Page 352 - Statistics for Dummies

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Part VI: The Part of Tens
Being critical of yourself is hard, and finding out you didn’t know something

you thought you knew is a little scary. But if you put yourself out there and
find your mistakes before they cost you points, you’ll zoom in on your weak-
nesses, turn them into strengths, boost your knowledge, and get a higher
exam score.
Make Friends with Formulas
Many students are not comfortable with formulas (unless you are a math
nerd, in which case formulas make you shout for joy). That unease is
understandable — I used to be intimidated by them too (formulas, that is —
not math nerds). The trouble is, you really can’t survive too long without
eventually using a formula in a statistics class, so becoming comfortable with
them right from the start is important. A formula tells you much more than
how to calculate something. It shows the thinking process behind the calcula-
tions. For example, the big picture regarding standard deviation can be seen
by analyzing its formula:
Subtracting the mean, , from a value in the data set, , measures how far
above or below the mean that number is. Because you don’t want the posi-
tive and negative differences to cancel each other out, you square them all
to make them positive (but remember that this gives you square units). Then
you add them up and divide by n – 1, which is near to finding an average, and
take the square root to get back into original units. In a general sense, you
are finding something like the average distance from the mean.
Stepping back even further, you can tell from the formula that the standard
deviation can’t be negative, because everything is squared. You also know
the smallest it can be is zero, which occurs when all the data are the same
(that is, all are equal to the mean). And you see how data that is far from the
mean will contribute a larger number to the standard deviation than data
that is close to the mean.
And here’s another perk. Because you understand the formula for standard
deviation now, you know what it’s really measuring: the spread of the data
around the mean. So when you get an exam question saying “Measure the
spread around the mean,” you’ll know what to do. Bam!

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