هذه المجموعة متاحة بلغتها الأصلية.
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.
أسئلة أصلية كتبها مدرّسو Studoli بأسلوب امتحان GCSE. ليست أسئلة رسمية.
Timed mode
10 questions in 15 minutes, one question at a time. Your answers are marked when you submit or when the time runs out.
الموضوع: Cumulative frequency
1. A cumulative frequency graph shows 80 values. At what cumulative frequency do you read the median?
الحل
A. 40
- The median is halfway through the data.
- 80 ÷ 2 = 40.
الموضوع: Interquartile range
2. The lower quartile is 14 and the upper quartile is 27. Find the interquartile range.
الحل
D. 13
- IQR = upper quartile − lower quartile.
- 27 − 14 = 13.
الموضوع: Histograms
3. The class 10 < x ≤ 30 has a frequency of 50. Find its frequency density.
الحل
C. 2.5
- Frequency density = frequency ÷ class width.
- Class width = 30 − 10 = 20, so 50 ÷ 20 = 2.5.
الموضوع: Grouped data
4. Estimate the mean: 0 < x ≤ 10 has frequency 4, and 10 < x ≤ 20 has frequency 6.
الحل
B. 11
- Use the midpoints 5 and 15.
- (5 × 4 + 15 × 6) ÷ (4 + 6) = (20 + 90) ÷ 10 = 11.
الموضوع: Box plots
5. What does the box in a box plot show?
الحل
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.
الموضوع: 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?
الحل
D. 12
- Year 11 is 240/1000 of the school.
- 240/1000 × 50 = 12.
الموضوع: Measures of spread
7. Which measure of spread is not affected by extreme values?
الحل
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.
الموضوع: Histograms
8. A bar on a histogram has frequency density 1.5 and class width 20. Find the frequency.
الحل
B. 30
- Frequency = frequency density × class width.
- 1.5 × 20 = 30.
الموضوع: 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.
الحل
A. 250
- The proportion tagged in the sample should match the lake: 8/50 = 40/N.
- N = 40 × 50 ÷ 8 = 250.
الموضوع: Averages
10. The mean of 10 numbers is 12. The number 30 is removed. Find the mean of the other 9.
الحل
D. 10
- Total of the 10 numbers: 10 × 12 = 120.
- Remove 30: 120 − 30 = 90.
- 90 ÷ 9 = 10.