GCSE · Averages & range

Averages from a frequency tableExam-style questions

Mean, median, mode and range from a discrete frequency table — why the mean is the sum of the fx column divided by the total FREQUENCY, not by the number of rows, and how to run it backwards to find a missing frequency.

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

DifficultyAllLevel 1Level 2Level 3Level 4Level 5
  1. 1
    The table shows the number of pets owned by each of 2020 students.
    Number of pets0123
    Frequency5843
    (a) Work out the mean number of pets. (3 marks)

    (b) Write down the median number of pets. (1 mark)
    Level 3 · 4 marksTry it
  2. 2
    The table shows the number of people travelling in each of 40 cars that passed a checkpoint.
    Number of people, xxFrequency, ff
    114
    212
    38
    44
    52
    Work out the mean number of people per car.
    Level 3 · 3 marksTry it
  3. 3
    The table shows the number of books read last month by each of 31 students.
    Number of books, xxFrequency, ff
    04
    111
    28
    35
    43
    (a) Write down the modal number of books.

    (b) Work out the median number of books.
    Level 3 · 3 marksTry it
  4. 4
    The table shows the number of times each of 50 pupils was late during one term.
    Number of times late, xxFrequency, ff
    021
    114
    29
    34
    42
    Ali says: "The mean is 22, because (0+1+2+3+4)÷5=2(0 + 1 + 2 + 3 + 4) \div 5 = 2."

    (a) Explain what is wrong with Ali's method.

    (b) Work out the correct mean number of times a pupil was late.
    Level 3 · 4 marksTry it