The mean value for a set of data may given us some information about the set itself, many varying sets can have the same mean value. To determine how the sets are different we need more information. Another way of examining single variable data is to look at how the data is spread out or dispersed about the mean.
Range
The simplest of our methods for measuring dispersion is range. Range is the difference between the largest value and the smallest value in the data set. While being simple to compute, the range is often unreliable as a measure of dispersion since it is based on only two values in the set.
A range of 50 tells us very little about how the values are dispersed.
Are the values all clustered to one end with the low value (12) or the high value (62) being an outlier?
Mean Absolute Deviation (MAD)
The mean absolute deviation is the mean (average) of the absolute value of the difference between the individual values in the data set and the mean. The method tries to measure the average distances between the values in the data set and the mean.
Variance
To find the variance:
- Subtract the mean,
, from each of the values in the data set,
.
- Square the result
- Add all of these squares
- And divide by the number of values in the data set.
Standard Deviation
Standard deviation is the square root of the variance. The formulas are:
Mean absolute deviation, variance and standard deviation are ways to describe the difference between the mean and the values in the data set without worrying about the signs of these differences.
These values are usually computed using a calculator.
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