Year 7 - Statistics - Free practice

Year 7 Statistics Worksheets & Practice Tests

Mean, median, mode, range - the four numbers everyone needs.

Quick answer

How do you find the mean, median, mode and range?

The mean is the sum of all values divided by the count. The median is the middle value when data is ordered (or the average of the two middle values if there is an even count). The mode is the most frequent value. The range is the maximum minus the minimum. For example, in {2, 4, 4, 6, 9}: mean = 5, median = 4, mode = 4, range = 7.

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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 7 statistics: 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 · Calculating the mean
Find the mean of the following data set: $8, 3, 6, 5, 8.$
Show worked solution
Key idea: The mean is the sum of all values divided by the number of values.
1. Count the values: there are $5$ values.
2. Add all values: $8 + 3 + 6 + 5 + 8 = 30$
3. Divide the sum by the count: $\text{Mean} = \frac{30}{5} = 6$
Answer: The mean is $6.$
Example 2 · Median, mode and range
Find the median, mode and range of this data set: $4, 7, 2, 7, 9, 1, 4, 7, 3.$
Show worked solution
Key idea: Sort the data first, then apply each definition.
1. Sort the values in ascending order: $1, 2, 3, 4, 4, 7, 7, 7, 9$
2. Median: There are $9$ values (odd count), so the median is the $5$ th value: $\text{Median} = 4.$
3. Mode: The value that appears most often is $7$ (appears $3$ times): $\text{Mode} = 7.$
4. Range: $\text{Range} = 9 - 1 = 8$
Answer: Median $= 4$ , Mode $= 7$ , Range $= 8.$
Example 3 · Comparing two data sets
Two students each recorded how many pages they read per day for $6$ days. Anika's results were: $12, 20, 15, 18, 10, 13.$ Ben's results were: $8, 25, 14, 22, 9, 16.$ Calculate the mean and range for each student, and use these to compare their reading habits.
Show worked solution
Key idea: The mean compares typical values; the range compares spread.
1. Anika's mean: $\frac{12 + 20 + 15 + 18 + 10 + 13}{6} = \frac{88}{6} \approx 14.7 \text{ pages}$
2. Ben's mean: $\frac{8 + 25 + 14 + 22 + 9 + 16}{6} = \frac{94}{6} \approx 15.7 \text{ pages}$
3. Anika's range: $20 - 10 = 10$
4. Ben's range: $25 - 8 = 17$
5. Ben reads slightly more pages per day on average (about $15.7$ compared to Anika's $14.7$ ), but Anika is more consistent because her range ( $10$ ) is much smaller than Ben's ( $17$ ).
Answer: Anika: mean $\approx 14.7$ , range $= 10$ . Ben: mean $\approx 15.7$ , range $= 17$ . Ben reads more on average but is less consistent.

Common mistakes

Where students usually lose marks

Forgetting to sort before finding the median

Median of 3, 7, 1, 5, 9 is the 3rd value $= 1$ (unsorted).

Always sort the data in ascending order first. The median of 1, 3, 5, 7, 9 is the 3rd value, which is $5.$

Even data count: taking one middle value instead of averaging two

Median of 2, 5, 8, 11 is $5$ (just the 2nd value).

When there is an even number of values, the median is the average of the two middle values. Here it is $\frac{5 + 8}{2} = 6.5.$

Dividing by the number of different values instead of the total count for the mean

Mean of 4, 4, 6, 8 is $\frac{4 + 6 + 8}{3} = 6$ (ignoring the repeated $4$ ).

Every value in the list counts, including repeats. The correct mean is $\frac{4 + 4 + 6 + 8}{4} = 5.5.$

Confusing range with the list of all values

Range of $3, 7, 10$ is $3, 7, 10.$

The range is a single number: subtract the smallest value from the largest. Here, $\text{range} = 10 - 3 = 7.$

Try one yourself

Your turn

The ages (in years) of eight players on a basketball team are: 14, 15, 13, 16, 15, 14, 15, 12. What is the median age?

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About this worksheet

Why we built it

Year 7 statistics centres on calculating the mean, median, mode and range from raw data and from frequency tables. These worksheets give your student varied datasets so they can't just memorise one example - they have to understand each measure.

What's covered

Sub-skills your student will practise

✓Mean from a list of numbers
✓Median (with both odd and even data counts)
✓Mode (and what to do when there are two modes)
✓Range
✓Comparing two datasets using their summary statistics

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Frequently asked

Questions parents ask about statistics

What's the difference between mean, median, and mode?

Mean is the average (add up all values, divide by the count). Median is the middle value when the data is sorted. Mode is the most common value. Range is the difference between the largest and smallest.

When does median matter more than mean?

When the dataset has outliers - one very large or small value pulls the mean but not the median. For house prices or incomes, median is the more honest 'typical' value.

What if there's no mode?

If every value appears exactly once, the dataset has no mode. If two values tie for most frequent, the dataset is bimodal. Some questions specifically test these edge cases.

Do students need to draw graphs at Year 7 statistics?

Yes - dot plots and stem-and-leaf plots are introduced at Year 7, along with describing and comparing distributions. Boxplots and scatterplots arrive in Year 10.

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