GCSE · Averages & range

Estimating averages from grouped dataExam-style questions

Why a mean from a grouped frequency table can only ever be an estimate, how to use midpoints in $\frac{\sum fx}{\sum f}$, and why the mode and median come out as a class rather than a number.

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13 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 times, tt minutes, that 3030 students took to finish a puzzle.
    Time (tt minutes)Frequency
    0<t≤100 < t \le 1055
    10<t≤2010 < t \le 201818
    20<t≤3020 < t \le 3077
    Write down the modal class.
    Level 1 · 1 markTry it
  2. 2
    The table shows the times, tt minutes, that 3030 students took to finish a puzzle.
    Time (tt minutes)Frequency
    0<t≤100 < t \le 1055
    10<t≤2010 < t \le 201818
    20<t≤3020 < t \le 3077
    Write down the midpoint of the class 10<t≤2010 < t \le 20, and explain why an estimate of the mean uses midpoints.
    Level 1 · 2 marksTry it
  3. 3
    The table shows the ages of 3030 members of a running club.
    Age, aa (years)Frequency
    10<a≤2010 < a \le 204
    20<a≤3020 < a \le 309
    30<a≤4030 < a \le 4012
    40<a≤5040 < a \le 505
    (a) Calculate an estimate of the mean age. [3]

    (b) Explain why your answer to part (a) is only an estimate. [1]
    Level 2 · 4 marksTry it
  4. 4
    The table shows information about the time, tt minutes, that each of 40 customers waited to be served in a post office.
    Time, tt (minutes)Frequency
    0<t≤20 < t \le 215
    2<t≤42 < t \le 49
    4<t≤64 < t \le 610
    6<t≤86 < t \le 86
    (a) Write down the modal class.

    (b) Find the class interval that contains the median.
    Level 2 · 3 marksTry it
  5. 5
    The table shows the times, tt minutes, that 3030 people waited at a clinic.
    Time, tt (minutes)Frequency
    0<t≤200 < t \le 206
    20<t≤4020 < t \le 4011
    40<t≤6040 < t \le 609
    60<t≤8060 < t \le 804
    (a) Work out an estimate for the mean waiting time. Give your answer correct to 1 decimal place. (3 marks)

    (b) Write down the modal class. (1 mark)
    Level 3 · 4 marksTry it

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