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Chapter 4 Practice Paper: Averages and Spread — question paper

QuizQuipPractice Series
QQ/S4EM/CH4

Secondary 4 · Elementary Mathematics (G2 / G3)

Chapter 4 Practice Paper

Averages and Spread

Duration: 40 minutes
Total: 30 marks
Name:
Class:
Register No.:
Date:

READ THESE INSTRUCTIONS FIRST

  • Write your name, class and register number in the spaces at the top of this page.
  • Answer all questions.
  • Show all necessary working. Omission of essential working will result in loss of marks.
  • Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
  • Geometrical instruments and an approved calculator may be used.
  • The number of marks is given in brackets [ ] at the end of each question or part question.
  • The total number of marks for each paper is shown on its cover.

Original practice material written for the MOE Elementary Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 4 (S1 averages and spread: mean, mode, median, grouped estimates, quartiles, percentiles, standard deviation, comparing data sets).

For Examiner’s Use
Section A/ 30
Total/ 30

Section A: Structured questions[30 marks]

Answer all questions in the spaces provided. Show all necessary working — omission of essential working will result in loss of marks. Give non-exact numerical answers correct to 3 significant figures.

  1. 1

    A barista records the number of cups sold per hour: 12, 15, 15, 18, 20, 22, 24, 24, 24, 29.

    1. (a)

      State the mode.

      mode =[1]
    2. (b)

      Find the median.

      [2]
    3. (c)

      Calculate the mean.

      [2]
  2. 2

    The mean of eight numbers is 15. Seven of the numbers are 11, 13, 14, 16, 17, 19 and 20.

    1. (a)

      Find the total of all eight numbers.

      [2]
    2. (b)

      Hence find the eighth number.

      [2]
  3. 3

    The table shows the masses of 30 parcels: 1–5 kg: 6; 6–10 kg: 12; 11–15 kg: 9; 16–20 kg: 3.

    1. (a)

      Complete the midpoint column (values in kg).

      [1]
    2. (b)

      Calculate an estimate of the mean mass.

      [4]
  4. 4

    Fifteen ordered examination scores: 8, 9, 11, 12, 14, 15, 17, 18, 20, 22, 23, 26, 28, 30, 33.

    1. (a)

      State the median score.

      median =[1]
    2. (b)

      Find the lower quartile, the upper quartile and the interquartile range.

      [3]
  5. 5

    Two backup drives transfer the same five test files. Drive A takes 2, 4, 6, 8 and 10 minutes. Drive B takes 4, 5, 6, 7 and 8 minutes.

    1. (a)

      Show that both drives have the same mean transfer time.

      [2]
    2. (b)

      Calculate the standard deviation of each drive’s times, correct to 3 significant figures.

      [3]
    3. (c)

      Which drive is more predictable in its transfer time? Justify your answer.

      [1]
  6. 6

    A factory records cycle times in groups: 5–15 s: 4; 15–25 s: 6; 25–35 s: 6; 35–45 s: 4. Using class midpoints and the statistics mode of a calculator,

    1. (a)

      Find the estimated mean cycle time.

      [2]
    2. (b)

      Find the estimated standard deviation, correct to 3 significant figures.

      [3]
    3. (c)

      A rival line reports an estimated mean of 25 s with an estimated SD of 4.6 s. Compare the consistency of the two lines.

      [1]

— End of paper —