Stem and leaf plot

Here you will learn about stem and leaf plots, including drawing, interpreting, and comparing them.

Students will first learn about stem and leaf plots as part of statistics and probability in 7 th grade.

What is a stem and leaf plot?

A stem and leaf plot is a method of organizing numerical data based on the place value of the numbers.

Each number is split into two parts:

• The first digit(s) form the stem.
• The last digit forms the leaf.

The number of digits for the stem can vary, but the number of digits for the leaf should only ever contain a single digit.

For example, if the numerical data contains all whole numbers, the numbers in the tens place and greater would make up the stem values while all numbers in the ones place would make up the leaf values.

Each piece of numerical data will be written with the last digit to the right of a vertical line and all other digits to the left of the vertical line. For example, the number 154 would be split into two parts where the digits \bf{15} would be the stem and \bf{4} would be the leaf.

To set up a stem and leaf plot you need to:

• Organize the data into ascending order, smallest to largest.
• Determine how the numbers are split into 2 parts by writing a key for the stem and leaf plot.
• Write the values for the ‘stem’ into the stem and leaf plot.
• Write the values for the ‘leaf’ into the stem and leaf plot.

NOTE: A stem and leaf plot must have a key (sometimes referred to as a legend). This explains how to convert the digits in the stem and leaf plot into a single data point.

You can use stem and leaf plots to calculate averages like the median, the mode and the mean, and to calculate measures of spread like the range and the interquartile range.

Dual stem and leaf plot

Comparing data sets is simplified by using a dual stem and leaf plot which have two sets of data represented back to back.

For example, here are two sets of data showing test scores of 20 males and 20 females.

By combining them together to form one dual stem and leaf plot, you can directly compare the two sets of data.

The data must be closely related for it to be compared effectively on the diagram. Note that the digits in the leaf for females is still in ascending order but from right to left, rather than left to right. Also, the key represents the data values for each side of the stem and leaf plot.

What is a stem and leaf plot?

Common Core State Standards

How does this relate to 7 th grade math?

• Grade 7 – Statistics and Probability (7.SP.B.4)
  Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

How to draw a stem and leaf plot

In order to draw a stem and leaf plot:

1. Order the numbers from smallest to largest.
2. Split the numbers into two parts; the last part must be one digit only.
3. Put the values into the diagram and create a key.

Stem and leaf plot examples

Example 1: two digit numbers

The data below shows the ages of people at a party.

35, \quad 50, \quad 37, \quad 44, \quad 53, \quad 41, \quad 39, \quad 45, \quad 48, \quad 56

Draw an ordered stem and leaf plot for the data. Remember to include a suitable key.

1. Order the numbers from smallest to largest.

35, \quad 50, \quad 37, \quad 44, \quad 53, \quad 41, \quad 39, \quad 45, \quad 48, \quad 56

becomes

35, \quad 37, \quad 39, \quad 41, \quad 44, \quad 45, \quad 48, \quad 50, \quad 53, \quad 56

2Split the numbers into two parts; the last part must be one digit only.

The numbers in the data will split into tens and ones, so 35 will be 3 and 5 ( 3 represents 30 or 3 tens, and 5 is 5 ones).

3Put the values into the diagram and create a key.

Example 2: three digit numbers

The data below shows the length in centimeters of 13 long jumps on a 9 th grade sports day.

153, 144, 148, 140, 149, 145, 144, \\\\ \quad 142, 158, 135, 140, 139, 160.

Draw an ordered stem and leaf plot for the following set of data. Remember to include a suitable key.

Put the values into the diagram and create a key.

Example 3: decimal values

A group of students are making model gargoyles out of clay. The weight of each gargoyle is written below.

1.5 \, kg \quad 2.3 \, kg \quad 1.6 \, kg \quad 3.1 \, kg \quad 3.1 \, kg \\\\ 1.4 \, kg \quad 2.5 \, kg \quad 1.7 \, kg \quad 1.8 \, kg \quad 2.4 \, kg

Draw an ordered stem and leaf plot for data. Remember to include a suitable key.

Put the values into the diagram and create a key.

How to interpret a stem and leaf plot

In order to interpret a stem and leaf plot:

1. Read the question(s).
2. Use the information in the stem and leaf plot to answer the question(s).

Example 4: answering questions using a stem and leaf plot

The stem and leaf plot below shows the ages of a group of people at a party.

Use the information in the stem and leaf plot to answer the question(s).

(a) How many people are there in the group?

Count all the numbers in the leaf, so the answer is 10 people.

(b) What age is the youngest member of the group?

The first number in the leaf is the smallest value, so the answer is 35 years old.

(c) What age is the oldest member of the group?

The last number in the leaf is the largest value, so the answer is 56 years old.

(d) How many people are under 45?

Count all the values in the leaf that are less than 45, so the answer is 5 people.

(e) How many people are 45 and over?

Count all the people in the leaf that are 45 and above, so the answer is 5 people.

Example 5: calculating averages and the range from a stem and leaf plot

The stem and leaf plot below shows the weight of 10 puppies in kilograms.

Example 6: dual stem and leaf plot

This dual stem and leaf plot shows test scores for the students in Miss Thomas’ class.

Use the information in the stem and leaf plot to answer the question(s).

(a) What is the range of the boys’ scores?

The range is found by subtracting the lowest from the highest values on the ‘boys’ side of the diagram.

45-12=33

The range is 33.

(b) What is the median of the girls’ scores?

The median is the middle value on the girls’ side of the diagram. There are 11 values, so the middle value is found by adding 1 and dividing by 2. 11+1 \div 2=6 \text{th} place. The median is therefore 26.

(c) What is the mode for the boys’ scores?

The mode is the most common number.

Here, the mode is 38 as it is the most frequent value for the boys.

(d) Compare the median and range of the boys’ and girls’ scores.

You need to compare the median and range for each set of data:

The boys did better on average (median =33 ) than the girls (median =26 ).

The girls’ scores (range =42 ) were more spread out than the boys (range =33 ).

Teaching tips for stem and leaf plot

• Start with simple data values ( 2 digit numbers whole numbers) and a clear explanation. Begin by explaining what a stem and leaf plot is and how it represents a set of data. Emphasize that it shows individual values split into stems (tens digit) and leaves (ones digit).

• Offer multiple guided examples where students can practice creating stem and leaf plots. Provide data sets and worksheets that gradually increase in complexity.

• Connect stem and leaf plots to real-life scenarios to make them more relatable. Use examples such as test scores, measurements, or survey data to show how stem and leaf plots can be used to analyze and interpret information.

• Provide visual aids or display examples around the classroom for students to differentiate between graph types including stem and leaf plots, bar graphs, histograms, and dot plots, and box plots.

Easy mistakes to make

• Incorrectly reading the numbers in the diagram
  For example, for the following stem and leaf plot, the value of 13|5 is misinterpreted as the value 5, instead of 135.
  
  

  

• Miscounting
  A common error is to incorrectly count the numbers in a stem and leaf plot when calculating an average or range. It is a good idea to mark off each number to avoid missing a number.

• More than one digit for the leaf
  The leaf must only be one digit, otherwise the data can be greatly misinterpreted. Make sure that the smallest place value for the data is used for the leaf.

Related representing data lessons

• Representing data
• Pie chart 
• Quartile
• Box plot
• Interquartile range
• Scatterplot
• Two way tables
• Line graph
• Time series graph

The next lessons are

• Frequency table
• Frequency graph
• Sampling methods
• Represent and interpret data

Still stuck?

At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.

Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.

Find out how we can help your students achieve success with our math tutoring programs.