# 3.21: Stem-and-Leaf Plots

**At Grade**Created by: CK-12

**Practice**Stem-and-Leaf Plots

The “Add It Up Ice Cream Stand” has had an excellent summer. Mr. Harris told all of his employees that he is thrilled with the number of ice cream cones that were sold each day. The last week of August was the most successful week of sales. Here are the counts that Mr. Harris collected on each day during this last week of August.

Mon - 78

Tues - 86

Wed - 52

Thurs - 67

Fri - 70

Sat - 75

Sun - 78

Julie wants to design a beautiful chart to give to Mr. Harris as a gift to show the best sales for the week.

“Why don’t you put those in a stem-and-leaf plot,” Jose suggests when Julie tells him the idea.

“Good idea,” Julie says and she gets to work.

**Now it is your turn. You are going to make a stem-and-leaf plot to show Mr. Harris’ ice cream sales for his best week ever.**

**The title of the stem-and-leaf plot is “THE BEST WEEK EVER.”**

**Pay attention throughout this Concept so that you can build a stem-and-leaf plot to organize the data.**

### Guidance

A ** stem-and-leaf** plot is a visual diagram where you organize numbers according to place value. The

**is organized in either**

*data***order.**

*ascending or descending*To build a stem-and-leaf plot, we use place value as our method of organizing data.

**If we had a 15 as our number, the stem would be a ten since that is the tens place value. The leaf would be the 5.**

**To write it as a stem-and-leaf plot, here is what it would look like.**

\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 we have a series of data, we can organize them according to place value.**

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

Let’s say that we want to organize this data in a stem-and-leaf plot. First, we organize them by the tens place since all of our numbers have tens places as the highest place value.

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

Next, we 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 we can put the ones or the stems on the right of the vertical line.

Each number in the data has been organized. 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.

This is our completed stem-and-leaf plot.

*Helpful Hint 1*

*Notice that we list repeated values in the chart.*

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

We start by organizing the stems separate from the leaves.

Notice that there isn’t a number in the fifties in the list of data. We still need to include it in the stem-and-leaf plot. Because of this, we can leave the leaf empty, but we still include the stem.

*Helpful Hint 2*

*List stems that are between numbers even if they don’t have leaves*

*Include zeros in the leaves for numbers that end in 0*

**Now that we know how to create a stem-and-leaf plot, how can we interpret the data?** Each stem and set of leaves creates an ** interval**.

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

The interval for the 30’s is 33 - 36.

The interval for 40’s is 40 - 45.

The interval for 60’s is 62 - 68.

Practice what you have learned. Answer these question about the stem - and - leaf plot above.

#### Example A

What is the smallest value in the plot?

**Solution: 33**

#### Example B

What is the first interval of the data?

**Solution: 33 - 36**

#### Example C

What is the greatest value in the data set?

**Solution: 68**

Now back to Julie and her chart. Take a look at the original problem once again.

Julie wants to design a beautiful chart to give to Mr. Harris as a gift to show the best sales for the week.

“Why don’t you put those in a stem-and-leaf plot,” Jose suggests when Julie tells him the idea.

“Good idea,” Julie says and she gets to work.

**The first thing that we are going to do is to organize the data in a stem-and-leaf plot. The smallest stem is 5 and the largest stem is 8.** **We can build the stem-and-leaf plot and fill in the stems and the leaves.**

**Now we have a stem and leaf plot with the data all arranged.**

### Vocabulary

Here are the vocabulary words used in this Concept.

- Stem-and-leaf plot
- a way of organizing numbers in a data set from least to greatest using place value to organize.

- Data
- information that has been collected to represent real life information

- Ascending
- from smallest to largest

- Descending
- from largest to smallest

- Interval
- a specific period or arrangement of data

### Guided Practice

Here is one for you to try on your own.

Use this stem - and - leaf plot.

What is the greatest value in the forties?

**Answer**

To figure this out, we look at the stem of 4. Then we can add the leaf to the stem.

**Our answer is 45.**

### Video Review

Here are videos for review.

Khan Academy Stem-and-Leaf Plots

Great video on organizing, building and interpreting a stem and leaf plot.

http://www.mathplayground.com/howto_stemleaf.html

### Practice

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

1. 42, 44, 45, 46, 51, 52, 53, 60, 81, 82

2. 13, 11, 20, 21, 22, 30, 31, 32

3. 44, 45, 46, 48, 51, 53, 55, 67, 69

4. 10, 19, 19, 10, 11, 13, 14, 14, 15

5. 12, 13, 13, 21, 22, 23, 33, 34, 37, 40

6. 45, 46, 46, 46, 52, 52, 54, 77, 78, 79

7. 60, 60, 62, 63, 70, 71, 71, 88, 87, 89

8. 80, 81, 82, 90, 91, 92, 93, 93, 93, 94

9. 11, 12, 12, 13, 14, 14, 20, 29, 30, 32, 32, 52

10. 33, 45, 46, 47, 60, 60, 72, 73, 74, 88, 89

11. 10, 23, 24, 25, 30, 31, 32, 33, 45, 46

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

12. What is the lowest value in the data set?

13. What is the greatest?

14. Are there any stems without leaves?

15. Which ones?

Ascending

Ascending order indicates that values are arranged from smallest to largest (to*ascend*means to move upward).

bins

Bins are groups of data plotted on the x-axis.Continuous

Continuity for a point exists when the left and right sided limits match the function evaluated at that point. For a function to be continuous, the function must be continuous at every single point in an unbroken domain.Data

Data is information that has been collected to represent real life situations, usually in number form.Descending

A descending pattern indicates that values in the pattern are arranged from greatest to least (to*descend*means to move downward).

Interval

An interval is a range of data in a data set.Stem-and-leaf plot

A stem-and-leaf plot is a way of organizing data values from least to greatest using place value. Usually, the last digit of each data value becomes the "leaf" and the other digits become the "stem".Truncate

To truncate is to cut off a decimal number at a certain point without rounding.### Image Attributions

Here you'll learn to organize a set of data in a stem - and - leaf plot.

## Concept Nodes:

Ascending

Ascending order indicates that values are arranged from smallest to largest (to*ascend*means to move upward).

bins

Bins are groups of data plotted on the x-axis.Continuous

Continuity for a point exists when the left and right sided limits match the function evaluated at that point. For a function to be continuous, the function must be continuous at every single point in an unbroken domain.Data

Data is information that has been collected to represent real life situations, usually in number form.Descending

A descending pattern indicates that values in the pattern are arranged from greatest to least (to*descend*means to move downward).

Interval

An interval is a range of data in a data set.Stem-and-leaf plot

A stem-and-leaf plot is a way of organizing data values from least to greatest using place value. Usually, the last digit of each data value becomes the "leaf" and the other digits become the "stem".Truncate

To truncate is to cut off a decimal number at a certain point without rounding.