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O-LevelMathematicsStatistics4024/22 · May/June 2015 · Q37 Marks

(a) In a survey, 50 students were asked how long they spent exercising during one particular week. The results are summarised in the table. Time (t minutes) | Frequency ---|--- 0 ≤ t < 30 | 10 30 < t < 60 | 15 60 < t < 90 | 11 90 ≤ t < 120 | 7 120 < t < 150 | 5 150 < t < 180 | 2

  1. (a)(i)Calculate an estimate of the mean time each student spent exercising that week.[3]
  2. (a)(ii)During that week, the time Simon spent exercising is shown below. Tuesday 12.37 p.m. until 1.24 p.m. Thursday 8.57 a.m. until 9.42 a.m. Which interval is his time recorded in?[1]
  3. (b)(i)A gym has four different types of machines. Carol is going to draw a pie chart to show how many times the machines are used in one day. She has started to make a table. Machine | Frequency | Angle of sector ---|---|--- Running | 90 | 120° Rowing | 75 | Cycling | 57 | Weights | | 64° Complete the table.[2]
  4. (b)(ii)Complete the pie chart. [Figure 3.1][1]

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Mark scheme

Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.

  1. [3] M1 for 15×10+45×15+75×11+105×7+135×5+165×2 i.e. 150+675+825+735+675+330 (=3390); B1 for ÷ 50 (independent of M mark); 67.8
  2. [1] 90 <= t < 120 Or clear equivalent
  3. [2] B1 for 100 and 76, or for 48; 100 and 76 and 48
  4. [1] Completed pie chart with at least one sector correctly labelled

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About this question

Topic
Statistics, O-Level Mathematics (syllabus 4024). Structured question, 7 marks.
Source
O-Level Mathematics, May/June 2015 Paper 2 Variant 2, question 3.

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