Calculating the mean for grouped data.

Sometimes the data for which we want to find a mean has been grouped into classes.
We don't know the individual values, only the number of values in each class.

As an example consider the times taken by 30 students to do a test. Their times have been summarised in a table

We make the assumption that within each class the mean of the values in that class equals the mid-point value of the class.
To find the mid-point value for each class add the values of the 2 end points together and divide by 2.
e.g. for the first class 0 + 5 = 5, and 5/2 = 2·5

Calculate the mid-points of the other two classes and place the cursor on the appropriate cell to check your answer. To find the total time taken by the students in each time interval multiply the mid point value by the number of students in that interval. Do the calculations and check your answers as before.	Minutes spent on test mid pt f mid pt x f 0 to less than 5 minutes 2·5 2 at least 5 but less than 10 mins 12 at least 10, less than 20 mins 16 Total 30
To find the mean we find the grand total of the time taken by all the students and divide by the number of students . 335/30 = 11·2 minutes to 1 decimal place.

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Sidney Tyrrell , MIS, Coventry University, January 2001