Averages and reading data
Maths · Key Stage 2 · The School
Four numbers that describe a set
MEAN: add them all, divide by how many — the fair share. MEDIAN: put them in order, take the middle — the typical one. MODE: the most common. RANGE: biggest minus smallest — how spread out they are. Range is not an average; it describes spread, and a set can have the same mean but a wildly different range.
When the mean lies
Wages 18, 19, 20, 21, 220 (thousands). The mean is 59.6 — a figure NOBODY earns. The median is 20, which honestly describes the group. One extreme value drags the mean; the median ignores it. Whenever you meet an average in the news, ask which one it is and whether an outlier is doing the talking.
Reading a graph properly
Check three things before believing any chart: does the vertical axis start at zero (if not, differences look bigger than they are)? What are the units? Where did the data come from? A bar chart with a chopped axis is the most common honest-looking way to mislead, and now you can spot it.
Five salaries, in thousands: 18, 19, 20, 21, 220. MEAN: total 298 ÷ 5 = 59.6. MEDIAN: put in order, take the middle = 20. MODE: no value repeats, so there is none. RANGE: 220 − 18 = 202. Which describes the group? The median, by a long way — nobody earns 59.6, and the mean has been dragged up by a single figure. Report the mean here and you have technically told the truth and completely misled the reader.