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 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
  2. 2
    The table shows information about the time, tt minutes, that each of 2020 students spent on homework one evening.
    Time, tt (minutes)Frequency
    0<t≤100 < t \le 104
    10<t≤2010 < t \le 206
    20<t≤3020 < t \le 308
    30<t≤4030 < t \le 402
    (a) Work out an estimate for the mean time spent on homework. (3 marks)
    (b) Write down the modal class. (1 mark)
    Level 3 · 4 marksTry it
  3. 3
    The table shows information about the lengths, xx cm, of 50 leaves collected from a tree.
    Length, xx (cm)Frequency
    0<x≤100 < x \le 108
    10<x≤2010 < x \le 2014
    20<x≤3020 < x \le 3018
    30<x≤4030 < x \le 4010
    Work out an estimate for the mean length of a leaf.
    Level 3 · 4 marksTry it
  4. 4
    30 shoppers each bought something from a market stall. The table shows information about the amount, £aa, each shopper spent.
    Amount spent, £aaFrequency
    0<a≤50 < a \le 57
    5<a≤105 < a \le 1012
    10<a≤1510 < a \le 158
    15<a≤2015 < a \le 203
    (a) Write down the modal class.

    (b) Work out an estimate for the mean amount spent by a shopper. Give your answer in pounds, correct to the nearest penny.
    Level 3 · 5 marksTry it
  5. 5
    A post office weighed 60 parcels. The table shows information about the weight, ww grams, of each parcel.
    Weight, ww (grams)Frequency
    0<w≤500 < w \le 5022
    50<w≤10050 < w \le 10019
    100<w≤150100 < w \le 15011
    150<w≤200150 < w \le 2008
    (a) Work out an estimate for the mean weight of a parcel. Give your answer correct to 1 decimal place.

    (b) Explain why your answer to part (a) can only be an estimate.
    Level 3 · 5 marksTry it