071. Stem-and-Leaf Plots

Learning Intentions

• interpret a stem-and-leaf plot
• represent data in a stem-and-leaf plot

Pre-requisite Summary

• Understand that numerical data can be organised to make patterns easier to see
• Be able to order a set of whole numbers from smallest to largest
• Understand place value, especially tens and ones
• Know that a data display should show each value clearly and accurately
• Be able to identify the smallest and largest values in a data set
• Understand that repeated values can occur in a data set

Worked Examples

Worked Example 1

A stem-and-leaf plot is shown below:

a) List the data values represented.
b) State the smallest and largest values.
c) How many data values are there?

Worked Example 2

A stem-and-leaf plot is shown below:

a) Interpret the plot by listing the data values.
b) State how many values are in the teens.
c) State the mode.

Worked Example 3

Represent the following data in a stem-and-leaf plot:
$12,15,19,21,23,25,31,36$

Worked Example 4

Represent the following data in a stem-and-leaf plot:
$4,7,8,11,13,13,18,22,24$

Worked Example 5

A stem-and-leaf plot is shown below:

a) Interpret the plot by writing the ordered data.
b) State the median.
c) State the range.

Worked Example 6

Represent the following data in a stem-and-leaf plot and then interpret it:
$16,18,21,22,22,25,27,30,34$
a) Draw the plot.
b) Identify the mode.
c) State the number of data values.

Problems

Problem 1

A stem-and-leaf plot is shown below:

a) List the data values represented.
b) State the smallest and largest values.
c) How many data values are there?

Problem 2

A stem-and-leaf plot is shown below:

a) Interpret the plot by listing the data values.
b) State how many values are less than $10$.
c) State the mode.

Problem 3

Represent the following data in a stem-and-leaf plot:
$11,14,18,20,22,27,33,35$

Problem 4

Represent the following data in a stem-and-leaf plot:
$3,6,9,12,14,14,17,21,25$

Problem 5

A stem-and-leaf plot is shown below:

a) Interpret the plot by writing the ordered data.
b) State the median.
c) State the range.

Problem 6

Represent the following data in a stem-and-leaf plot and then interpret it:
$15,17,20,23,23,26,28,31,35$
a) Draw the plot.
b) Identify the mode.
c) State the number of data values.

Exercises

Understanding and Fluency

1. Interpret the stem-and-leaf plot:

   $$\begin{array}{cccc}1& 2& 5& 8\\ 2& 1& 4& 7\end{array}$$

   a) List the data values.
   b) State the smallest value.
   c) State the largest value.

2. Interpret the stem-and-leaf plot:

   $$\begin{array}{ccccc}0& 3& 6& 8& 9\\ 1& 2& 5& 7& 7\end{array}$$

   a) List the data values.
   b) How many values are shown?
   c) State the mode.

3. Represent the data in a stem-and-leaf plot:
   a) $12,14,17,19,21,26$
   b) $5,8,11,13,16,18$

4. Represent the data in a stem-and-leaf plot:
   a) $22,24,25,28,31,34$
   b) $7,9,12,15,15,19$

5. Interpret the stem-and-leaf plot:

   $$\begin{array}{ccccc}1& 0& 4& 6& 9\\ 2& 2& 5& 7\\ 3& 1\end{array}$$

   a) Write the data in order.
   b) State the median.
   c) State the range.

6. Interpret the stem-and-leaf plot:

   $$\begin{array}{ccccc}2& 1& 3& 6& 8\\ 3& 0& 4& 4\\ 4& 2\end{array}$$

   a) Write the data in order.
   b) State the mode.
   c) State the number of data values.

7. Represent the data in a stem-and-leaf plot, then answer the questions:
   a) $14,16,18,20,21,21,24,29$
   b) State the mode.
   c) State the largest value.

8. Represent the data in a stem-and-leaf plot, then answer the questions:
   a) $3,7,11,11,15,18,22,25,27$
   b) State the median.
   c) State the range.

Reasoning

9. Explain why the leaves in each row of a stem-and-leaf plot should be written in ascending order.

10. A student reads the row

as $2,3,5,8$. Explain the mistake.

11. Explain why a stem-and-leaf plot is useful for showing the actual data values.

12. A student places the number $27$ in the row $7\mid 2$. Explain why this is incorrect.

Problem-solving

13. The test scores are $11,13,15,18,21,21,24,27$.
    a) Draw a stem-and-leaf plot.
    b) State the mode.
    c) State the range.

14. The numbers of books read are $4,6,9,12,14,14,17,23$.
    a) Draw a stem-and-leaf plot.
    b) State the median.
    c) State how many values are in the teens.

15. The daily temperatures are $15,17,19,20,22,22,25,28,31$.
    a) Draw a stem-and-leaf plot.
    b) State the mode.
    c) State the number of temperatures above $20$.

16. The ages are $8,9,11,13,13,16,18,21,24$.
    a) Draw a stem-and-leaf plot.
    b) State the median.
    c) State the range.

17. A class records the times in minutes: $12,14,14,15,18,22,24,27,29$.
    a) Draw a stem-and-leaf plot.
    b) State the mode.
    c) State the largest time.

18. The scores in a game are $3,5,8,11,11,14,17,19,23,25$.
    a) Draw a stem-and-leaf plot.
    b) State the number of scores in the twenties.
    c) State the median.

Potential Misunderstandings

• Students may confuse the stem with the leaf and reverse the digits
• Students may not realise that each leaf represents a separate data value
• Students may forget to order the leaves in ascending order
• Students may join leaves together and treat them as one number instead of separate values
• Students may read $2\mid 4$ as $2.4$ instead of $24$ in this context
• Students may place a value in the wrong stem because of weak place-value understanding
• Students may think a stem-and-leaf plot only shows grouped data rather than the actual values
• Students may make errors finding the median or range if they do not interpret the plot correctly

Next: 072e. Pie Charts and Divided Bar Graphs