GCSE · Data representation

Frequency polygonsExam-style questions

Turn a grouped frequency table into a frequency polygon (each frequency plotted at the midpoint of its class, the points joined with straight lines) and read one back into a table. Find the modal class, the class containing the median and an estimate of the mean from a polygon, compare two polygons on one grid in context, and spot the mistakes that cost marks.

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15 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4
  1. 1
    The table shows information about the masses of 5050 tomatoes.
    Mass (mm grams)Frequency
    40<m≤5040 < m \le 5066
    50<m≤6050 < m \le 601111
    60<m≤7060 < m \le 701717
    70<m≤8070 < m \le 801010
    80<m≤9080 < m \le 9066
    Draw a frequency polygon for this information.4050607080905101520Mass (m grams)Frequency(2 marks)
    Level 2 · 2 marksTry it
  2. 2
    The table shows information about the times, tt minutes, that 3030 people took to complete an online survey.
    Time (tt minutes)Frequency
    0<t≤100 < t \le 1022
    10<t≤2010 < t \le 2099
    20<t≤3020 < t \le 301313
    30<t≤4030 < t \le 4066
    Kyle is going to draw a frequency polygon for this information.

    Write down the coordinates of the four points he should plot.

    (2 marks)
    Level 2 · 2 marksTry it
  3. 3
    The table shows information about the times, tt minutes, that 3030 students spent reading on Sunday.
    Time (tt minutes)Frequency
    0<t≤100 < t \le 1066
    10<t≤2010 < t \le 201111
    20<t≤3020 < t \le 3099
    30<t≤4030 < t \le 4044
    Four students each drew a diagram for this information.

    Diagram 12468101214161820222426283032343638401234567891011121314Time (minutes)FrequencyDiagram 22468101214161820222426283032343638401234567891011121314Time (minutes)FrequencyDiagram 32468101214161820222426283032343638401234567891011121314Time (minutes)FrequencyDiagram 42468101214161820222426283032343638401234567891011121314Time (minutes)Frequency(a) Which diagram is a correct frequency polygon for the information in the table? Write down its number.

    (1 mark)
    (b) Explain what is wrong with Diagram 4.

    (1 mark)
    Level 2 · 2 marksTry it
  4. 4
    The frequency polygon shows information about the times, tt minutes, that some students spent practising a musical instrument on Saturday.

    The classes are 0<t≤100 < t \le 10, 10<t≤2010 < t \le 20, 20<t≤3020 < t \le 30 and 30<t≤4030 < t \le 40.246810121416182022242628303234363840246810121416Time (minutes)Frequency(a) How many students are shown on the frequency polygon?

    (1 mark)
    (b) Find the class interval that contains the median.

    (1 mark)
    (c) What percentage of the students practised for more than 2020 minutes?

    (2 marks)
    Level 3 · 4 marksTry it
  5. 5
    The frequency polygon shows information about the distances, dd km, that 2020 members of a walking club walked one Sunday.

    The classes are 0<d≤40 < d \le 4, 4<d≤84 < d \le 8, 8<d≤128 < d \le 12 and 12<d≤1612 < d \le 16.24681012141612345678910Distance (km)Frequency(a) Work out an estimate for the mean distance walked.

    (3 marks)
    (b) Explain why your answer to part (a) is only an estimate.

    (1 mark)
    Level 3 · 4 marksTry it

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