Interpret stem-and-leaf plots

key notes:

1. What is a Stem-and-Leaf Plot?

  • A stem-and-leaf plot is a way to organize and display data so that it is easy to read and analyze.
  • It shows data in numerical order and breaks each number into two parts:
    • The stem is the leading digit(s) (e.g., tens place).
    • The leaf is the trailing digit(s) (e.g., ones place).

2. Understanding the Structure

  • The stem is listed vertically on the left side.
  • The leaves are listed next to their corresponding stems.
  • Example:

Stem | Leaf
2 | 1, 3, 5
3 | 0, 2, 8
4 | 5, 6

In this example, the numbers are 21, 23, 25, 30, 32, 38, 45, and 46.

3. How to Read a Stem-and-Leaf Plot

  • Each stem represents a group of numbers.
  • The leaves represent the individual numbers within that group.
  • Example: The stem “2” with leaves “1, 3, 5” represents the numbers 21, 23, and 25.

3. How to Read a Stem-and-Leaf Plot

  • Each stem represents a group of numbers.
  • The leaves represent the individual numbers within that group.
  • Example: The stem “2” with leaves “1, 3, 5” represents the numbers 21, 23, and 25.

4. Interpreting Data

  • Sorting data: Stem-and-leaf plots help organize data in ascending or descending order.
  • Counting data: You can count how many data points are in each group.
  • Finding the range: You can find the smallest and largest values easily from the plot.
  • Identifying patterns: You can see clusters, gaps, and the spread of data points.

Learn with an example

1) At a candy factory, butterscotch candies were packaged into bags of different sizes.

Butterscotch candies per bag
 Stem  Leaf 
3     3 8 9
4     4
5     1
6     0 4
7    
8    
9     0

How many bags had fewer than 94 butterscotch candies?

  • 6
  • 4
  • 8
  • 7
  • Count all the leaves in the rows with stems 3, 4, 5, 6, 7, and 8.
Butterscotch candies per bag
 Stem  Leaf 
3     3 8 9
4     4
5     1
6     0 4
7    
8    
9     0
  • In the row with stem 9, count all the leaves less than 4.
Butterscotch candies per bag
 Stem  Leaf 
3     3 8 9
4     4
5     1
6     0 4
7    
8    
9     0
  • You counted 8 leaves, which are blue in the stem-and-leaf plots above. 8 bags had fewer than 94 butterscotch candies.

2) A food magazine published a listing of local restaurant ratings.

Restaurant ratings
 Stem  Leaf 
1     2 8
2     2 5 9
3     0 1 3 5 6 8
4     3 7
5     0

How many restaurants were rated fewer than 35 points?

  • 7
  • 8
  • 5
  • 6
  • Count all the leaves in the rows with stems 1 and 2.
Restaurant ratings
 Stem  Leaf 
1     2 8
2     2 5 9
3     0 1 3 5 6 8
4     3 7
5     0
  • In the row with stem 3, count all the leaves less than 5.
Restaurant ratings
 Stem  Leaf 
1     2 8
2     2 5 9
3     0 1 3 5 6 8
4     3 7
5     0
  • You counted 8 leaves, which are blue in the stem-and-leaf plots above. 8 restaurants were rated fewer than 35 points.

3) A researcher recorded the number of cows on each farm in the county.

Cows per farm
 Stem  Leaf 
1     1 1 2 2 7
2     7
3     1 3
4     2 2
5    
6    
7     0 1 5 8
8     0 3 4 5 6 9
9     0 0

What is the smallest number of cows?

  • 7 cows
  • 11 cows
  • 10 cows
  • 9 cows
Cows per farm
 Stem  Leaf 
1     1 1 2 2 7
2     7
3     1 3
4     2 2
5    
6    
7     0 1 5 8
8     0 3 4 5 6 9
9     0 0
  • Look at the first row of the stem-and-leaf plot. The first row has the lowest stem. The stem for the first row is 1.
  • Now find the lowest leaf in the first row. The lowest leaf is 1.
  • The smallest number of cows has a stem of 1 and a leaf of 1. Write the stem first, then the leaf: 11.
  • The smallest number of cows is 11 cows.

Let’s practice!🖊️