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KS3 Maths · Year 7 · Chapter 16: Comparing data · Lesson 2

Drawing frequency diagrams

Year 7About 70 minutesNo calculator45 marks
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Date
A

Do Now

Quick questions to start.

  1. A1
    Needed today

    What number is exactly halfway between and ?

    [1 mark]
    Answer
  2. A2
    Needed today

    On an axis, and are squares apart. What does one square stand for?

    [1 mark]
    Answer
  3. A3
    Last lesson

    How many of these times are in the class ? , , , ,

    [1 mark]
    Answer
  4. A4
    From chapter 15

    Solve .

    [1 mark]
    Answer
B

Example, then your turn

Year 7

Your teacher works through each example with you. Then try the one beside it.

Example 1

The table shows the times runners took in a race. Draw a frequency diagram for the data.

Time, t (min)Frequency20 < t ≤ 30330 < t ≤ 40740 < t ≤ 50650 < t ≤ 604
Hint Time is continuous, so the bars touch. The biggest frequency is , so the frequency axis must reach at least .
  1. B1

    The table shows the heights of sunflowers. Draw a frequency diagram for the data.

    [3 marks]
    Height, h (cm)Frequency100 < h ≤ 1205120 < h ≤ 1409140 < h ≤ 16011160 < h ≤ 1805
Example 2

The table shows how long pupils spent on homework. Draw a line graph for the data.

Time, t (min)Frequency0 < t ≤ 20420 < t ≤ 401040 < t ≤ 60760 < t ≤ 803
Hint Plot each frequency above the middle of its class. The middle of is .
  1. B2

    The table shows the masses of parcels. Draw a line graph for the data. Write down the points you plot.

    [3 marks]
    Mass, m (kg)Frequency0 < m ≤ 464 < m ≤ 8118 < m ≤ 12812 < m ≤ 162
Example 3

Should the bars touch? Give a reason each time. (a) The shoe sizes of pupils. (b) The times pupils take to run m.

Hint Can the data take any value between two of its numbers, or only certain values?
  1. B3

    Should the bars touch? Give a reason each time. (a) The numbers of goals scored in matches. (b) The masses of apples. (c) The lengths of worms.

    [3 marks]
C

Practice

Year 7
  1. C1

    A line graph is drawn for the table. Write down the four points that are plotted.

    [2 marks]
    Distance, d (km)Frequency0 < d ≤ 272 < d ≤ 4124 < d ≤ 696 < d ≤ 84
    Answer
  2. C2

    A frequency diagram shows the ages of people. The table gives the heights of its bars. How tall is the missing bar?

    [2 marks]
    Age, a (years)Bar height0 < a ≤ 20820 < a ≤ 401540 < a ≤ 60?60 < a ≤ 805
    Answer
  1. C3

    Jo draws a frequency diagram of the masses of cats. She leaves gaps between the bars. Explain why this is wrong.

    [2 marks]
  2. C4

    On a line graph, Leo plots the point for the class above . Explain his mistake and give the right value of .

    [2 marks]
D

Exam-style questions

GCSE Foundation
  1. D1

    The frequency diagram shows how long some people queued at a post office. Raj says, "More than half of the people queued for longer than minutes."

    Is Raj right? You must show your working.

    [3 marks]
    024681012010203040Time, t (minutes)Frequency
    Answer
  1. D2

    The frequency diagram shows the masses of some suitcases at an airport.

    05101551015202530Mass, m (kg)Frequency
    (a)

    Write down the modal class.

    [1 mark]
    Answer
    (b)

    How many suitcases are there altogether?

    [1 mark]
    Answer
    (c)

    A suitcase over kg pays a fee. What fraction of the suitcases pay the fee? Give your answer in its simplest form.

    [2 marks]
    Answer
    (d)

    A line graph is drawn from the same data. Write down the point plotted for the class .

    [2 marks]
    Answer
    Total for D2: 6 marks
  2. D3

    The bar chart shows the mean temperature in two towns, Ashby and Brook, for four months.

    048121620MonthTemperature (°C)MarAprMayJunAshbyBrook
    (a)

    In which month is the difference between the two towns largest?

    [1 mark]
    Answer
    (b)

    Work out that difference.

    [1 mark]
    Answer
    (c)

    In how many of the months is Ashby warmer than Brook?

    [1 mark]
    Answer
    (d)

    Work out the range of the temperatures in Ashby.

    [2 marks]
    Answer
    Total for D3: 5 marks
  3. D4

    The table shows the travel times of pupils.

    Time, t (min)Frequency0 < t ≤ 10910 < t ≤ 20?20 < t ≤ 301430 < t ≤ 408
    (a)

    Work out the missing frequency.

    [2 marks]
    Answer
    (b)

    Draw a frequency diagram for the data.

    [3 marks]
    Total for D4: 5 marks
E

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

  1. E1

    A frequency diagram shows the times pupils took to finish a puzzle. It has four bars. The second bar is twice as tall as the first. The third bar is shorter than the second. The fourth bar has height . Work out the height of each bar.

    [5 marks]
    Hint 1 · What to try

    Call the height of the first bar .

    Hint 2 · The first line

    Hint 3 · The full method

    , so . Then the bars are , , and .

    Answer
F

How did it go?

Colour one circle on each line.
Not yetNearlyYes
I can draw a frequency diagram from a table.
I can draw a line graph from a table.
I can say when the bars should touch.
I can read values off frequency diagrams.

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