Cumulative frequency graphs
A cumulative frequency graph is plotting using data which adds up the cumulative frequency or running total of a given data set.
The first step is to complete a cumulative frequency table. In the example below, the table repesents the time spent for 100 people waiting for a taxi.
Time in seconds Cumulative frequency
0 < t ≤ 35 9
0 < t ≤ 40 21
0 < t ≤ 45 45
0 < t ≤ 50 73
0 < t ≤ 55 89
0 < t ≤ 60 100
Plotting a cumulative frequency graph
In the above graph, the upper bound for each class interval is plotted against the cumulative frequency and a smooth curve is created through the points.
As per the graph above, the median time has been estimated to be the 50th person at 47 seconds.
The interquartile range
One the data set has been added to a table and the graph has been plotted, the interquartile range can then be calculated.
The interquartile range is represented as the middle 50% of the data therefore the lower quartile is the data 25% above the list and the upper quartile is the data below the 75% of the list.
As per the above graph:
Lower quartile = 25th person (42 seconds)
Upper quartile = 75th person (51 seconds)
Interquartile range = 51 seconds – 42 seconds = 9 seconds