Exam-style Questions: Representing Data

  1. The heights of 100 plants were measured. The results are shown in the table below.

    Height (h cm) 4 < h ≤ 5 5 < h ≤ 6 6 < h ≤ 7 7 < h ≤8 8 < h ≤ 9 9 < h ≤ 10 10 < h ≤ 11 11 < h ≤ 12
    Frequency 3 7 11 28 24 17 8 2

    a) Complete the cumulative frequency table for the 100 plants.

    (1 mark)

    Height (h cm) h ≤ 4 h ≤ 5 h ≤ 6 h ≤ 7 h ≤ 8 h ≤ 9 h ≤ 10 h ≤ 11 h ≤ 12
    Cumulative Frequency 0 3

    b) Draw the cumulative frequency diagram on the grid below.

    (3 marks)

    Copyright S-cool

    c) Use your graph to estimate how many plants are less than 9.4cm high.

    (1 mark)

    d) Use your cumulative frequency diagram to estimate the inter-quartile range of the heights.

    (2 marks)

    (Marks available: 7)

    Answer

    Answer outline and marking scheme for question: 1

    a)

    Height (h cm) h ≤ 4 h ≤ 5 h ≤ 6 h ≤ 7 h ≤ 8 h ≤ 9 h ≤ 10 h ≤ 11 h ≤ 12
    Cumulative Frequency 0 3 10 21 49 73 90 98 100

    (1 mark)

    b) 9 points plotted correctly, curve or straight lines.

    (3 marks)

    c) 78 to 82

    (1 mark)

    d) 1.7 to 2.2

    (2 marks)

    (Marks available: 7)

  2. a) Ian and Alex decide to conduct a survey on the use of computers.

    They want to know whether boys or girls use a computer in their coursework for word-processing, spreadsheets or both.

    In the space below, design an observation sheet to collect information from a group of boys and girls.

    (3 marks)

    b) Alex used a spell-check on her computer to find spelling mistakes in some course-work.

    The table below shows the distribution of spelling mistakes

    Number of spelling mistakes on the page 0 1 2 3 4
    Number of pages 10 6 1 1 2

    Calculate the mean number of spelling mistakes per page.

    (3 marks)

    (Marks available: 6)

    Answer

    Answer outline and marking scheme for question: 2

    a) Two way table with boys/girls

    Columns for WP, SS, both, neither.

    One way table or questionnaire

    Gender column or box

    Columns or boxes for WP & SS

    (3 marks)

    b) 0.95 or 19/20

    (3 marks)

    (Marks available: 6)

  3. The graph shows the speed of a car in kilometres per hour (km/h).

    Copyright S-cool

    a) What is the speed of the car after 10 seconds?

    (1 mark)

    b) After 30 seconds, the car travels at a steady speed of 60 km/h for 1 minute. Continue the graph by drawing a line AB to show this.

    (1 mark)

    c) Draw a straight line from B to the point C (110, 0).

    (1 mark)

    d) What does the graph between B and C tell you about what the car is doing?

    (1 mark)

    (Marks available: 4)

    Answer

    Answer outline and marking scheme for question: 3

    a) 20km/h

    b) Horizontal straight line, ending at (90,60).

    c) Straight line from (90,60) to (110,0)

    d) 'Slowing down' or 'stopping'

    (Marks available: 4)