A frequency distribution table is a table that shows how often a data point or a group of data points appears in a given data set. To make a frequency distribution table, first divide the numbers over which the data ranges into intervals of equal length. Then count how many data points fall into each interval.
If there are many values, it is sometimes useful to go through all the data points in order and make a tally mark in the interval that each point falls. Then all the tally marks can be counted to see how many data points fall into each interval. The "tally system" ensures that no points will be missed.
Example: The following is a list of prices (in dollars) of
birthday cards found in various drug stores:
1.45 | 2.20 | 0.75 | 1.23 | 1.25 |
1.25 | 3.09 | 1.99 | 2.00 | 0.78 |
1.32 | 2.25 | 3.15 | 3.85 | 0.52 |
0.99 | 1.38 | 1.75 | 1.22 | 1.75 |
Intervals (in dollars) | Frequency |
0.50 - 0.99 | 4 |
1.00 - 1.49 | 7 |
1.50 - 1.99 | 3 |
2.00 - 2.49 | 3 |
2.50 - 2.99 | |
3.00 - 3.49 | 2 |
3.50 - 3.99 | 1 |
Total | 20 |
A histogram is a bar graph which shows frequency distribution.
To make a histogram, follow these steps:
Histograms are useful because they allow us to glean certain information at a glance. The previous example shows that more birthday cards cost between $1.00 and $1.49 than any other price, because the bar which corresponds to those values is highest. We can also see that twice as many cards cost between $3.00 - $3.49 as cost between $3.50 - $3.99, because the bar which corresponds to $3.00 - $3.49 is twice as high as the bar which corresponds to $3.50 - $3.99.