We've already looked at how to display a data set in a stem-and-leaf plots. However, in this chapter, we're going to look at how to display two data sets simultaneously in a back-to-back stem-and-leaf plot. These types of stem and leaf plots are a great way to make comparisons between data sets.

Reading a back-to-back stem-and-leaf plot

Reading a back-to-back stem-and-leaf plot is very similar to a regular stem-and-leaf plot. The "stem" is used to group the scores and each "leaf" indicates the individual scores within each group.

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. In a back-to-back stem-and-leaf plot, one set of data is displayed on the left and one set of data is written on the right. The "leaf" values are still written in ascending order from the stem outwards.

Remember!

If you have to create your own stem-and-leaf plot, it's easier to write all your scores in ascending order before you start putting them into a stem and leaf plot.

Worked Examples

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 $4$4 $6$6 $7$7

$7$7

$3$3 $5$5 $6$6 $6$6 $7$7

$8$8

$2$2 $4$4 $4$4 $5$5 $7$7

$9$9

$1$1 $4$4 $6$6 $7$7 $9$9

$10$10

$4$4

Stem	Leaf
$6$6	$0$0 $7$7
$7$7	$0$0 $0$0 $3$3 $4$4
$8$8	$0$0 $5$5 $6$6 $6$6
$9$9	$1$1 $1$1 $3$3 $4$4 $6$6
$10$10	$1$1 $4$4 $4$4 $5$5 $6$6

Key: $1$1$\mid$∣$2$2$=$=$12$12

What was the most expensive ticket price at the international venue?

$\editable{}$ $dollars$
What was the median ticket price at the international venue? Leave your answer to two decimal places if needed.
What percentage of local ticket prices were cheaper than the international median?
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
A
II and III
B
None of the statements are correct.
C
III only
D
II only
E
I only
F

Outcomes

S5-1

Plan and conduct surveys and experiments using the statistical enquiry cycle:– determining appropriate variables and measures;– considering sources of variation;– gathering and cleaning data;– using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets;– comparing sample distributions visually, using measures of centre, spread, and proportion;– presenting a report of findings

S5-2

Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings

Create and Interpret Back to back stem and leaf plots