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AQA GCSE Maths

Statistics: averages, spread and diagrams — AQA GCSE Maths revision

Free revision notes, key terms, common exam traps and 5 practice questions with answers. About 7 minutes to read.

Averages

  • Mean = total of values ÷ number of values.
  • Median is the middle value when data is ordered; for n values use position (n+1)/2.
  • Mode is the most frequent value; modal class is the class with highest frequency in grouped data.

Spread and grouped data

  • Range = highest value − lowest value.
  • Estimated mean for grouped data uses midpoints: Σ(midpoint × frequency) ÷ Σfrequency.
  • Interquartile range (IQR) = upper quartile − lower quartile, showing the spread of the middle 50%.

Key terms

Mean
Sum of values divided by the number of values.
Median
The middle value of ordered data.
Mode
The most frequently occurring value.
Range
Highest value minus lowest value.
Interquartile range
Upper quartile minus lower quartile.
Frequency density
Frequency ÷ class width, used for histogram bar heights.

Common exam traps

  • Using frequency instead of frequency density for histogram bar heights with unequal widths.
  • Forgetting to use midpoints when estimating the mean of grouped data.
  • Reading the median from a cumulative frequency graph at the wrong height (should be n/2, not n).

Practice questions with answers

  1. 1. Find the mean of 4, 7, 9, 12, 8.

    Answer: 8

    Sum = 40, 40÷5 = 8.

  2. 2. Find the median of 3, 8, 5, 1, 9.

    Answer: 5

    Ordered: 1,3,5,8,9. Middle value is 5.

  3. 3. Find the range of 12, 5, 19, 8, 15.

    • • 7
    • • 14
    • • 19
    • • 12

    Answer: 14

    19 − 5 = 14.

  4. 4. Find the mode of 2, 3, 3, 5, 5, 5, 7.

    Answer: 5

    5 appears 3 times, more than any other value.

  5. 5. Estimate the mean using midpoints: class 0-10 (freq 4), 10-20 (freq 6). Midpoints 5 and 15.

    Answer: 11

    (5×4 + 15×6)/(4+6) = (20+90)/10 = 110/10 = 11.

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