Representation of data — AS & A Level Mathematics (9709) questions by topic
Combining two data summaries to find an overall mean, working out the probability that a sample mean from a normal population exceeds a value, and comparing grouped race times for two teams from a table are typical of the 23 representation of data questions from 2023 to 2025, worth 4 to 12 marks.
Find, draw, calculate and estimate are the leading command words, with state used for definitions of summary measures. Because combining sigma-notation summaries from two samples is a frequent source of arithmetic slips, submit your working for instant marking, so a wrongly combined total or an incorrectly estimated grouped mean is caught before it feeds into a later comparison.
May–June 2025, Paper 51
Last Sunday, teams of runners took part in a charity event. The time taken, in seconds, to run 50 m was recorded, correct to 1 decimal place, for each runner. The times recorded…
Answer this question and get it marked →May–June 2025, Paper 52
The times taken, t minutes, by 300 students to travel to Hollowton College are recorded. The results are summarised in the table below. Time (t minutes) t ≤ 10 t ≤ 20 t ≤ 30 t ≤…
Answer this question and get it marked →May–June 2025, Paper 53
For a set of 40 values of x, it is found that Sum(x − k) = 836.0, Sum(x − k)^2 = 25410.8, where k is a constant. Given that the mean of these 40 values is 124.0, find the value of…
Answer this question and get it marked →84 people attempt a particular puzzle. The times taken, in minutes, to complete the puzzle are recorded. These times are represented in the cumulative frequency graph below. The…
Answer this question and get it marked →May–June 2025, Paper 55
The Smarts and the Teasers are two quiz teams that each contain 11 members. Both complete a puzzle and the following table gives the times taken, in minutes, by the members of…
Answer this question and get it marked →May–June 2025, Paper 61
The random variable X has the distribution B(8, 3/4). A random sample of 100 values of X is chosen, and the sample mean, X-bar, is found. Find P(X-bar 6.2). You are not expected…
Answer this question and get it marked →The time, T minutes, for a certain daily bus journey is normally distributed. The bus company claims that the mean of T is 45. A passenger believes that the mean of T is actually…
Answer this question and get it marked →May–June 2024, Paper 51
A summary of 20 values of x gives Σ(x − 30) = 439 and Σ(x − 30)^2 = 12405. A summary of another 25 values of x gives Σ(x − 30) = 470 and Σ(x − 30)^2 = 11346. Find the mean of all…
Answer this question and get it marked →The heights, in cm, of 200 adults in Barimba are summarised in the following table. Height (h cm) 130 ≤ h < 150 150 ≤ h < 160 160 ≤ h < 170 170 ≤ h < 175 175 ≤ h < 195 --- --- ---…
Answer this question and get it marked →May–June 2024, Paper 52
The back-to-back stem-and-leaf diagram shows the annual salaries of 19 employees at each of two companies, Petral and Ravon (see the shared stem-and-leaf diagram, with key 2 31 5…
Answer this question and get it marked →May–June 2024, Paper 53
The times taken, in seconds, by 15 members of each of two swimming clubs, the Penguins and the Dolphins, to swim 50 metres are shown in the following table. Penguins 35 39 42 44…
Answer this question and get it marked →October–November 2024, Paper 51
The time taken, in minutes, to walk to school was recorded for 200 pupils at a certain school. These times are summarised in the following table. Time taken (t minutes) t ≤ 15 t ≤…
Answer this question and get it marked →October–November 2024, Paper 52
Teams of 15 runners took part in a charity run last Saturday. The times taken, in minutes, to complete the course by the runners from the Falcons and the runners from the Kites…
Answer this question and get it marked →October–November 2024, Paper 53
On a certain day, the heights of 150 sunflower plants grown by children at a local school are measured, correct to the nearest cm. These heights are summarised in the following…
Answer this question and get it marked →October–November 2024, Paper 62
A population is normally distributed with mean 35 and standard deviation 8.1. A random sample of size 140 is chosen from this population and the sample mean is denoted by X̄. Find…
Answer this question and get it marked →May–June 2023, Paper 51
A summary of 50 values of x gives Σ(x − q) = 700 and Σ(x − q)^2 = 14235, where q is a constant. Find the standard deviation of these values of x.
Answer this question and get it marked →The populations of 150 villages in the UK, to the nearest hundred, are summarised in the table. Population 100 – 800 900 – 1200 1300 – 2000 2100 – 3200 3300 – 4800 --- --- --- ---…
Answer this question and get it marked →May–June 2023, Paper 52
The back-to-back stem-and-leaf diagram represents the monthly salaries, in dollars, of 27 employees at each of two companies, A and B. Find the median and the interquartile range…
Answer this question and get it marked →May–June 2023, Paper 53
The times taken, in minutes, to complete a cycle race by 19 cyclists from each of two clubs, the Cheetahs and the Panthers, are represented in the back-to-back stem-and-leaf…
Answer this question and get it marked →October–November 2023, Paper 51
The times taken by 120 children to complete a particular puzzle are represented in the cumulative frequency graph. The horizontal axis shows Time (seconds) from 0 to 50 and the…
Answer this question and get it marked →The times, to the nearest minute, of 150 athletes taking part in a charity run are recorded. The results are summarised in the table. Time in minutes 101 – 120 121 – 130 131 – 135…
Answer this question and get it marked →October–November 2023, Paper 52
The heights, in cm, of the 11 players in each of two teams, the Aces and the Jets, are shown in the table provided. Draw a back-to-back stem-and-leaf diagram to represent this…
Answer this question and get it marked →October–November 2023, Paper 53
The weights, x kg, of 120 students in a sports college are recorded and summarised in the cumulative frequency table provided. Draw a cumulative frequency graph to represent this…
Answer this question and get it marked →Other AS & A Level Mathematics topics
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- Trigonometry (57)
- Series (37)
- Integration (33)
- Kinematics (33)
- The normal distribution (32)
- Energy, work and power (31)
- The Poisson distribution (31)
- Complex numbers (28)
- Sampling and estimation (28)
- Permutations and combinations (27)