Grade by Grade
D. Data · Data and Probability

Stem-and-Leaf Plots

D1.2 D1.6About 45 minutes
Learning goals
  • I can split a two-digit number into a stem (tens) and a leaf (ones).
  • I can organize data in a stem-and-leaf plot with a key.
  • I can read a stem-and-leaf plot to find the smallest value, the largest value and how many values there are.
  • I can answer questions about data in a stem-and-leaf plot.

Words to know

stem-and-leaf plot
A way to organize numbers by their tens digit (stem) and their ones digit (leaf), so every value is shown in order.
stem
The left part of a number in the plot. For two-digit numbers, it is the tens digit.
leaf
The right part of a number in the plot: the ones digit.
key
A note that shows how to read the plot, like "3 | 4 means 34".
value
One number in a data set.

New this year

Stem-and-leaf plots are new in Grade 4. They use what you already know about place value: every two-digit number has a tens digit and a ones digit.

Jumping jacks in one minute

In gym class, 12 students counted how many jumping jacks they could do in one minute:

34, 41, 28, 45, 37, 41, 29, 52, 38, 41, 33, 47

That's a jumble of numbers! Who did the fewest? How many did more than 40? It is hard to tell. A stem-and-leaf plot organizes these numbers so you can see all of them, in order, grouped by tens.

34stem = 3 (tens)leaf = 4 (ones)
Each number splits into a stem and a leaf. In 34, the stem is 3 (tens) and the leaf is 4 (ones).
Worked example

Example 1: Make a stem-and-leaf plot

Make a stem-and-leaf plot of the jumping jacks data: 34, 41, 28, 45, 37, 41, 29, 52, 38, 41, 33, 47.

  1. Find the smallest and largest values: 28 and 52. So the stems go from 2 to 5.
  2. Write the stems 2, 3, 4, 5 in a column, with a line to their right.
  3. Go through the data in order and write each leaf beside its stem. 34 → leaf 4 beside stem 3. 41 → leaf 1 beside stem 4. Keep going until every number has a leaf. Cross off each number as you use it.
  4. Rewrite each row with its leaves in order from least to greatest. Write 1 three times, because 41 appears three times.
  5. Count the leaves: 2 + 4 + 5 + 1 = 12, the same as the number of students. ✓
  6. Add a title and a key: 3 | 4 means 34 jumping jacks.

See the plot below.

Stem (tens)Leaf (ones)
28 9
33 4 7 8
41 1 1 5 7
52
Jumping jacks in one minute. Key: 3 | 4 means 34.

Reading the plot

Now it's easy to see:

  • The smallest value is the first leaf in the top row: 28.
  • The largest value is the last leaf in the bottom row: 52.
  • The longest row is the 40s. More students did 40 to 49 jumping jacks than any other group of ten.
  • 41 appears three times, more than any other value.

The plot also has a shape. Turn your head sideways and the rows look like bars on a bar graph. But unlike a bar graph, you can still see every single value.

StemLeaves2893347841115752longest row: the 40ssmallest: 28 (first leaf)largest: 52 (last leaf)Key: 3 | 4 means 34
Draw each leaf in its own box and the rows look like bars: the 40s row is longest. You can still read every value.
Worked example

Example 2: Numbers less than 10

Goals scored by 8 hockey players this season: 3, 7, 12, 15, 15, 21, 8, 18. Make a stem-and-leaf plot.

  1. A one-digit number like 3 has 0 tens, so its stem is 0 and its leaf is 3.
  2. The stems go from 0 to 2.
  3. Stem 0: 3, 7, 8. Stem 1: 2, 5, 5, 8. Stem 2: 1.
  4. Check: 3 + 4 + 1 = 8 leaves for 8 players. ✓

See the plot below. Key: 1 | 5 means 15 goals.

Stem (tens)Leaf (ones)
03 7 8
12 5 5 8
21
Goals scored this season. Key: 1 | 5 means 15.
Worked example

Example 3: An empty stem

The ages of the people at a family picnic are shown below. Why does stem 2 have no leaves? How many people were younger than 20?

  1. Stem 2 stands for the twenties (20 to 29). It has no leaves, so nobody at the picnic was in their twenties.
  2. We still write stem 2 (and stem 5) so the plot shows the gaps. Never skip a stem in the middle.
  3. Younger than 20 means stems 0 and 1: 3, 6, 8, 10, 12. That is 5 people.

Nobody was 20 to 29 years old. 5 people were younger than 20.

Stem (tens)Leaf (ones)
03 6 8
10 2
2
34 5 9
41
5
67
Ages at the family picnic. Key: 3 | 4 means 34 years old.

Every good stem-and-leaf plot has

  • a title
  • stems in order, with no stems skipped (even empty ones)
  • leaves in order from least to greatest, with repeated values written each time
  • leaves lined up neatly, evenly spaced
  • a key, like 3 | 4 means 34
Just for fun

Why are stem-and-leaf plots such good gardeners?

They know every leaf belongs on the right stem!

Hands-on activity

Clapping data

You need: a timer (a phone or a kitchen timer), paper and a pencil.

  1. A grown-up says "Go!" and times 10 seconds. Clap as many times as you can while someone counts.
  2. Each person in your family does it 3 times, or ask some friends to join. Try to collect at least 10 values.
  3. Make a stem-and-leaf plot: write the stems, add the leaves, then rewrite the leaves in order.
  4. Add a title and a key.
  5. Answer: What was the smallest value? The largest? Which row has the most leaves? Did any value appear more than once?

Math talk: "Why is it easier to find the biggest number in the plot than in the list?"

Your turn

1

Use the jumping jacks plot. How many students are in the data?

2

What is the smallest number of jumping jacks?

3

What is the largest number?

4

Which value appears most often?

5

How many students did 40 or more jumping jacks?

6

What does 3 | 7 mean in this plot?

7

Make a stem-and-leaf plot of: 15, 22, 18, 31, 24, 12, 27.

More practice: warm-up

1

In the number 46, what is the stem and what is the leaf?

2

The key says "5 | 2 means 52". What does 6 | 0 mean?

3

A row says 2 | 1 3 3 9. Which numbers does it show?

4

What stem does the number 7 have?

5

Why do we write the leaves in order?

More practice: on your own

1

Use the family picnic plot. How many people were at the picnic?

2

Who was the youngest and who was the oldest at the picnic? Give their ages.

3

Make a stem-and-leaf plot of: 44, 38, 51, 47, 38, 56, 42, 39.

4

Kai wrote the row 2 | 7 3 5. What is wrong? Fix it.

5

Lena's data is 12, 15, 41, 44. She wrote only stems 1 and 4. What did she forget?

Challenge

1

Two classes counted how many maple leaves each student collected.

Class A: 1 | 5 8 / 2 | 0 3 4 6 / 3 | 1

Class B: 1 | 9 / 2 | 2 5 8 / 3 | 0 3 5 7

Which class generally collected more leaves? Explain.

2

Make a stem-and-leaf plot of: 98, 104, 112, 104, 95. (Hint: the stem can be the number of tens, even if it is more than 9.)

3

Write a data set of 6 numbers whose stem-and-leaf plot has stems 1, 2 and 3, and where 25 appears more than any other number.

Check your understanding

Quiz

1.

In a stem-and-leaf plot, what is the leaf of 63?

2.

The row 4 | 0 2 2 7 shows which numbers?

3.

What is the stem of the number 8 in a plot of two-digit and one-digit numbers?

4.

Why does a stem-and-leaf plot need a key?

5.

A plot has stems 1, 2, 3, 4. Stem 3 has no leaves. What should you do?

6.

Plot: 1 | 3 6 / 2 | 0 5 5 8 / 3 | 2. How many values are there?

For parents and teachers

What this lesson teaches: organizing quantitative data in a stem-and-leaf plot (new in Grade 4, part of D1.2) and reading it to answer questions (D1.6). The stem is the tens digit, the leaf is the ones digit, leaves go in order, and a key explains how to read it.

How to help at home:

  • Collect quick number data together: claps in 10 seconds, ages of relatives, minutes spent on homework each day for two weeks.
  • Ask your child to explain what a row like 2 | 1 3 3 9 means. Saying "21, 23, 23, 29" out loud builds understanding.

Common difficulties:

  • Leaving out repeated values (writing 41 once instead of three times).
  • Forgetting stem 0 for one-digit numbers, or skipping empty stems.
  • Not putting leaves in order. Suggest writing a messy first plot, then a neat ordered one.
  • Forgetting the key and title.