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Edexcel 1MA1 GCSE Maths · 4 Worked Solutions

Edexcel GCSE Maths: Statistics Worked Solutions

Real mark-scheme-derived worked solutions for Edexcel GCSE Maths Statistics questions. Every solution includes step-by-step working, the correct final answer, marks awarded, and a common mistake callout — with question-level AO breakdown from the official 1MA1 spec.

Q1 Higher 3 marks
Edexcel 1MA1 · 2022

Question

There are 30 women and 20 men at a gym. The mean height of all 50 people is 167.6 cm. The mean height of the 20 men is 182 cm. Work out the mean height of the 30 women.

Worked Solution

  1. Find the total height of all 50 people: 50 × 167.6 = 8380 cm.

  2. Find the total height of the 20 men: 20 × 182 = 3640 cm.

  3. The total height of the 30 women must be: 8380 – 3640 = 4740 cm.

  4. The mean height of the women is 4740 ÷ 30 = 158 cm.

Final Answer

158

Common Mistake

A common error is to average 167.6 and 182 directly to find the women's mean — this ignores the different group sizes (30 women vs 20 men).

Assessment Objectives (question level, Edexcel 1MA1 spec — not per step)

AO1 Use standard techniques — 40%
AO2 Reason and communicate — 30%
AO3 Solve problems — 30%
Q2 Higher 3 marks
Edexcel 1MA1 · 2022

Question

Faiza is studying the population of rabbits in a park. She wants to estimate the number of rabbits in the park. On Monday she catches a random sample of 20 rabbits in the park, marks each rabbit with a tag and releases them back into the park. On Tuesday she catches a random sample of 42 rabbits in the park. 12 of the rabbits are marked with a tag. Find an estimate for the number of rabbits in the park.

Worked Solution

  1. The capture-recapture method uses the formula: estimated population = (first sample size × second sample size) ÷ number recaptured with tags.

  2. First sample size = 20 (all tagged and released). Second sample size = 42. Number in second sample with tags = 12.

  3. Estimated population = (20 × 42) ÷ 12 = 840 ÷ 12 = 70.

Final Answer

70

Common Mistake

A common error is to add the sample sizes rather than multiply them — remember you need to find what fraction of the second sample was tagged, then scale the first sample up accordingly.

Assessment Objectives (question level, Edexcel 1MA1 spec — not per step)

AO1 Use standard techniques — 40%
AO2 Reason and communicate — 30%
AO3 Solve problems — 30%
Q3 Higher 3 marks
Edexcel 1MA1 · 2022

Question

The table gives information about the distances, in miles, that some Year 10 students live from school. Distance (d miles): 0 < d ≤ 1.0 (Frequency 90), 1.0 < d ≤ 1.5 (Frequency 48), 1.5 < d ≤ 2.0 (Frequency 22), 2.0 < d ≤ 3.0 (Frequency 8), 3.0 < d ≤ 5.0 (Frequency 12). On the grid, draw a histogram for this information.

Worked Solution

  1. In a histogram the y-axis shows frequency density, not frequency. Frequency density = frequency ÷ class width.

  2. Calculate frequency density for each class: 0–1.0: 90 ÷ 1.0 = 90. 1.0–1.5: 48 ÷ 0.5 = 96. 1.5–2.0: 22 ÷ 0.5 = 44. 2.0–3.0: 8 ÷ 1.0 = 8. 3.0–5.0: 12 ÷ 2.0 = 6.

  3. Draw bars at these frequency density heights. Note that the bars have different widths, reflecting the unequal class intervals.

Final Answer

Histogram with frequency density bars at heights 90, 96, 44, 8, 6

Common Mistake

Using the raw frequency as the bar height gives a misleading histogram when class widths are not equal — always divide frequency by class width to get frequency density.

Assessment Objectives (question level, Edexcel 1MA1 spec — not per step)

AO1 Use standard techniques — 40%
AO2 Reason and communicate — 30%
AO3 Solve problems — 30%
Q4 Higher 2 marks
Edexcel 1MA1 · 2024

Question

Mina also records the speeds of some cars on the same road on Sunday. She uses her results to draw a box plot. Compare the distribution of the speeds on Friday with the distribution of the speeds on Sunday.

Worked Solution

  1. Read the median from each box plot. The median speed on Friday is 40 mph; the median speed on Sunday is 42 mph. The median speed on Sunday was higher than on Friday, meaning cars were generally travelling faster on Sunday.

  2. Compare the spread using the interquartile range (IQR) or the overall range. The IQR on Friday is 12 mph; the IQR on Sunday is 15 mph. The speeds on Sunday were more spread out (greater IQR) than on Friday.

Final Answer

The median speed on Sunday (42 mph) was greater than on Friday (40 mph), and the spread of speeds (IQR) was larger on Sunday (15 mph) than on Friday (12 mph).

Common Mistake

Simply quoting the numerical values from the box plot is not enough — you must explicitly compare them and use the context (speeds, mph) in your answer.

Assessment Objectives (question level, Edexcel 1MA1 spec — not per step)

AO1 Use standard techniques — 40%
AO2 Reason and communicate — 30%
AO3 Solve problems — 30%

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