Every card in Statistics

7

HintAdd them all together, then share the total equally between the values.

WhyThe three values total 21, and dividing by how many there are gives the mean. The mean is what each value would be if the total were shared out evenly.

Subtract the smallest value from the largest

HintIt measures spread by using only the two ends of the data.

WhyThe range describes how far apart the data reaches, so it is a measure of spread rather than an average. One extreme reading can stretch it a long way.

4

HintPut the numbers in order first, then look at the one in the middle.

WhyIn order the data reads 1, 3, 4, 7, 9, and the middle value is the median. With an even number of values you take the mean of the middle pair instead.

As a line drawn across the previous four

HintThe marks are bundled in fives so a long total can be counted quickly.

WhyCounting bundles rather than single marks makes a long list quick to total. The frequency column then records those totals as ordinary numbers.

So the heights alone show the frequencies

HintA fatter bar would look bigger to the eye even with an identical count.

WhyEqual widths keep the comparison honest, because the eye judges area as well as height. Bar charts also need gaps between the bars, since the categories are separate things.

The key

HintWithout it the pictures mean nothing — look for the small note beside the chart.

WhyOne symbol might stand for 10 people, so half a symbol would mean 5. Read it before counting anything, or every figure will come out wrong.

No change

HintThe line neither climbs nor falls across that stretch.

WhyA flat section means the measurement stayed the same through that period. A steep rise shows a fast increase, and a downward slope shows a fall.

9°

HintShare a full turn out between everyone in the survey.

WhyA full circle is 360°, and dividing that between 40 people gives each one a slice of 9°. Multiplying by a category frequency then gives that slice its angle.

The mode

HintThe shop wants the size that turns up most often, not a calculated middle.

WhyIt is the only average that works for categories such as favourite colour, and it is what a shop needs when deciding which sizes to restock.

It pulls the mean upwards

HintEvery reading goes into the total, so an extreme one drags the average with it.

WhyBecause all the data is added in, a single extreme reading shifts the answer. The median barely moves, which is why it is preferred for figures such as house prices.

positive correlation

HintAs one measurement goes up, the other tends to go up as well.

WhyA line of best fit summarises that trend and can be used to predict, though only within the range of the data collected. Points falling from left to right show the opposite relationship.

The hot weather

HintAsk what else changes outdoors between June and December.

WhyThis is the classic example of correlation without causation: temperature drives both figures, and neither one causes the other. Always ask what else could explain a pattern before claiming a cause.