MEASURE OF DISPERSION
In order to understand the data, you need to be aware of the dispersion or variability of the data. To do so, you need more information than just the mean. Different distributions may have the same mean, so the mean alone is not that informative.
The range measures variability and is merely the lowest item and the highest item. IDEA's field statistics displays a minimum value and a maximum value, which is the range of the data in that particular field. The range gives some indication of the distribution of the data. Certainly, it advises you of the extremes. For example, data in a particular accounts payable file may have a range from $9.00 to $1,004,462.00. While this may not be meaningful alone, additional information will give you a better sense of the data. More useful types of ranges might include transaction numbers, check numbers, or transaction date starting and ending information.
MEASURE OF VARIABILITY
Measuring variability is the determination of how far the data is spread out. It is the extent to which data points in a data set diverge from the mean or average value. Knowledge of the variability of the data provides the auditor or investigator with a sense of whether transactions are outside of the normal area or pattern.
Deviations from the Mean
Deviation from the mean is how far a number is away from the mean of the distribution. This is calculated by subtracting the mean from the individual numbers. Some numbers will be below the mean, resulting in negative differences, and some will be above the mean, resulting in positive differences. The total or sum of these differences will always net to zero.
The Mean Deviation
This is also known as the average deviation that describes (on the average) how far each number is from the mean. This is calculated by subtracting the mean from the individual numbers, but the differences are in absolute values—that is, the negative signs are ignored. The sums of these differences are calculated and then divided by the number of records in the distribution.