Statistics：全部卡片

7

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

为什么The 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

提示It measures spread by using only the two ends of the data.

为什么The 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

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

为什么In 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

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

为什么Counting 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

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

为什么Equal 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

提示Without it the pictures mean nothing — look for the small note beside the chart.

为什么One 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

提示The line neither climbs nor falls across that stretch.

为什么A 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°

提示Share a full turn out between everyone in the survey.

为什么A 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

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

为什么It 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

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

为什么Because 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

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

为什么A 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

提示Ask what else changes outdoors between June and December.

为什么This 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.