GCSE Maths Statistics questions by topic

One hour of texting.

1. (a)Ten pupils sent 3, 7, 3, 9, 5, 3, 8, 2, 6 and 4 texts in an hour. Find the mode.[2]
2. (b)Find the median.[2]

How Year 7 gets to school.

1. (a)Of 30 pupils, 12 walk, 8 cycle, 6 take the bus and 4 come by car. Calculate the pie-chart angle for walking.[2]
2. (b)Calculate the angle for the bus.[2]

A library pictogram.

1. (a)In a pictogram one book icon stands for 4 books. Class 8B’s row shows 5½ icons. How many books did 8B read?[2]
2. (b)Class 8C read 34 books. How many icons (including parts) should their row show?[2]

The missing score.

1. (a)Five test scores have a mean of 14. Work out the total of the five scores.[2]
2. (b)Four of the scores are 12, 15, 9 and 18. Find the fifth score.[2]

Shoe sizes in a shop log.

1. (a)A shop logs shoe sizes: size 4 (5 sold), size 5 (8), size 6 (6) and size 7 (1). Write down the modal shoe size.[1]
2. (b)Work out the total number of shoes sold.[1]
3. (c)Work out the mean shoe size, to 2 decimal places.[2]

A pictogram counts library books.

1. (a)A pictogram uses one book icon for 4 books. Class A shows 3½ icons. Work out the books Class A read.[1]
2. (b)Class B shows 5 icons and Class C shows 2 icons. Work out the books read by B and C together.[2]
3. (c)Class D read 10 books. Write down how many icons that is.[1]

Pets in a class.

1. (a)25 pupils keep 0, 1, 2 or 3 pets, with frequencies 7, 10, 6 and 2. State the mode and the range of the number of pets.[2]
2. (b)Calculate the mean number of pets.[3]

Two cafés at lunchtime.

1. (a)Café P’s queue times, in minutes, were 4, 7, 5, 9 and 5. Calculate the mean.[2]
2. (b)Café Q’s times were 2, 11, 3, 8 and 6. Calculate the range of Q’s times.[1]
3. (c)Compare the two cafés’ queue times. Give two different comments.[2]

Plants and leaves.

1. (a)A scatter graph of the height of ten plants (5 cm to 25 cm) against their number of leaves shows points rising from bottom-left to top-right. Describe the correlation.[1]
2. (b)A line of best fit gives about 14 leaves for a 20 cm plant. Write down the estimate for a 20 cm plant and name the type of estimate.[2]
3. (c)Explain why using the same line to estimate the leaves on a 60 cm plant would be unreliable.[2]

A representative year-group sample.

1. (a)A school survey hands questionnaires to 60 pupils waiting at the school gate at 8 am. Give one reason this sample may be biased.[2]
2. (b)The school has 1,200 pupils, of whom 720 are juniors. How many juniors should a representative sample of 60 contain?[3]

Waiting times at a clinic. (Higher)

1. (a)The waiting times of 60 patients: 0 < t ≤ 10 min (6 patients), 10 < t ≤ 20 (15), 20 < t ≤ 30 (21), 30 < t ≤ 40 (12), 40 < t ≤ 50 (6). Write down the cumulative frequency for each class boundary.[1]
2. (b)How many patients waited more than 30 minutes?[2]
3. (c)On the cumulative frequency graph, estimate the median waiting time.[2]
4. (d)State one assumption made when reading a median from a grouped cumulative frequency graph.[1]

Seedling heights on a histogram. (Higher)

1. (a)Heights of 80 seedlings: 0–10 cm (4), 10–20 (12), 20–40 (32), 40–60 (24), 60–80 (8). Explain why the bars of the histogram must be drawn with different widths.[1]
2. (b)Calculate the frequency density of each class.[2]
3. (c)How many seedlings are between 40 and 60 cm tall?[1]
4. (d)Estimate how many seedlings are at least 50 cm tall.[2]

Two classes’ test scores. (Higher)

1. (a)Class A’s marks (out of 80) for 100 pupils have a median of 47, a lower quartile of 32 and an upper quartile of 60. Find the interquartile range.[1]
2. (b)A’s minimum mark is 8 and maximum is 78. Use the 1.5 × IQR rule to show that neither mark is an outlier.[2]
3. (c)Class B’s median is 52 and its IQR is 10. Which class scored better in the middle, and which was more consistent?[3]

Quarterly ice-cream sales. (Higher)

1. (a)A shop’s quarterly sales (£1000): 2023 — Q1 42, Q2 48, Q3 61, Q4 55; 2024 — Q1 45, Q2 52, Q3 66, Q4 58. Describe the long-term trend, quoting evidence.[2]
2. (b)Describe the seasonal pattern.[2]
3. (c)Estimate the Q3 2025 sales, and state one reason your figure is uncertain.[2]

A grouped table is averaged. (Higher)

1. (a)Seedling heights: 0 ≤ x < 10 (6 seedlings), 10 ≤ x < 20 (9) and 20 ≤ x < 30 (5). Write down the midpoint of each class.[1]
2. (b)Work out an estimate of the mean height.[3]

Clinic waiting times are charted. (Higher)

1. (a)A cumulative frequency graph of 60 waiting times passes through (10, 12), (20, 30), (30, 48) and (40, 60). Work out the median waiting time.[2]
2. (b)Work out how many patients waited more than 30 minutes.[2]

Two delivery services are boxed. (Higher)

1. (a)Service A has quartiles 12 and 30; service B has quartiles 16 and 22. Both medians are 18. Work out each interquartile range.[2]
2. (b)State which service is more consistent, with a reason.[2]
3. (c)The medians are equal. What does the rest of the box plot suggest about which service is typically faster?[2]

A revision graph makes predictions. (Higher)

1. (a)A line of best fit on a scatter graph of revision time x (hours) against test score y passes through (0, 20) and (10, 80). Find its equation.[3]
2. (b)Use your equation to predict the score for 6 hours of revision.[2]
3. (c)Explain why predicting a score for 30 hours would be unreliable.[1]