Year 9 - Comparing data sets - Free practice

Year 9 Comparing Data Sets Worksheets & Practice

Read, draw and describe comparative displays. Worked solutions every time, free.

Quick answer

How do you compare data sets in Year 9 maths?

Compare data sets by displaying them side by side using back-to-back stem-and-leaf plots or parallel box plots, then describe each distribution's shape (symmetric, skewed or bi-modal), centre (median) and spread (IQR or range). For example, if one group's median is 65 and another's is 80, you can conclude the second group typically scored higher.

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Six questions across Foundation, Standard and Extension, with full worked solutions, written to the Australian Curriculum.

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Worked examples

Year 9 comparing data sets: worked examples

Three examples, from a standard question to a worded problem. Have a go at each one before you open the solution.

Example 1 · Reading a back-to-back stem-and-leaf plot
A back-to-back stem-and-leaf plot shows the scores of two groups of students on a quiz. The stems are in the middle, with Group A leaves on the left and Group B leaves on the right.

Group A Stem Group B
8 4 1 2 6
9 5 3 1 2 0 3 7
7 2 3 1 5 8

Find the median score for Group B.
Show worked solution
Key idea: In a stem-and-leaf plot, each leaf is combined with its stem to form a data value. Read Group B leaves from left to right.
1. List Group B values in order: 12, 16, 20, 23, 27, 31, 35, 38
2. There are $8$ values, so the median is the mean of the 4th and 5th values.
3. The 4th value is $23$ and the 5th value is $27$ .
  $\text{Median} = \frac{23 + 27}{2} = \frac{50}{2} = 25$ Answer: The median score for Group B is $25$ .
Example 2 · Finding the IQR from a data set
Two basketball players recorded their points scored in $8$ games each.

Player A: 5, 9, 12, 15, 18, 22, 25, 28

Player B: 3, 7, 10, 14, 19, 21, 26, 30

Find the interquartile range (IQR) for each player, then find the difference between their IQRs.
Show worked solution
Key idea: With $8$ values, split into a lower half (first 4) and upper half (last 4). $Q_1$ is the median of the lower half and $Q_3$ is the median of the upper half.
1. Player A lower half: 5, 9, 12, 15 and upper half: 18, 22, 25, 28.
  $\begin{gathered}Q_1 = \frac{9+12}{2} = 10.5, Q_3 = \frac{22+25}{2} = 23.5 \\ \text{IQR}_A = 23.5 - 10.5 = 13\end{gathered}$
2. Player B lower half: 3, 7, 10, 14 and upper half: 19, 21, 26, 30.
  $\begin{gathered}Q_1 = \frac{7+10}{2} = 8.5, Q_3 = \frac{21+26}{2} = 23.5 \\ \text{IQR}_B = 23.5 - 8.5 = 15\end{gathered}$
3. Difference between IQRs: $15 - 13 = 2$ .
Answer: The difference between the IQRs is $2$ .
Example 3 · Comparing data sets in a real-life context
A gym tracks the number of minutes two groups of members spend exercising in a week. The data for $8$ members in each group is listed below.

Group A: 20, 35, 40, 45, 50, 60, 65, 75

Group B: 15, 25, 30, 45, 55, 70, 80, 90

Find the median for each group, then find the difference between the two medians.
Show worked solution
Key idea: With $8$ values, the median is the mean of the 4th and 5th values.
1. Group A values are already in order: 20, 35, 40, 45, 50, 60, 65, 75.
  $\text{Median}_A = \frac{45 + 50}{2} = \frac{95}{2} = 47.5$
2. Group B values are already in order: 15, 25, 30, 45, 55, 70, 80, 90.
  $\text{Median}_B = \frac{45 + 55}{2} = \frac{100}{2} = 50$
3. Difference between medians: $50 - 47.5 = 2.5$ .
Answer: The difference between the two medians is $2.5$ minutes.

Group A	Stem	Group B
8 4	1	2 6
9 5 3 1	2	0 3 7
7 2	3	1 5 8

Common mistakes

Where students usually lose marks

Reading leaves in the wrong direction

Group A leaf row '9 5 3 1 | 2' is read as 29, 25, 23, 21 instead of 21, 23, 25, 29.

For the left-hand group in a back-to-back plot, always read the leaves from the stem outward (right to left), then list the values from smallest to largest to find the median or IQR correctly.

Including the median value in both halves when finding quartiles

For the data set 3, 7, 11, 15, 19, 23, a student includes 11 and 15 in both halves when finding Q1 and Q3.

With an even number of values, split the list exactly in half. The lower half is the first half of the list and the upper half is the second half. No value appears in both halves.

Confusing IQR with range

IQR = highest value − lowest value = 28 − 5 = 23.

The range uses the maximum and minimum of the whole data set. The IQR uses only $Q_3$ and $Q_1$ : $\text{IQR} = Q_3 - Q_1$ . The IQR measures the spread of the middle $50\%$ of the data.

Forgetting to order the data before finding the median or quartiles

For 15, 3, 9, 22, 7, 18, a student takes Q1 = 9 without sorting first.

Always arrange all values from smallest to largest before finding the median, Q1 or Q3. Skipping this step produces incorrect quartiles and an incorrect IQR.

Try one yourself

Your turn

The results of a fitness test for two classes are summarised below.

	Class A	Class B
Minimum	42	38
Lower quartile ( $Q_1$ )	55	60
Median	68	74
Upper quartile ( $Q_3$ )	76	85
Maximum	90	97

What is the interquartile range (IQR) of Class B?

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About this worksheet

Why we built it

Comparing data sets is where Year 9 students move beyond single graphs and start placing two or more distributions side by side to spot patterns and differences. These worksheets build skills from reading back-to-back stem-and-leaf plots and parallel box plots through to describing shape in precise terms like symmetric, skewed and bi-modal, with fully worked solutions so students can check every step of their reasoning.

What's covered

Sub-skills your student will practise

✓Reading and drawing back-to-back stem-and-leaf plots
✓Constructing and interpreting parallel box plots
✓Describing distribution shape: symmetric, skewed, bi-modal
✓Comparing centre and spread across two or more data sets
✓Identifying outliers in comparative displays
✓Writing justified conclusions using data as evidence

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Frequently asked

Questions parents ask about comparing data sets

What does it mean for a distribution to be skewed or symmetric?

A symmetric distribution has data spread roughly evenly around the centre, like a hill. A skewed distribution has a longer tail on one side, pulling the mean away from the median. Students need to spot this from stem-and-leaf plots and box plots.

What is a bi-modal distribution and how do students identify one?

Bi-modal means the data has two distinct peaks or clusters rather than one. On a dot plot or histogram it looks like two humps. Students learn to recognise this pattern and explain what it might mean in context.

How are back-to-back stem-and-leaf plots different from ordinary ones?

A back-to-back plot shares one central stem column, with one data set reading left and the other reading right. This layout makes it easy to compare two groups at a glance, and Year 9 students are expected to draw and interpret them.

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