Leo+DadMade for Leo
Picturing Data
Rung 2 of 4 · The method

Summarising the Middle

You can see the data now. Next move: squeeze a whole dataset down to one or two honest numbers — mean, median, mode and range.

NESA SC4-DA1-01 Mean · median · mode · range

Play Drag the seven data dots along the number line. Mean, median, mode and range recalculate live.
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A chart shows everything at once, but sometimes you need a single number that stands for the whole lot — "on average, how warm was it?" Those single numbers are measures of the middle, and there are three of them, plus one number for the spread.

The Three Middles and the Spread

Mean — add them all up, divide by how many there are. For 4, 6, 6, 8, 11 you get 35 ÷ 5 = 7. It uses every value, which is its strength and (next rung) its weakness. Median — line them up smallest to largest and take the middle one; for that set it's 6. It only cares about order, so a wild value can't yank it around. Mode — the value that turns up most often, here 6; it's the only average you can use on categories. Range — largest minus smallest, 11 − 4 = 7; not a middle at all, but a measure of how spread out the data is.

Say it plainly: mean = add and divide. Median = middle of the ordered list. Mode = most common. Range = biggest minus smallest. Three of them find the centre; the range tells you how tightly the data hugs it.

The Method for Any Dataset

One — order the data. Write the values smallest to largest. Half the mistakes in this topic come from skipping this; the median and range both need it, and ordering makes the mode obvious. Two — pick the average that fits the question. Mean for a balanced spread of numbers, median when you suspect an odd value is lurking, mode for categories or when "most common" is what you actually want. Three — add the range for context. Two classes can both average 70% on a test while one was all 68–72 and the other half 45s and half 95s — the range is what tells them apart.

A Worked One, Slowly

Seven students timed a paper spinner falling (seconds): 3, 4, 4, 5, 6, 4, 9. First order them: 3, 4, 4, 4, 5, 6, 9. The mode is 4 (it appears three times). The median is the fourth, middle value — also 4. The mean is 35 ÷ 7 = 5. The range is 9 − 3 = 6. Notice the mean (5) sits above the median and mode (both 4) — that's the lone 9 pulling it up, which is exactly what the next rung is about. Order it, name your four numbers, and the whole experiment fits on one line.

Us, Thinking Out Loud

Could you teach me mean, median and mode back, using your own seven numbers?

Two classes both average 70%. What could the range tell you that the average can't?