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GCSE Maths Higher: Statistics practice questions
Ten free GCSE Maths Higher tier questions on cumulative frequency, quartiles, histograms, grouped data, box plots, sampling and capture-recapture, each with a worked solution. Suitable for AQA, Edexcel and OCR.
Questions originales rédigées par les professeurs Studoli dans l’esprit de l’examen GCSE. Ce ne sont pas des sujets officiels.
Mode chronométré
10 questions en 15 minutes, une question à la fois. Vos réponses sont corrigées à la fin ou quand le temps est écoulé.
Notion: Cumulative frequency
1. A cumulative frequency graph shows 80 values. At what cumulative frequency do you read the median?
Correction
A. 40
- The median is halfway through the data.
- 80 ÷ 2 = 40.
Notion: Interquartile range
2. The lower quartile is 14 and the upper quartile is 27. Find the interquartile range.
Correction
D. 13
- IQR = upper quartile − lower quartile.
- 27 − 14 = 13.
Notion: Histograms
3. The class 10 < x ≤ 30 has a frequency of 50. Find its frequency density.
Correction
C. 2.5
- Frequency density = frequency ÷ class width.
- Class width = 30 − 10 = 20, so 50 ÷ 20 = 2.5.
Notion: Grouped data
4. Estimate the mean: 0 < x ≤ 10 has frequency 4, and 10 < x ≤ 20 has frequency 6.
Correction
B. 11
- Use the midpoints 5 and 15.
- (5 × 4 + 15 × 6) ÷ (4 + 6) = (20 + 90) ÷ 10 = 11.
Notion: Box plots
5. What does the box in a box plot show?
Correction
A. The middle 50% of the data
- The box runs from the lower quartile to the upper quartile.
- So it covers the middle half of the data, the interquartile range.
Notion: Sampling
6. A school of 1000 students takes a stratified sample of 50. Year 11 has 240 students. How many Year 11 students should be in the sample?
Correction
D. 12
- Year 11 is 240/1000 of the school.
- 240/1000 × 50 = 12.
Notion: Measures of spread
7. Which measure of spread is not affected by extreme values?
Correction
C. The interquartile range
- The range uses the largest and smallest values, so one extreme value changes it.
- The IQR uses the quartiles, so it ignores the extremes.
Notion: Histograms
8. A bar on a histogram has frequency density 1.5 and class width 20. Find the frequency.
Correction
B. 30
- Frequency = frequency density × class width.
- 1.5 × 20 = 30.
Notion: Capture-recapture
9. 40 fish are tagged and released. Later 50 fish are caught and 8 are tagged. Estimate the number of fish in the lake.
Correction
A. 250
- The proportion tagged in the sample should match the lake: 8/50 = 40/N.
- N = 40 × 50 ÷ 8 = 250.
Notion: Averages
10. The mean of 10 numbers is 12. The number 30 is removed. Find the mean of the other 9.
Correction
D. 10
- Total of the 10 numbers: 10 × 12 = 120.
- Remove 30: 120 − 30 = 90.
- 90 ÷ 9 = 10.