Even More About MAD

Although MAD sounds like anger or insanity, it’s not really the craziest statistic around. The real name is Mean Absolute Deviation. Or MAD, for short.

s the name suggests, mean absolute deviation (sometimes called mean variance) is a measure of deviation (variation) from the mean. To find the average amount of variation, the mean is subtracted from each score.

In the first column is a variable we’ll call X. The mean of this variable is 5. So 5 (column 2) is deducted from each score and the result forms column 3. Since the result is a measure of deviation from the mean, the third column is labeled d (little d).

        7     5     2
        5     5     0
        5     5     0
        5     5     0
        3     5    -2

Mean variance sounds like it should be the mean of those little d’s (column 3). We would simply sum the column and divide by the number of scores. But there is a problem. When the little d’s are added up, they total zero (2+0+0+0-2=0).

But this is to be expected. We started at the mean, which is the balance point of the variable, and measured deviations from it. Since the mean is the center point of the distribution, deviations from it will always add up to 0. So we have two choices. We can take the absolute value of the deviations (which leads us to mean variance) or we can square them (as we’ll do in Sums of Squares below).

If we take the absolute value of the deviations, we ignore the sign (positive or negative) of each number. By ignoring the sign, the magnitude of the deviation is added and the result is no longer 0. In the above example, ignoring the positive and negative signs results in a sum of 4 (2+0+0+0+2) and a mean variance (average of the little d’s) of .80 (4 divided by 5).

So mean variance is the average of the absolute values of the deviations from the mean. The mean is subtracts from each raw score and the resulting little d’s are averaged (ignoring whether they are positive or negative).

The mean variance is a bit more complicated to calculate than range but more useful as a measure of dispersion. Mean variance is tied to the mean, gives a quick way to describe dispersion from the mean, and is useful when describing skewed distributions.

The down side is that mean variance doesn’t describe the underlying distribution. A mean variance of 7 is larger than a mean variance of 1.2, but it doesn’t describe the interrelationship of the scores well.

NOW YOU CHOOSE:
    Day 3: Dispersion
    A Bit More About Dispersion
    Even More About Dispersion
        Range
        MAD
        Sum of Squares
        Variance
        Standard Deviation
    How To Calculate
        Range
        MAD
        Sum of Squares
        Variance
        Standard Deviation
    Formulas For Dispersion
    Practice Problems
    More Practice Problems
    Basic Facts About Dispersion
    Vocabulary
    Quiz 3
    Summary