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CAIE A Level Mathematics 9709

Representation of data questions

Exam-style questions on Representation of data, ordered from foundation to challenge. Pick one, write your answer the way you would in the exam, and it comes back marked against the mark scheme, point by point.

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Written by Markquill to follow the Cambridge International syllabus. Markquill is independent and is not affiliated with or endorsed by Cambridge International.

  1. 2 marksFoundationThe cumulative frequency table shows the distribution of heights (cm) of 200 plants. Height (cm) Cumulative frequency 25 10 30 30 35 100 40 160 45 200 Estimate the median height of the plants.
  2. 3 marksStandardThe coded sums for a set of 3 values are given as Σ(x – 41) = -9 and Σ(x – 41)² = 800. Find the mean of x.
  3. 3 marksStandardThe table shows the times, in minutes, taken by a group of people to complete a task. Time (minutes) Mid-value Frequency first class 10 10 second class 35 10 third class 55 5
  4. 3 marksStandardThe following is a sorted dataset of 11 integers: 10, 15, 25, 36, 42, 62, 66, 71, 74, 84, 111. Find the interquartile range.
  5. 4 marksStandardFive measurements are recorded as 8, 13, 18, 23 and 28.
  6. 3 marksStandardThe cumulative frequency graph for the times taken by 100 athletes to complete a race has the following points: Time (seconds) Cumulative frequency 10 15 20 60 30 75 40 100 Estimate the number of athletes who took more…
  7. 4 marksChallengeThe following data are coded using the transformation y = x - 4. The totals are: sum y = 0 and sum y^2 = 90. The number of data points is n = 10. Find the standard deviation of the original x values.
  8. 3 marksChallengeFor a set of 20 values of x, the coded values y = (x - 50)/( 4 ) are used. It is given that sum y = 120.