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
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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.
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 | ||||||||||||||||||||||||||||||
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| Key: $1$1$\mid$∣$2$2$=$=$12$12 |
What was the most expensive ticket price at the international venue?
$\editable{}$ dollars
At the international venue, what percentage of tickets cost between $\$90$$90 and $\$110$$110 (inclusive)?
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$6∣1∣2 | $=$= | $16$16 and $12$12 |
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
AII and III
BNone of the statements are correct.
CIII only
DII only
EI only
F