# GCSE Maths: Histograms

A histogram can be used to display continuous data. The area of each rectangle represents the frequency. When drawing a histogram, if there are intervals with different widths, take care because frequency is equal to the area of a rectangle, not its height. In the absence of any other information, it must be assumed that within each rectangle the individual data points are evenly distributed.

Example

The histogram below shows information about the distances 600 people travel to work.

(i) How many people travel more than 20 miles to work?

(ii) 224 of these people travel further to work than I do. Estimate the distance I travel to work.

Solutions

(i) The last box in the histogram is everyone who travels more than 20 to work:

width = 60 - 20 = 40 and height = 5, so the area = 40 x 5 = 200 people.

(ii) Everybody in the 20-60 mile bracket travels further than me, which is 200 people.

This leaves another 24 people who travel further than me, but there is only a total of 80 people in the 10-20 mile bracket.

So I must be in this bracket and 24/80 = 3/10 of the other people in it travel further than me, and 3/10 of the people is represented by 3/10 of the width of the bracket.

Width = 20 - 10 = 10,    3/10 x 10 = 3, 20 – 3 = 17

I travel 17 miles to work

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