Year 9 - Statistics - Free practice

Year 9 Statistics Worksheets & Practice Tests

Choosing displays, comparing distributions, describing skew.

Quick answer

How do you choose the right graph for data in Year 9 Statistics?

Match the display to the data type and purpose. Use dot plots or stem-and-leaf plots for small datasets to show every value; histograms for large datasets to show distribution shape; and boxplots to summarise spread and compare two or more groups. Always justify your choice by the insight the display gives.

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Worked examples

Year 9 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 · Finding the median from a dot plot
A dot plot shows the number of hours of screen time per day for 8 students. The values in order are: 1, 2, 2, 3, 4, 5, 6, 6. Find the median.
Show worked solution
Key idea: For an even number of values, the median is the mean of the two middle values.
1. There are $n = 8$ values, already in order: 1, 2, 2, 3, 4, 5, 6, 6.
2. The two middle values are the 4th and 5th: $3$ and $4$ .
3. Median $= \dfrac{3 + 4}{2} = 3.5$ hours.
Answer: $3.5$ hours.
Example 2 · Finding the interquartile range
The ages (in years) of 8 members of a sports team are listed below.

$14,\; 15,\; 15,\; 16,\; 17,\; 18,\; 19,\; 21$

Find the interquartile range (IQR) of these ages.
Show worked solution
Key idea: Split the data into a lower half and an upper half, then find the median of each half.
1. There are $n = 8$ values in order: 14, 15, 15, 16, 17, 18, 19, 21.
2. Lower half (first 4 values): 14, 15, 15, 16 $\Rightarrow Q_1 = \dfrac{15 + 15}{2} = 15$ .
3. Upper half (last 4 values): 17, 18, 19, 21 $\Rightarrow Q_3 = \dfrac{18 + 19}{2} = 18.5$ .
4. $\text{IQR} = Q_3 - Q_1 = 18.5 - 15 = 3.5$ years.
Answer: $3.5$ years.
Example 3 · Identifying an outlier in a real-life context
A school canteen records the number of sandwiches sold each day for 8 days.

$18,\; 21,\; 22,\; 24,\; 25,\; 26,\; 27,\; 56$

A value is an outlier if it is more than $1.5 \times \text{IQR}$ above $Q_3$ or below $Q_1$ . Find the lower and upper outlier boundaries, then state which value is the outlier.
Show worked solution
Key idea: Calculate $Q_1$ , $Q_3$ and the IQR, then apply the outlier rule.
1. Lower half (first 4 values): 18, 21, 22, 24 $\Rightarrow Q_1 = \dfrac{21 + 22}{2} = 21.5$ .
2. Upper half (last 4 values): 25, 26, 27, 56 $\Rightarrow Q_3 = \dfrac{26 + 27}{2} = 26.5$ .
3. $\text{IQR} = 26.5 - 21.5 = 5$ .
4. Lower boundary: $Q_1 - 1.5 \times \text{IQR} = 21.5 - 7.5 = 14$ . Upper boundary: $Q_3 + 1.5 \times \text{IQR} = 26.5 + 7.5 = 34$ .
5. The value $56$ is above $34$ , so $56$ is the outlier.
Answer: $56$ sandwiches is the outlier.

Common mistakes

Where students usually lose marks

Including the median in both halves when finding quartiles

Data: 14, 15, 16, 17, 18, 19, student uses 14, 15, 16, 17 as the lower half and 16, 17, 18, 19 as the upper half.

When the data set has an even number of values, split it cleanly into a lower half and an upper half with no overlap. Neither half should contain values from the other.

Forgetting to sort the data before finding the median or quartiles

Data given as 5, 1, 8, 3, student writes Q1 = 5 because it is the first value listed.

Always arrange the data in ascending order before locating the median, Q1 or Q3. The order the values are listed in a question is not always sorted.

Subtracting the wrong way for IQR or range

$\text{IQR} = Q_1 - Q_3 = 15 - 18.5 = -3.5$

The IQR is always $Q_3 - Q_1$ (larger minus smaller), so it must be a positive number. If your answer is negative, you have subtracted in the wrong order.

Using the wrong formula for the outlier boundary

Upper boundary $= Q_3 + \text{IQR} = 26.5 + 5 = 31.5$ (leaving out the factor of 1.5).

The outlier rule multiplies the IQR by $1.5$ before adding or subtracting. Always use $Q_3 + 1.5 \times \text{IQR}$ for the upper boundary and $Q_1 - 1.5 \times \text{IQR}$ for the lower boundary.

Try one yourself

Your turn

A class of 25 students recorded how many hours they spent on screens last weekend. The results are listed below.

Hours	Frequency
0	2
1	3
2	5
3	7
4	5
5	2
6	1

What is the interquartile range (IQR) of this dataset?

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About this worksheet

Why we built it

Year 9 statistics is about interpretation - choosing the right display for a dataset, describing whether it's skewed or symmetric, and comparing two datasets fairly. These worksheets practise exactly that judgment.

What's covered

Sub-skills your student will practise

✓Choosing between histograms, stem-and-leaf, dot plots, boxplots
✓Describing shape (symmetric, skewed, bi-modal)
✓Comparing two distributions using summary stats
✓Sampling and its effect on results
✓Interpreting survey data for bias

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Frequently asked

Questions parents ask about statistics

What's a skewed distribution?

A distribution where one tail is longer than the other. Right-skewed (positive skew) has a longer right tail - household incomes are like this. Left-skewed has a longer left tail. Symmetric distributions have neither.

When does Year 9 use a boxplot vs a histogram?

Histograms show the full shape of a distribution. Boxplots (formally introduced in Year 10) show the five-number summary. Year 9 uses dot plots, stem-and-leaf, and histograms.

What does 'bimodal' mean?

A distribution with two peaks. Often indicates two underlying groups in the data - say, men's and women's heights combined. Recognising bimodality is part of Year 9 distribution description.

What's a fair sampling method?

Random sampling where every member of the population has an equal chance of selection. Year 9 also covers stratified sampling (sampling proportionally from subgroups) and systematic sampling (every nth member).

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