Measures of Variability

Measures of Variability

Answers the question "how much variation is there in this class?"

"how far can I get from the average before
I should start worrying/gloating"

"Hey I got 8 points above class average -- is that good?" If you're the only one 8 points above average, I'm impressed; if half the class is 10 points above, you're not doing as well, right?

Range

Simplest and most common
difference between the top and bottom score
limited use because sensitive to extremes -- addition or elimination of high or low score can change it
- e.g., should you count '0' score for absent student
- top or bottom student appeals mark, you change it, you change the range

Standard Deviation

Second most common measure of variability

measures degree to which scores cluster around the mean

the smaller the standard deviation, the closer the scores are to the mean

if all the scores are the same, standard deviation would = 0

varies between samples less than does the range because it uses all the scores, not just those at the extreme ends

--> so it is a more stable statistic

So how do we calculate it?

Now, I understood all that for about the three weeks I was in my grad stats course -- we're doing the five minute university version in this class -- I survived 10 years just knowing that's how you got it, what you do with it

75% of the scores will lie between 2 SD above and below the mean, no matter what the shape of the graph
the point of the Standard Deviation is to compare

Standard Scores

Once you have calculated your Standard Deviation, you will need something to compare it too. Here are two Standard Scores.

z scores: number of standard deviations that a particular raw score is above or below the mean of the raw score distribution
T scores: standard scores having mean of 50 and a standard deviation of 10
take a z score

multiply by ten to get rid of decimal
add 50 to get rid of negatives

ETS (Educational Testing Service) scores have means of 500 and standard deviations of 100 --> mostly to mystify the public...