GCSE Foundation — Statistics
This is the statistics practice for GCSE Foundation, the content area that carries 7.5% of the paper. The 5 statements below are the whole of statistics for this tier — nothing outside them can be asked, which makes the revision list finite. The list includes sampling and inference about populations, tables, charts and diagrams for data, averages, spread and comparing distributions, describing a population with statistics and scatter graphs, correlation and lines of best fit. Everything on this page is Foundation content, which means a Higher student needs it too — Higher is Foundation plus more, not instead of. With 50% AO1 and 50% across AO2 and AO3, fluency alone is not enough — the paper repeatedly asks what your answer means. Questions here turn up on all three papers, which means you need the written method and the calculator method.
- S1 — Sampling and inference about populations
- S2 — Tables, charts and diagrams for data
- S4 — Averages, spread and comparing distributions
- S5 — Describing a population with statistics
- S6 — Scatter graphs, correlation and lines of best fit
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Statistics at GCSE Foundation: the 5 DfE statements
Every question on this site is filed against one of these statements. Pick one to practise it on its own.
Sample statistics questions for GCSE Foundation
- The marks scored by four pupils in a quiz were 8, 8, 8, 8. Work out the mean, the median and the mode of these marks.(a)mean = 2, median = 8, mode = 8(b)mean = 8, median = 8, mode = 4(c)mean = 8, median = 8, mode = 8(d)mean = 32, median = 8, mode = 8
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mean = 8, median = 8, mode = 8 — Method: work out each measure separately — the mean is the total divided by how many values there are, the median is the middle value once the data are in order, and the mode is the value that occurs most often. Working: the total is 8 + 8 + 8 + 8 = 32 and there are 4 marks, so the mean is 32 ÷ 4 = 8; in order the marks read 8, 8, 8, 8, and the mean of the middle pair is (8 + 8) ÷ 2 = 8; the value 8 occurs 4 times and no other value occurs at all, so the mode is 8. Answer: mean = 8, median = 8, mode = 8 — when every value in a data set is the same, all three measures of central tendency take that value. The distractors: a mean of 32 comes from stopping at the total and never dividing by 4; a mode of 4 comes from writing down how many times 8 occurs instead of the value that occurs; a mean of 2 comes from dividing a single value, 8, by the 4 marks instead of dividing the total by 4. - The mean of 5 numbers is 8. Work out the total of the 5 numbers.(a)40(b)1.6(c)13(d)8
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40 — Method: the mean is the total divided by how many values there are, so rearranging gives total = mean × number of values. Working: the mean is 8 and there are 5 numbers, so the total is 8 × 5 = 40. Answer: 40, and checking, 40 ÷ 5 = 8, which is the mean given. The distractors: 13 comes from adding the mean and the count, 8 + 5, instead of multiplying them; 1.6 comes from dividing the mean by the count, 8 ÷ 5, which reverses the relationship; 8 comes from quoting the mean itself as the total, which is only true when there is a single number. - Work out the median of these five numbers: 2, 4, 7, 12, 26(a)24(b)14(c)7(d)10.2
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7 — Method: the median is the middle value when the data are written in order of size, and with an odd number of values there is exactly one middle value. Working: the numbers are already in order, 2, 4, 7, 12, 26, and there are 5 of them, so the middle position is the third and the value sitting there is 7. Answer: 7, with two values below it and two above it. The distractors: 10.2 comes from working out the mean, 51 ÷ 5, instead of the median; 14 comes from taking the value halfway between the smallest and the largest, (2 + 26) ÷ 2; 24 comes from working out the range, 26 − 2, which measures spread rather than centre. - A shop sold seven pairs of shoes in these sizes: 4, 4, 5, 6, 6, 6, 9. Write down the modal size.(a)3(b)9(c)4(d)6
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6 — Method: the mode, or modal value, is the value that occurs most often in the data set, and it is a value from the data rather than a count. Working: size 4 occurs twice, size 5 occurs once, size 6 occurs three times and size 9 occurs once, so the highest frequency is three and the size it belongs to is 6. Answer: 6. The distractors: 3 comes from writing down the frequency of the most common size instead of the size itself; 9 comes from picking the largest size in the list, which confuses the mode with the maximum; 4 comes from stopping at the first size that repeats rather than checking which size repeats most often. - A shop recorded the number of books it sold on five days: 100, 40, 70, 20, 60. Work out the range of the numbers of books sold.(a)100(b)58(c)80(d)60
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80 — Method: the range is a measure of spread and is found by subtracting the smallest value from the largest. Working: the largest number sold is 100 and the smallest is 20, so the range is 100 − 20 = 80. Answer: 80. The distractors: 100 comes from writing down the largest value and never subtracting the smallest; 60 comes from working out the median, the middle value of 20, 40, 60, 70, 100, instead of the range; 58 comes from working out the mean, 290 ÷ 5, which measures centre rather than spread.
Frequently asked questions
How much of the GCSE Foundation paper is statistics?
7.5% of the total marks, and the three papers each carry an equal share of the qualification, so it is spread across all of them rather than concentrated in one.
How many topics are there in statistics at GCSE Foundation?
5 DfE content statements, coded S1 to S6 within this area. Every question in the bank is tagged to one of them.
Is any statistics content on this page Higher only?
No. Foundation pages only show statements a Foundation entry may be asked. The Higher-only statistics material is on the GCSE Higher page for this area.
Can I use a calculator for statistics questions?
Paper 1 is non-calculator; Papers 2 and 3 allow one. Of the 5 statements in this area, 0 are naturally non-calculator and 0 naturally calculator, with the rest workable either way — so practise both.
What kind of marks does statistics carry?
The GCSE Foundation split is 50% AO1 (use and apply standard techniques), 25% AO2 (reason, interpret and communicate) and 25% AO3 (solve problems in and out of context). Questions in this area are set across all three.
Are these past paper questions?
No. Every question at /gcse-foundation is original, written to the DfE content statements and checked before it is published. We do not host past papers or mark schemes.
Do I need an account?
No — you can start practising straight away. Progress is saved automatically in your browser.
Is it free?
Yes. The questions, worked answers and printable worksheets are all free, with no adverts.
Tips for statistics at GCSE Foundation
- Know the three averages: the mean (total divided by how many), the median (the middle value once the data is in order) and the mode (the most common value), and know when each is the right one.
- Always put the data in order before finding the median. With an even number of values the median is the mean of the two middle values.
- The range is the largest value minus the smallest. It measures spread — how widely the data is scattered.
- In a frequency table the mean is Σ(value × frequency) divided by the total frequency. Do not forget to weight each value by its frequency.
- An outlier pulls the mean a long way but barely moves the median, so with outliers the median usually represents the data better.
Common mistakes (and how to avoid them)
- Finding the median without ordering the data first — taking the middle of the list as given.
- With an even number of values, picking one middle value instead of averaging the two middle values.
- Working out a plain mean of the values in a frequency table without weighting by the frequencies.
- Working out the range as largest plus smallest instead of largest minus smallest.
Worked examples
- Mean: (70 + 85 + 90 + 85 + 60) ÷ 5 = 390 ÷ 5 = 78.
- Order the data: 60, 70, 85, 85, 90.
- There are 5 values (odd), so the median is the third value: 85.
- Order from smallest to largest: 1, 2, 4, 5, 7, 9.
- There are 6 values (even), so the middle two are the third and fourth: 4 and 5.
- Median = (4 + 5) ÷ 2 = 4.5.
- Weighted total: 2 × 3 + 5 × 4 + 8 × 3 = 6 + 20 + 24 = 50.
- Total frequency: 3 + 4 + 3 = 10.
- Mean = 50 ÷ 10 = 5.
Statistics turns a pile of numbers into a story. At Foundation you not only calculate the mean, median, mode and range, you decide which average is fair for the data in front of you and how an outlier distorts the picture. Order the data before finding the median, weight by frequency in a table, and read the scale on every chart before you compare bars. Those habits are worth marks on the paper and are the same habits that protect you from misleading graphs in the news.
More GCSE Foundation maths:
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