Histograms

Definition of Histogram:Histogram mean graphical display of tabular frequencies, shown as adjacent rectangles. Each quadrilateral is erecting over an interval, with an area the same to the frequency of the interval. The height of a rectangle is also the same to the frequency density of the interval. The total area of the histogram is the same to the number of data. Learning Histogram may also be based on the relative frequency.
Histograms are similar to bar charts apart from the consideration of areas. In a bar chart, all of the bars are the same width and the only thing that matters is the height of the bar. In a histogram, the area is the important thing.

Example

Draw a histogram for the following information.

Height (feet):Frequency Relative Frequency

0-2 0 0

2-4 1 1

4-5 4 8

5-6 8 16

6-8 2 2

(Ignore relative frequency for now). It is difficult to draw a bar chart for this information, because the class divisions for the height are not the same. The height is grouped 0-2, 2-4 etc, but not all of the groups are the same size. For example the 4-5 group is smaller than the 0-2 group.

When drawing a histogram, the y-axis is labelled 'relative frequency' or 'frequency density'. You must work out the relative frequency before you can draw a histogram. To do this, first you must choose a standard width of the groups. Some of the heights are grouped into 2s (0-2, 2-4, 6-8) and some into 1s (4-5, 5-6). Most are 2s, so we shall call the standard width 2. To make the areas match, we must double the values for frequency which have a class division of 1 (since 1 is half of 2). Therefore the figures in the 4-5 and the 5-6 columns must be doubled. If any of the class divisions were 4 (for example if there was a 8-12 group), these figures would be halved. This is because the area of this 'bar' will be twice the standard width of 2 unless we half the frequency.

If you are having problems working out the height of each of the bars, you can use the formula

Area of bar = frequency x standard width