topic badge

10.085 Stem and leaf plots

Lesson

 

Stem-and-leaf plot

A stem-and-leaf plot, or stemplot, is used for organising and displaying numerical data. It is appropriate for small to moderately sized data sets.

In a stem-and-leaf plot, the right-most digit in each data value is split from the other digits, to become the 'leaf'. The remaining digits become the 'stem'.

All of the values in a stem-and-leaf plot are arranged in ascending order (from lowest to highest). For this reason, it is often called an ordered stem-and-leaf plot.

The data values $10,13,16,21,26,27,28,35,35,36,41,41,45,46,49,50,53,56,58$10,13,16,21,26,27,28,35,35,36,41,41,45,46,49,50,53,56,58 are displayed in the stem-and-leaf plot below.

  • The stems are arranged in ascending order, to form a column, with the lowest value at the top 
  • The leaf values are arranged in ascending order, in rows, next to their corresponding stem 
  • A single vertical line separates the stem and leaf values 
  • There are no commas or other symbols between the leaves, only a space between them 
  • In order to correctly display the distribution of the data, the leaves must line up in imaginary columns, with each data value directly below the one above
  • A stem-and-leaf plot includes a key that describes the way in which the stem and the leaf combine to form the data value 

 

Back-to-back stem-and-leaf plots

Two sets of data can be displayed side-by-side using a back-to-back stem-and-leaf plot.

In the example below, the pulse rates of $18$18 students were recorded before and after exercise.

Reading a back-to-back stem-and-leaf plot is very similar to reading a regular stem-and-leaf plot.

Referring to the example above:

  • The central column displays the stems, with the leaf values on each side.
  • The values on the left are the pulse rates of the students before exercise, while the values on the right are their pulse rates after exercise.
  • In this example, the fourth row of the plot, $4$4 $3$3 $0$0 | $8$8 | $2$2 $2$2 $6$6, displays pulse rates of $80$80, $83$83 and $84$84 before exercise and pulse rates of $82$82, $82$82 and $86$86 after exercise. They are not necessarily the pulse rates of the same students. 
  • On both sides of the stem column, the leafs are displayed in ascending order with the lowest value closest to the stem. 
     
Remember!

To create a stem-and-leaf plot, it is usually easier to arrange all of the data values in ascending order, before ordering them in the plot.

 

Practice questions

Question 1

The data below shows the results of a survey conducted on the price of concert tickets locally and the price of the same concerts at an international venue.

Local International
Stem Leaf
$6$6 $0$0 $5$5 $5$5 $8$8
$7$7 $0$0 $5$5 $6$6 $7$7 $9$9
$8$8 $0$0 $1$1 $1$1 $4$4 $7$7
$9$9 $0$0 $2$2 $3$3 $3$3 $3$3
$10$10 $9$9
 
Stem Leaf
$6$6 $3$3 $9$9
$7$7 $2$2 $4$4 $7$7 $7$7
$8$8 $0$0 $3$3 $4$4 $8$8
$9$9 $1$1 $1$1 $1$1 $2$2 $3$3
$10$10 $0$0 $1$1 $1$1 $3$3 $9$9
 
Key: $1$1$\mid$$2$2$=$=$12$12
  1. What was the most expensive ticket price at the international venue?

    $\editable{}$ dollars

  2. At the international venue, what percentage of tickets cost between $\$90$$90 and $\$110$$110 (inclusive)?

  3. At the local venue, what percentage of tickets cost between $\$90$$90 and $\$100$$100 (inclusive)?

QUESTION 2

The stem-and-leaf plot shows the number of pieces of paper used over several days by Maximilian’s and Charlie’s students.

Maximilian Stem Charlie
$7$7 $0$0 $7$7
$3$3 $1$1 $1$1 $2$2 $3$3
$8$8 $2$2 $8$8
$4$4 $3$3 $3$3 $2$2 $3$3 $4$4
$7$7 $6$6 $5$5 $4$4 $9$9
$3$3 $2$2 $5$5 $2$2
Key: $6\mid1\mid2$612 $=$= $16$16 and $12$12
  1. Which of the following statements are true?

    I. Maximilian's students did not use $7$7 pieces of paper on any day.

    II. Charlie's median is higher than Maximilian’s median.

    III. The median is greater than the mean in both groups.

    I and II

    A

    II and III

    B

    None of the statements are correct.

    C

    III only

    D

    II only

    E

    I only

    F

Outcomes

MS11-2

represents information in symbolic, graphical and tabular form

MS11-7

develops and carries out simple statistical processes to answer questions posed

What is Mathspace

About Mathspace