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 information about the amount, £mm, spent by each of 50 customers in a shop.
    Amount spent, £mmFrequency
    0<m≤100 < m \le 1012
    10<m≤2010 < m \le 2020
    20<m≤3020 < m \le 3013
    30<m≤6030 < m \le 605
    (a) Work out an estimate for the mean amount spent by a customer.

    (b) The manager checks the till and finds that each of the 5 customers in the last class actually spent less than £40.

    Explain what this tells you about your estimate in part (a).
    Level 4 · 5 marksTry it
  2. 2
    The table shows information about the lengths, cc minutes, of 90 phone calls made from an office.
    Length, cc (minutes)Frequency
    0<c≤50 < c \le 524
    5<c≤105 < c \le 1031
    10<c≤1510 < c \le 1520
    15<c≤2015 < c \le 2015
    (a) Find the class interval that contains the median.

    (b) Work out an estimate for the mean length of a call. Give your answer correct to 1 decimal place.

    (c) Sam says that the median must be exactly the midpoint of the class interval found in part (a).

    Explain why Sam is wrong.
    Level 4 · 7 marksTry it