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 time, tt minutes, that each member of a gym class spent on a rowing machine. The frequency of one class is unknown.
    Time, tt (minutes)Frequency
    0<t≤100 < t \le 106
    10<t≤2010 < t \le 20xx
    20<t≤3020 < t \le 3010
    30<t≤4030 < t \le 404
    An estimate for the mean time is 18 minutes.

    (a) Work out the value of xx.

    (b) Find the class interval that contains the median.
    Level 5 · 6 marksTry it
  2. 2
    Two farms record the mass, mm grams, of every egg they collect one morning.

    Farm A collected 100 eggs.
    Mass, mm (grams)Frequency
    40<m≤5040 < m \le 5012
    50<m≤6050 < m \le 6038
    60<m≤7060 < m \le 7034
    70<m≤8070 < m \le 8016
    Farm B collected 80 eggs.
    Mass, mm (grams)Frequency
    40<m≤5040 < m \le 509
    50<m≤6050 < m \le 6021
    60<m≤7060 < m \le 7032
    70<m≤8070 < m \le 8018
    (a) Work out an estimate for the mean mass of an egg from Farm A.

    (b) Work out an estimate for the mean mass of all 180 eggs from the two farms together. Give your answer correct to 1 decimal place.

    (c) A worker at Farm B says: "Our modal class is 60<m≤7060 < m \le 70, so most of our eggs weigh 65 g."

    Write down two things that are wrong with what the worker says.
    Level 5 · 8 marksTry it