S2StatisticsFoundation & Higher

Frequency Tables

Frequency tables record how many times each value occurs. Finding averages from them uses an extra step — and for grouped data you can only estimate the mean using midpoints.

40 min Video by Maths Genie AQA GCSE Maths

Averages from Frequency Tables (incl. Estimating the Mean)Watch the walkthrough, then read the notes below.

Open on YouTube

What you'll learn

Find the mean from a frequency table
Find the median and mode from a table
Estimate the mean for grouped data
Use midpoints correctly

Mean from a frequency table

Add a “frequency × value” column. The mean is the total of that column divided by the total frequency — not divided by the number of rows.

mean = \frac{\sum ( f \times x )}{\sum f}

f = frequency, x = value.

f \times x

3 \times 2 = 6

and

2 \times 5 = 10

2Total

= 16

, total frequency

= 5

16 \div 5 = 3.2

Answer3.2

Grouped data

With grouped data you do not know the exact values, so use the $midpoint$ of each group as $x$ . This gives an $estimate$ of the mean. The modal class is the group with the highest frequency.

Tip — Divide by the total frequency (Σf), not by the number of groups.

Remember these

mean = \frac{\sum f x}{\sum f}

Mean from a frequency table.

midpoint = \frac{lower + upper}{2}

For grouped data.

Watch out for these

Dividing by the number of rows instead of the total frequency.

Divide Σfx by Σf (the total frequency).

Using the exact mean for grouped data.

Grouped data gives an estimate using midpoints.

Key takeaways

Mean = Σ(f × x) ÷ Σf.
Grouped data: use midpoints to estimate the mean.
Modal class = group with the highest frequency.

Test yourself

Ready to practise Frequency Tables? Pick a mode and earn XP & Dobloons.