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Chapter 3 Practice Paper: Statistical Diagrams — question paper

QuizQuipPractice Series
QQ/S4EM/CH3

Secondary 4 · Elementary Mathematics (G2 / G3)

Chapter 3 Practice Paper

Statistical Diagrams

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 3 (S1 diagrams: pie charts, stem-and-leaf, histograms, cumulative frequency, box plots, misleading diagrams).

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

    40 students were asked their favourite sport: football 16, basketball 10, swimming 8, tennis 6.

    1. (a)

      Find the four sector angles for a pie chart of these results.

      [3]
    2. (b)

      What percentage of students chose swimming?

      [1]
  2. 2

    A stem-and-leaf diagram of ten test scores has key 1 | 2 = 12. The rows are: 1 | 2 5 8; 2 | 0 3 3 7; 3 | 1 4 9.

    1. (a)

      State the number of scores and the mode.

      [2]
    2. (b)

      Find the median score.

      [2]
  3. 3

    A histogram shows masses of 30 parcels: 10–20 kg: 5; 20–30 kg: 12; 30–40 kg: 9; 40–50 kg: 4.

    1. (a)

      State the modal class.

      [1]
    2. (b)

      What fraction of the parcels lie in the modal class? Give your answer in simplest form.

      [1]
    3. (c)

      Explain why an exact mass of one individual parcel cannot be read from this diagram.

      [2]
  4. 4

    The cumulative frequency table for 30 test times (minutes) is: t ≤ 10: 3; t ≤ 20: 11; t ≤ 30: 22; t ≤ 40: 28; t ≤ 50: 30.

    1. (a)

      How many tests took between 20 and 30 minutes?

      [2]
    2. (b)

      Between which boundaries does the median time lie?

      [2]
    3. (c)

      How many tests took longer than 40 minutes?

      [1]
  5. 5

    A box plot of daily earnings shows minimum $8, Q1 $15, median $22, Q3 $27 and maximum $35.

    1. (a)

      Find the interquartile range.

      [2]
    2. (b)

      Find the range.

      [1]
    3. (c)

      What percentage of the days lie inside the box (between Q1 and Q3)?

      [2]
  6. 6

    A grouped table of journey distances uses midpoints 15, 25 and 35 with frequencies 8, 12 and 5.

    1. (a)

      State the total number of journeys.

      [1]
    2. (b)

      Estimate the mean journey distance.

      [3]
  7. 7

    A company graph shows monthly profits of $98k, $99k and $103k drawn with the y-axis starting at $95k. The report claims "profits have tripled".

    1. (a)

      Explain why the graph is misleading.

      [2]
    2. (b)

      State the honest percentage increase from $98k to $103k, correct to 1 decimal place.

      [2]

— End of paper —