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Bivariate Data
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Secondary

Create and Interpret Back to back stem and leaf plots

Lesson
Practice
Lesson

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

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

    $\editable{}$ pounds

  2. What was the median ticket price at the international venue? Leave your answer to two decimal places if needed.

  3. What percentage of local ticket prices were cheaper than the international median?

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

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

QUESTION 2

The back-to-back stem plots show 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

  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

 

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