# Histograms

## Introduction

Histograms are useful tools for dealing with data that is measured on an interval scale. There are two types of histogram, those that plot frequency (which are really more like bar charts) and those that plot frequency-density or relative frequency.

Histograms essentially group the obtained data into sets, known as bins. Frequency histograms have equally sized bins and plot the number of times data points appear in that bin. This is the same as you would have come across at school.

Frequency-density histograms are subtly different. These histograms have varying bin widths, and it is the unit area which is the measure of frequency, not the height. To illustrate this, consider the data shown in table 1.

 Height Interval(m) Frequency Relative Frequency 1.2-1.3 3 3 1.3-1.4 5 5 1.4-1.5 20 20 1.5-1.55 11 22 1.55-1.6 14 28 1.6-1.65 16 32 1.65-1.7 14 28 1.7-1.8 15 15 1.8-1.9 4 4

Relative frequency, uses the idea that if the bin is half the size of the others, the frequency of that bin should be multiplied by two. The reason for this is that the density of the frequency is twice that of the larger bin. A frequency density histogram has been plotted below. Frequency density histogram