use the stem-and-leaf plot below to answer this question.

What is the greatest value in the twenties?

First, locate the stem.

2

Next, locate the last leaf for that stem.

4

Then, write the number.

24

The answer is 24. The greatest value in the twenties is 24.

#### Example 4

Use the stem-and-leaf plot in example 3 to answer this question.

What is the first interval of the data?

First, look at the first stem.

1

Next, look at the lowest leaf and the highest leaf in the stem.

1 and 5

Then, write the interval.

11 - 15

The answer is 11 - 15. The interval is 11 - 15.

#### Example 5

Use the stem-and-leaf plot in example 3 to answer this question.

What is the greatest value in the data set?

First, locate the highest stem.

4

Next, locate the highest leaf.

5

Then, write the number.

45

The answer is 45. The greatest value in the data set is 45.

### Review

Build a stem-and-leaf plot for each of the following data sets.

- 42, 44, 45, 46, 51, 52, 53, 60, 81, 82
- 13, 11, 20, 21, 22, 30, 31, 32
- 44, 45, 46, 48, 51, 53, 55, 67, 69
- 10, 19, 19, 10, 11, 13, 14, 14, 15
- 12, 13, 13, 21, 22, 23, 33, 34, 37, 40
- 45, 46, 46, 46, 52, 52, 54, 77, 78, 79
- 60, 60, 62, 63, 70, 71, 71, 88, 87, 89
- 80, 81, 82, 90, 91, 92, 93, 93, 93, 94
- 11, 12, 12, 13, 14, 14, 20, 29, 30, 32, 32, 52
- 33, 45, 46, 47, 60, 60, 72, 73, 74, 88, 89
- 10, 23, 24, 25, 30, 31, 32, 33, 45, 46

Look at the first stem-and-leaf plot you created and answer the following questions.

- What is the lowest value in the data set?
- What is the greatest?
- Are there any stems without leaves?
- Which ones?

### Review (Answers)

To see the Review answers, open this PDF file and look for section 3.21.