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 frequency polygon shows information about the times, tt minutes, that 4040 customers spent in a charity shop.

    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) Assume that every customer in a class spent the time at the midpoint of the class.

    Work out an estimate of the mean time.

    (3 marks)
    (b) In fact, most of the customers in the class 30<t≤4030 < t \le 40 spent close to 3030 minutes in the shop.

    What does this mean about your answer to part (a)?

    Tick one box.

    ☐ It is too small ☐ It is too big ☐ It is correct ☐ It is impossible to tell

    (1 mark)
    Level 4 · 4 marksTry it
  2. 2
    The table shows information about the masses, mm kg, of 3030 lambs on a farm.
    Mass (mm kg)Frequency
    0<m≤40 < m \le 433
    4<m≤84 < m \le 877
    8<m≤128 < m \le 121010
    12<m≤1612 < m \le 1666
    16<m≤2016 < m \le 2044
    Sam draws this frequency polygon for the information.246810121416182022123456789101112Mass (kg)Frequency(a) Give two criticisms of Sam's frequency polygon.

    (2 marks)
    (b) Write down the coordinates of the points Sam should have plotted.

    (2 marks)
    Level 4 · 4 marksTry it
  3. 3
    Ella has two playlists. Each playlist has 2020 songs.

    The frequency polygons show information about the lengths, ll minutes, of the songs on each playlist.

    The classes are 0<l≤20 < l \le 2, 2<l≤42 < l \le 4, 4<l≤64 < l \le 6 and 6<l≤86 < l \le 8.12345678123456789101112Playlist 1Playlist 2Length (minutes)FrequencyElla says,

    "On average, the songs on Playlist 2 are longer than the songs on Playlist 1."

    Is Ella correct?

    You must show how you get your answer.

    (4 marks)
    Level 4 · 4 marksTry it
  4. 4
    Club A has 4040 members and Club B has 2525 members. One Saturday, every member of both cycling clubs went for a ride.

    The frequency polygons show information about the distances, dd km, they cycled.

    The classes are 0<d≤100 < d \le 10, 10<d≤2010 < d \le 20, 20<d≤3020 < d \le 30 and 30<d≤4030 < d \le 40.24681012141618202224262830323436384024681012141618Club AClub BDistance (km)FrequencyRaj says,

    "A member of Club A is more likely to have cycled more than 2020 km than a member of Club B, because more Club A members cycled more than 2020 km."

    Is Raj correct?

    You must show how you get your answer.

    (4 marks)
    Level 4 · 4 marksTry it