d. The sum of the last column is divided by the number of cases to get
A fallacy inherent in this process, and which can sometimes
lead to small errors, grows out of the assumption that the scores in each
interval are symmetrically grouped about the midpoint.
e. Another shortcut method involves the use of an assumed mean.
Averaging of the differences is then applied to the assumed mean to produce
the true mean. For example, using the same 100 readings, it appears that
the average will be somewhere near 100.
Using this value as an assumed
mean we subtract it (100) from each of the readings to get the differences.
The work is shown in the following tabular form.
f. The average of all of the differences equals the sum of the (+)
differences minus the sum of the (-) differences divided by the number of
The true mean is the assumed mean plus the average of the