Suppose 200 people rate a film out of 5. Writing out 200 separate scores would be madness — so instead we record how many people gave each score in a frequency table. "Frequency" is just a posh word for how many times something happened.
Finding the mean from a frequency table
You can't just add the values in the left column — that would treat a score earned by 50 people the same as one earned by a single person. You have to weight each value by how often it happened. So: multiply each value by its frequency, add those products up, then divide by the total frequency.
The analogy: it's the ordinary "add-them-all-up-and-divide" mean, but instead of writing the number 3 out five separate times, you take a shortcut and do 3 × 5 in one go.
• value × frequency: 1·2 + 2·3 + 3·5 = 2 + 6 + 15 = 23.
• total frequency = 2 + 3 + 5 = 10.
• Mean = 23 ÷ 10 = 2.3.
Grouped data and the modal class
Sometimes the data is bundled into classes such as 0–10, 10–20, 20–30. Now we've lost the exact values — we only know which group each item fell into. To estimate a mean we use the midpoint of each class as a fair stand-in for everything in it, so the answer is an estimate, not the exact mean.
The modal class is simply the group with the highest frequency — the "mode" idea applied to groups. You don't need midpoints for it; just read off which row has the biggest count.
| Task | What to use |
|---|---|
| Mean from a list of values | Σ(value × frequency) ÷ Σ(frequency) |
| Estimated mean from groups | same, but use class midpoints |
| Modal class | the group with the highest frequency |
In a nutshell: mean from a table = Σ(value × frequency) ÷ Σ(frequency); for grouped data use the class midpoints, which makes it an estimate; the modal class is the group with the biggest frequency.