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Statistics · Histograms

Chapter 1 · 3

The idea

Interpreting histograms

Getting information back out of a histogram — a frequency is an area, so part of a class is the matching proportion of a bar's area. Why that rests on values being spread evenly within a class (and is therefore an estimate), and how to read off a total, a mean, the median class, a range that cuts across class boundaries, and a comparison of two groups.

A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.

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Statistics · Histograms

Interpreting histograms

Getting information back out of a histogram — a frequency is an area, so part of a class is the matching proportion of a bar's area. Why that rests on values being spread evenly within a class (and is therefore an estimate), and how to read off a total, a mean, the median class, a range that cuts across class boundaries, and a comparison of two groups.

Why it works

Reading turns areas back into frequencies

Building a histogram turns frequencies into areas. Reading one turns areas back into frequencies. That is the whole of this page. The height of a bar is the frequency density, so

area of a bar  =  width×frequencywidth  =  frequency,\text{area of a bar} \;=\; \text{width} \times \frac{\text{frequency}}{\text{width}} \;=\; \text{frequency},

and every question below is secretly the same question: which area am I being asked for?

Here is the histogram we will read all the way through. It shows the times, in minutes, that 100100 people took to finish a task.

Keep reading — free

The rest of the explanation, plus 3 worked examples you step through move by move.

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Takes a minute — no card.