d. The sum of the last column is divided by the number of cases to get

the average.

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

cases (100).

The true mean is the assumed mean plus the average of the

differences.