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Statistics
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New Zealand
Level 4

Create and interpret stem and leaf plots

Lesson
Practice
Lesson

Stem-and-leaf plots are a great way to display moderately sized data sets as they give a good overview of the shape of the data. This means we can identify any skew, outliers and/or clustering. Further, since each individual score is recorded in a stem-and-leaf plot, they also make it easy to identify the mode in a data set.

 

Reading a stem-and-leaf plot

In a stem-and-leaf plot, the last digit in a score is split from the other digits in the score. The last digit becomes the "leaf" and the other digits become the "stem."

The scores $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.

Notice how the stem is a column and the stem values are written downwards in that column. The leaf values are written across in the rows corresponding to the stem value. The leaf values are written in ascending order from the stem outwards.

The stem is used to group the scores and each leaf indicates the individual scores within each group.

 

Notice that all the scores are written in ascending order. When creating stem-and-leaf plots it can be easier to first write all the scores in order from smallest to largest.

Now let's look at some stem-and-leaf questions!

 

Worked Examples

Question 1

Which of the following is true of a stem-and-leaf plot?

Stem Leaf
$0$0 $7$7
$1$1  
$2$2  
$3$3 $1$1 $3$3 $3$3 $3$3
$4$4 $1$1 $2$2 $3$3 $4$4 $9$9
$5$5 $1$1 $2$2 $4$4 $5$5 $5$5
$6$6 $0$0
 
Key: $1$1$\mid$∣$2$2$=$=$12$12
A stem-and-leaf plot is displayed. The plot is divided into two columns: "Stem" on the left, and "Leaf" on the right. The "Stem" column lists the digits in the order 0, 1, 2, 3, 4, 5, and 6, starting with 0 at the topmost column. Each digit in the "Stem" column is paired with aligned with a group of digits in the "Leaf" column. For stem 0, the leaf is 7. For stems 1 and 2, there are no leaves. For stem 3, the leaves are 1, 3, 3, and 3. For stem 4, the leaves are 1, 2, 3, 4, and 9. For stem 5, the leaves are 1, 2, 4, 5, and 5. For stem 6, the leaf is 0. Below the plot is a row named "Key," which explains the notation. On the "Key" row, it is written that 1 | 2 = 12.

  1. The scores are ordered.

    A

    A stem-and-leaf plot does not give an idea of outliers and clusters.

    B

    It is only appropriate for data where scores have high frequencies.

    C

    The individual scores cannot be read on a stem-and-leaf plot.

    D

QUESTION 2

The stem-and-leaf plot below shows the age of people to enter through the gates of a concert in the first $5$5 seconds.

Stem Leaf
$1$1 $1$1 $2$2 $4$4 $5$5 $6$6 $6$6 $7$7 $9$9 $9$9
$2$2 $2$2 $3$3 $5$5 $5$5 $7$7
$3$3 $1$1 $3$3 $8$8 $9$9
$4$4  
$5$5 $8$8
 
Key: $1$1$\mid$∣$2$2$=$=$12$12
years old

  1. How many people passed through the gates in the first $5$5 seconds?

  2. What was the age of the youngest person?

    The youngest person was $\editable{}$ years old.

  3. What was the age of the oldest person?

    The oldest person was $\editable{}$ years old.

  4. What proportion of the concert-goers were under $20$20 years old?

Outcomes

S4-1

Plan and conduct investigations using the statistical enquiry cycle:– determining appropriate variables and data collection methods;– gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends;– comparing distributions visually;– communicating findings, using appropriate displays.

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