AQA GCSE Mathematics 8300: Statistics – Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – examination boards hold copyright in their own papers. Use these alongside the official past papers from your board or school.

These questions cover Topic 6, Statistics (S1 to S6), of the AQA GCSE Mathematics (8300) specification, for teaching from September 2015 with exams from May/June 2017 (version 1.0). Questions 9, 10 and 11 test histograms, box plots and cumulative frequency, and are labelled “Higher tier only”; everything else is for both tiers. Each question says whether it is calculator-free (Paper 1 style) or calculator allowed (Papers 2 and 3 style).

Learn the content first in the study guide and the revision notes. The course hub is AQA GCSE Mathematics and the printable checklist lists every statement.

Questions

1. (calculator-free) For each of these, write the correct type of data.

(a) The number of siblings each student has: discrete or continuous? [1] (b) The time each student takes to run 100 m: discrete or continuous? [1] (c) Population figures Nina copies from a government website: primary or secondary? [1]

2. (calculator-free) 90 students chose their favourite fruit: apple 30, banana 25, orange 20, grape 15. Work out the angle for each sector of a pie chart. [3]

3. (calculator allowed) The table shows the number of pets owned by 40 people.

Number of pets	0	1	2	3	4
Frequency	8	12	9	6	5

(a) Write down the mode. [1] (b) Work out the median. [1] (c) Calculate the mean. [2]

4. (calculator allowed) The masses, m kg, of 50 parcels are recorded.

Mass (kg)	0 < m ≤ 2	2 < m ≤ 4	4 < m ≤ 6	6 < m ≤ 8	8 < m ≤ 10
Frequency	7	16	14	9	4

(a) Write down the modal class. [1] (b) Work out an estimate of the mean mass. [3] (c) Explain why your answer to (b) is only an estimate. [1]

5. (calculator allowed) Eight people recorded their journey times in minutes:

24, 26, 27, 27, 29, 30, 32, 53

(a) Work out the range. [1] (b) Calculate the mean with and without the value 53. [2] (c) State which average, mean or median, better represents a typical time. Give a reason. [1]

6. (calculator-free) Two cafés record their daily number of customers for a month. Café P has a mean of 142 and a range of 38. Café Q has a mean of 156 and a range of 71. Make two comparisons between the cafés. [2]

7. (calculator-free) A café records the daily maximum temperature (°C) and the number of hot chocolates sold on 10 days. The points on a scatter graph slope downwards, close to a straight line. A line of best fit passes through (8, 62) and (20, 26).

(a) Describe the correlation. [1] (b) Explain what this tells you about temperature and sales. [1] (c) Use the line of best fit to estimate the sales on a day with a maximum of 14 °C. [2] (d) The temperatures recorded were all between 5 °C and 22 °C. Explain why using the line for a day of 35 °C may not be reliable. [1]

8. (calculator allowed) A council wants to know what the 12 000 residents of a town think about a new cycle lane. Kai asks 60 people at the bus station at 9 am on a Monday.

(a) Give two reasons why Kai’s sample may be biased. [2] (b) Suggest one way to improve the sample. [1] (c) In a random sample of 80 residents, 28 support the cycle lane. Estimate the number of residents who support it. [1]

9. (calculator allowed, Higher tier only) The waiting times, t minutes, of 125 patients are shown.

Time (minutes)	0 < t ≤ 5	5 < t ≤ 10	10 < t ≤ 20	20 < t ≤ 40	40 < t ≤ 60
Frequency	20	35	40	24	6

(a) Work out the frequency densities needed to draw a histogram. [2] (b) Estimate the number of patients who waited more than 15 minutes. [2] (c) Write down the class that contains the median. [1] (d) Work out an estimate of the mean waiting time. [3]

10. (calculator-free, Higher tier only) The marks of 15 students in Group A, in order, are:

21, 24, 27, 29, 30, 32, 34, 35, 37, 38, 40, 41, 44, 48, 55

(a) Find the median, lower quartile and upper quartile. [3] (b) Work out the interquartile range. [1] (c) Draw a box plot for Group A. [2] (d) Group B has minimum 18, lower quartile 26, median 31, upper quartile 45 and maximum 52. Make two comparisons between the groups. [2]

11. (calculator-free, Higher tier only) 80 people timed how long a task took.

Time (minutes)	0 < t ≤ 10	10 < t ≤ 20	20 < t ≤ 30	30 < t ≤ 40	40 < t ≤ 50
Frequency	6	15	24	22	13

(a) Complete a cumulative frequency table. [1] (b) Draw the cumulative frequency graph. [2] (c) Use your graph to estimate the median. [1] (d) Estimate how many people took more than 35 minutes. [2] (e) Explain why your answer to (c) is an estimate. [1]

12. (calculator-free) Quarterly ice-cream sales (thousands) for a shop over two years were: 12, 30, 41, 15, 14, 33, 45, 18.

(a) Name a suitable diagram to show these data. [1] (b) Describe the trend. [1] (c) Describe the pattern within each year. [1]

Answers

1. (a) Discrete [1] (b) Continuous [1] (c) Secondary [1] Examiner insight: Each part is a separate mark, so a wrong answer in (a) does not affect (b) or (c).

2. 360 ÷ 90 = 4° per student [1]; two angles correct [1]; apple 120°, banana 100°, orange 80°, grape 60° [1] Examiner insight: The method mark is for 360 ÷ 90 or a correct fraction of 360 for any one sector; angles that do not total 360° lose the final mark.

3. (a) 1 [1] (b) 20th and 21st values are 1 and 2, so median = 1.5 [1] (c) Σfx = 0 + 12 + 18 + 18 + 20 = 68 [1]; 68 ÷ 40 = 1.7 [1] Examiner insight: Giving the mode as 12 (the frequency) instead of 1 (the value) scores zero.

4. (a) 2 < m ≤ 4 [1] (b) Midpoints 1, 3, 5, 7, 9 [1]; Σfx = 7 + 48 + 70 + 63 + 36 = 224 [1]; 224 ÷ 50 = 4.48 kg [1] (c) The exact masses are not known; midpoints are used for every value in a class [1] Examiner insight: Dividing by 5 (the number of classes) is a method error, so only the midpoint mark is available.

5. (a) 53 − 24 = 29 minutes [1] (b) With 53: 248 ÷ 8 = 31 [1]; without: 195 ÷ 7 = 27.9 (to 1 d.p.) [1] (c) Median, because the outlier 53 raises the mean but hardly changes the median [1] Examiner insight: In (c) the reason must mention the outlier (or extreme value) 53; “the median is more accurate” is not enough.

6. On average Café Q had more customers, as its mean is higher [1]; Café P’s numbers were more consistent, as its range is smaller [1] Examiner insight: Each comparison needs the measure and the context; “Q’s mean is higher” without saying “more customers” often loses the mark.

7. (a) Negative correlation (strong) [1] (b) As the temperature rises, fewer hot chocolates are sold [1] (c) Gradient = (26 − 62) ÷ (20 − 8) = −3 per °C [1]; 62 − 3 × 6 = 44 [1] (d) 35 °C is outside the range of the data, so this is extrapolation and the trend may not continue [1] Examiner insight: For (b) you must describe the relationship in context; repeating “negative correlation” earns nothing.

8. (a) Only people at the bus station, who may not cycle [1]; only one time and day, so people at work or school are missed [1] (b) Choose a random sample from the whole town, e.g. from a list of residents [1] (c) 28/80 × 12 000 = 4200 [1] Examiner insight: The two reasons in (a) must be different; “too small” and “not enough people” count as one point.

9. (a) 20 ÷ 5 = 4, 35 ÷ 5 = 7, 40 ÷ 10 = 4 [1]; 24 ÷ 20 = 1.2, 6 ÷ 20 = 0.3 [1] (b) Half of the 10–20 class: 40 × 5/10 = 20 [1]; 20 + 24 + 6 = 50 [1] (c) 63rd value; running totals 20, 55, 95, so 10 < t ≤ 20 [1] (d) Midpoints 2.5, 7.5, 15, 30, 50 [1]; Σfx = 50 + 262.5 + 600 + 720 + 300 = 1932.5 [1]; 1932.5 ÷ 125 = 15.5 minutes (15.46) [1] Examiner insight: In (b) taking all 40 from the 10–20 class ignores the part below 15 minutes and loses the method mark.

10. (a) Median = 8th value = 35 [1]; LQ = 4th value = 29 [1]; UQ = 12th value = 41 [1] (b) 41 − 29 = 12 [1] (c) Box from 29 to 41 with median line at 35 [1]; whiskers to 21 and 55, on a labelled scale [1] (d) Group A has a higher median (35 vs 31), so did better on average [1]; Group A has a smaller IQR (12 vs 19), so its marks were more consistent [1] Examiner insight: Comparing the ranges in (d) instead of the IQRs is allowed for a spread mark only if it is interpreted in context; the IQR is the safer choice.

11. (a) 6, 21, 45, 67, 80 [1] (b) Points at (10, 6), (20, 21), (30, 45), (40, 67), (50, 80) [1]; starting at (0, 0), joined with a curve or lines [1] (c) Read across at 40: about 28 minutes (accept 27 to 29) [1] (d) Cumulative frequency at 35 is about 56 [1]; 80 − 56 = 24 (accept 22 to 26) [1] (e) It is read from a graph built from grouped data, so the exact times are not known [1] Examiner insight: Points plotted at the class midpoints (5, 15, 25, …) lose the plotting mark, and the readings in (c) and (d) then only earn follow-through credit.

12. (a) A line graph (time series graph) [1] (b) Sales are increasing from one year to the next (each quarter is higher than the same quarter the year before) [1] (c) Sales are highest in the third quarter and lowest in the first quarter each year [1] Examiner insight: For (b), “sales go up and down” describes the seasonal pattern, not the trend, and scores zero.

Where marks are usually lost

• Dividing by the number of classes instead of the total frequency for a grouped mean.
• Giving the frequency instead of the value when asked for a mode.
• Plotting cumulative frequency at midpoints, or not starting at 0.
• Using frequency, not frequency density, for an unequal-width histogram.
• Taking a whole class instead of the correct fraction of it when estimating from a histogram.
• Comparing distributions without context, or with two comparisons of the same kind.
• Describing correlation with no reference to what the variables are.
• Using the line of best fit outside the data without comment.
• Giving two versions of the same reason for bias.

Next steps

• Statistics revision notes
• Statistics study guide
• Probability practice questions
• AQA GCSE Mathematics course hub
• Printable checklist
• All free 10-minute diagnostics
• Book a free trial class

Official syllabus

AQA GCSE Mathematics (8300) specification, for teaching from September 2015, exams from May/June 2017, version 1.0, published by AQA – section 3.6 Statistics (S1 to S6).