Frequency Tables

The data available for analysis is often only available as a frequency table.  This page describes how the common summary statistics can be derived.  The calculations are based on the mid-point of the intervals.

The example is based on set of measurements of solar radiation for first week of the year at a location in southern England.  The dataset is shown below in the form of a histogram:

The frequency table, together with the calculation of the mean is shown below.  The first column is the interval.  The second, is the mid-point of the interval (named X for simplicity).  The third column is the number of observations (the frequency) which have been recorded for the interval.  The fourth column is the product of the mid point of the interval and the number of observations.

Interval	X	F	X*F
0.0-0.2	0.1	20	2.0
0.2-0.4	0.3	25	7.5
0.4-0.6	0.5	24	12.0
0.6-0.8	0.7	24	16.8
0.8-1.0	0.9	11	9.9
1.0-1.2	1.1	5	5.5
1.2-1.4	1.3	2	2.6
1.4-1.6	1.5	1	1.5

The next step is to calculate the sums of X and X*F

Sums

112

57.8

The final stage is to calculate the mean, as shown below:

Mean

sum(X*F)/sum(F)

0.52

The clip below shows how the calculation might be performed in Excel.

Page updated: 06-May-2006

For more information: info@brighton-webs.co.uk