Arithmetic Mean of Frequency Distribution

In case of frequency distribution the raw data is arranged by intervals having corresponding frequencies. So if we are interested to find the mean of the data having class intervals we must know the variable x. This variable can be obtained by calculating the mid point of each interval.

Problem: Find the arithmetic mean of the data given in the table below.



In frequency distribution actual values of the data are not known therefore an assumption is made that the values of the data are mid-points of the intervals. The calculation of these mid points and arithmetic mean  is given in the table below.



In the above table we have calculated the mid points (variable x) by adding the lower class limit (L.C.L) of each class interval with upper class limit (U.C.L) and divided the sum by 2.  Similarly mean is obtained by multiplying x with corresponding frequencies f and dividing the sum of fx with total frequency.

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