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: 
02 
0 
0 
24 
1 
1 
45 
4 
8 
56 
8 
16 
68 
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 02, 24 etc, but not all of the groups are
the same size. For example the 45 group is smaller than the 02
group.
When drawing a histogram, the yaxis 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 (02, 24, 68) and
some into 1s (45, 56). 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 45 and the
56 columns must be doubled. If any of the class divisions were 4 (for example
if there was a 812 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
Copyright © Matthew Pinkney 2003
