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Statistics (Mean, Mode, Median and Range) (F)

Understand mean, median, mode and range for GCSE: calculate averages from lists and frequency tables, compare data spreads, and choose the best average for context.

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Fascinating Fact:

In a frequency table, use weighted totals. Scores 3, 4, 5 with frequencies 2, 1, 3 give mean = (3×2 + 4×1 + 5×3) ÷ (2 + 1 + 3) = 25 ÷ 6.

In GCSE Maths, you summarise data using averages and spread. You’ll calculate mean, median, mode and range from raw lists and frequency tables, then interpret which measure best represents the data.

Key Terms

Mean: The arithmetic average; add all values and divide by how many there are.
Median: The middle value when the data are in order; if two middles, average them.
Range: A measure of spread; largest value minus smallest value.

Frequently Asked Questions (Click to see answers)

How do I find the mean from a frequency table?

Multiply each value by its frequency, add those products, then divide by the total frequency: mean = Σ(x×f) ÷ Σf.

What’s the difference between mean, median, mode and range?

Mean uses all values but is sensitive to outliers. Median is the middle and is robust. Mode is the most frequent value. Range measures spread.

Which average should I use in GCSE Maths?

Use the median if outliers skew results, the mean for balanced data, and the mode for most common categories. Quote the range to show variability.

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You can find more about this topic by visiting BBC Bitesize - Representing data

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

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