OpenRevise

Exam questions · Maths · Statistics

Pie Charts, Bar Charts and Stem-and-Leaf Diagrams

  • 6 exam questions
  • 20 marks
  • 9 quick checks
  1. 1 Work out [3 marks]

    Some children are asked their favourite colour. 9 choose blue, 6 choose red, 5 choose green and 4 choose yellow. The results are shown in a pie chart. Work out the angle for each colour. [3 marks]

    Show answerHide answer

    Model answer

    There are 24 children, so each child is \(\dfrac{360}{24} = 15^\circ\). Blue: \(9 \times 15 = 135^\circ\). Red: \(6 \times 15 = 90^\circ\). Green: \(5 \times 15 = 75^\circ\). Yellow: \(4 \times 15 = 60^\circ\).

    Mark scheme

    • \(24\) children and \(360 \div 24 = 15\) — M1
    • At least two angles correct — A1
    • \(135^\circ, 90^\circ, 75^\circ, 60^\circ\) — A1
  2. 2 Work out [5 marks]

    The pie chart shows the favourite subjects of 40 pupils. The angle for dance is not shown. (a) How many pupils chose music? [2 marks] (b) Work out the angle for dance. [1 mark] (c) How many pupils chose dance? [1 mark] (d) What fraction of the pupils chose art? Give your answer in its simplest form. [1 mark]

    A pie chart of the favourite subject of 40 pupils with angles of 135 degrees for music, 90 degrees for art, 81 degrees for drama, and dance unlabelled.
    Show answerHide answer

    Model answer

    (a) Each pupil is \(\dfrac{360}{40} = 9^\circ\), so \(\dfrac{135}{9} = 15\) pupils. (b) \(360 - 135 - 90 - 81 = 54^\circ\). (c) \(\dfrac{54}{9} = 6\). (d) \(\dfrac{90}{360} = \dfrac{1}{4}\).

    Mark scheme

    • (a) \(\dfrac{135}{360} \times 40\) or \(135 \div 9\) — M1
    • (a) 15 — A1
    • (b) \(54^\circ\) — B1
    • (c) 6 — B1
    • (d) \(\dfrac{1}{4}\) — B1
  3. 3 Work out [4 marks]

    The stem-and-leaf diagram shows the masses of 13 parcels. (a) Write down the mode. [1 mark] (b) Work out the median. [2 marks] (c) Work out the range. [1 mark]

    A stem-and-leaf diagram of the masses of 13 parcels with a key where 4 bar 2 means 42 kg.
    Show answerHide answer

    Model answer

    (a) 42 occurs twice. (b) There are 13 values, so the median is the 7th value, which is 49 kg. (c) \(64 - 34 = 30\) kg.

    Mark scheme

    • (a) 42 — B1
    • (b) The 7th value identified — M1
    • (b) 49 — A1
    • (c) 30 — B1
  4. 4 Explain [2 marks]

    Give a reason why each of these charts may be misleading. (a) A pie chart with a 3D effect. [1 mark] (b) A bar chart where the vertical scale starts at 50 instead of 0. [1 mark]

    Show answerHide answer

    Model answer

    (a) The 3D effect distorts the sizes of the sectors, so they are hard to compare. (b) A small difference between the bars looks much bigger than it really is.

    Mark scheme

    • (a) Distorts the sizes of the sectors — B1
    • (b) Exaggerates the differences between the bars — B1
  5. 5 Work out [3 marks]

    The stem-and-leaf diagram shows the heights of some plants. The stem 4 has leaves 1, 3 and 7. The stem 5 has leaves 0, 2, 2 and 8. The stem 6 has leaves 3 and 5. The key says that 4 bar 1 means 41 cm. Work out (a) the mode, (b) the median, (c) the range. [3 marks]

    Show answerHide answer

    Model answer

    (a) 52 occurs twice. (b) There are 9 values, so the median is the 5th value, 52 cm. (c) \(65 - 41 = 24\) cm.

    Mark scheme

    • (a) 52 — B1
    • (b) 52 — B1
    • (c) 24 — B1
  6. 6 Work out [3 marks]

    A pie chart shows the favourite pets of 72 people. The angle for cats is \(160^\circ\) and the angle for dogs is \(120^\circ\). (a) Work out the number of people who chose cats. [2 marks] (b) How many more people chose cats than dogs? [1 mark]

    Show answerHide answer

    Model answer

    (a) Each person is \(\dfrac{360}{72} = 5^\circ\), so cats is \(\dfrac{160}{5} = 32\). (b) Dogs is \(\dfrac{120}{5} = 24\), so \(32 - 24 = 8\) more chose cats.

    Mark scheme

    • (a) \(360 \div 72 = 5\) or \(\dfrac{160}{360} \times 72\) — M1
    • (a) 32 — A1
    • (b) 8 — B1

Quick check

  1. 1

    60 students choose a sport. 24 choose football. What is the angle for football on a pie chart?

    1. A\(24^\circ\)
    2. B\(120^\circ\)
    3. C\(144^\circ\)
    4. D\(60^\circ\)
    Show answerHide answer

    C: \(144^\circ\)

    Each student is \(\dfrac{360}{60} = 6^\circ\), so \(24 \times 6 = 144^\circ\).

  2. 2

    A pie chart shows 40 people. How many degrees represent each person?

    1. A\(40^\circ\)
    2. B\(9^\circ\)
    3. C\(4^\circ\)
    4. D\(90^\circ\)
    Show answerHide answer

    B: \(9^\circ\)

    \(\dfrac{360}{40} = 9\).

  3. 3

    A pie chart shows 36 people. A sector is \(100^\circ\). How many people does it represent?

    1. A\(10\)
    2. B\(100\)
    3. C\(36\)
    4. D\(3.6\)
    Show answerHide answer

    A: \(10\)

    \(\dfrac{100}{360} \times 36 = 10\).

  4. 4

    What fraction of a pie chart is a \(90^\circ\) sector?

    1. A\(\dfrac{1}{3}\)
    2. B\(\dfrac{1}{2}\)
    3. C\(\dfrac{9}{10}\)
    4. D\(\dfrac{1}{4}\)
    Show answerHide answer

    D: \(\dfrac{1}{4}\)

    \(\dfrac{90}{360} = \dfrac{1}{4}\).

  5. 5

    What must every stem-and-leaf diagram have?

    1. AA title only
    2. BGaps between the rows
    3. CA key
    4. DLeaves in a random order
    Show answerHide answer

    C: A key

    Without a key the values cannot be read.

  6. 6

    A stem-and-leaf diagram has 14 ordered values. The 7th is 26 and the 8th is 29. What is the median?

    1. A\(26\)
    2. B\(27.5\)
    3. C\(29\)
    4. D\(28\)
    Show answerHide answer

    B: \(27.5\)

    \(\dfrac{26 + 29}{2} = 27.5\).

  7. 7

    The values in a stem-and-leaf diagram run from 12 to 45. What is the range?

    1. A\(33\)
    2. B\(57\)
    3. C\(28.5\)
    4. D\(45\)
    Show answerHide answer

    A: \(33\)

    \(45 - 12 = 33\).

  8. 8

    Which of these makes a bar chart misleading?

    1. AThe bars have labels
    2. BThe chart has a title
    3. CThe bars are the same width
    4. DThe vertical scale does not start at zero
    Show answerHide answer

    D: The vertical scale does not start at zero

    A scale that does not start at zero exaggerates differences.

  9. 9

    On a pie chart for 60 people, a sector is \(54^\circ\). What percentage is that?

    1. A\(54\%\)
    2. B\(9\%\)
    3. C\(15\%\)
    4. D\(30\%\)
    Show answerHide answer

    C: \(15\%\)

    \(\dfrac{54}{360} = 0.15\).