Your class sits a test and the scores are all over the place — how did the class "do", as a single number? An average answers exactly that: it's one value that stands in for a whole set of data, a typical value. There are three kinds of average, and the trick is knowing what each one is really telling you.
Why this matters: averages are everywhere the moment you leave the classroom — average pay, average rainfall, a game's average score, a shop's average sale. Choosing and reading the right one lets you summarise a pile of numbers honestly instead of being fooled by it.
The three averages
- Mean — add up all the values and divide by how many there are. Think of it as the "share it out equally" average: if everyone pooled their scores and split them fairly, that's the mean.
- Median — put the values in order and take the middle one. It's the "person standing in the exact middle of the queue".
- Mode — the value that appears most often. Handy hook: mode and most both start with "mo".
4, 7, 8, 5, 6
• Mean = (4+7+8+5+6) ÷ 5 = 30 ÷ 5 = 6.
• Median: order → 4, 5, 6, 7, 8 → the middle one is 6.
• Mode: no value repeats here, so there's no mode.
• Mean = (4+7+8+5+6) ÷ 5 = 30 ÷ 5 = 6.
• Median: order → 4, 5, 6, 7, 8 → the middle one is 6.
• Mode: no value repeats here, so there's no mode.
Which average when?
They can give quite different answers, so each has its moment:
| Average | How to find it | Best when… |
|---|---|---|
| Mean | total ÷ count | data is fairly even, no wild values |
| Median | middle of ordered list | there's an extreme value pulling the mean |
| Mode | most common value | data isn't numerical (e.g. favourite colour) |
Why the median can be fairer: in the wages 15, 16, 17, 18, 400 (thousand), the mean is a misleading 93 — nobody earns near that. The median, 17, describes the group far better because a single huge value can't drag it up.
Common mistake: the median needs the data ordered first — always sort the numbers before picking the middle. And with an even count there are two middle values, so the median is halfway between them (add them and divide by 2). For 4, 8, 2, 6 → order 2, 4, 6, 8 → median = (4+6)÷2 = 5.
Range — a measure of spread
The range isn't an average at all — it doesn't tell you the typical value, it tells you how spread out the data is, from lowest to highest.
Range = largest value − smallest value
12, 5, 8, 20, 3: range = 20 − 3 = 17. A big range means the data is widely spread; a small range means the values huddle close together.
In a nutshell: mean = add ÷ count; median = middle of the ordered list; mode = most common; range = biggest − smallest (that's spread, not an average).