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.

Start practising Read the lesson

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