srandard deviaton and correlation coefficientWatch
Standard Deviation is the number of points scores are away from the mean. I measures how much scores fluctuate from the mean.
There is another way of doing this which is simpler. This is called the mean absolute deviation. This involves just taking the absolute values of the differences from the mean, and then taking the mean of those values.
Two of the big reasons why standard deviation (SD) is used more than mean absolute deviation (MAD) are:
1) SD is easier for computers to update, because they have to store fewer figures in their memory. The best way to understand this is...check it out . Whether or not this is mentioned is a good indicator of whether an introductory statistics textbook is the real McCoy or whether it's just been hacked out.
2) you can use a 'false zero' with SD, which allows the alternative formula
SD = square root of ([mean of squares] minus [square of mean].
You can think of this as moving the mean to zero, then using the differences from there , i.e. the values themselves, then taking away the square of the mean, etc.
Many undergraduate courses on quantitative methods give social science students (the subset who hate stats and are just doing it because they have to) the impression that SD is some sort of 'best' measure of spread, but this isn't true. As with other statistics (e.g. average), it depends on what you want, and it's worth bearing in mind that ease of calculation is often a factor in choosing SD rather than MAD.