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Hello and welcome to MySecretMathTutor, In this example we want to take a look at
a z-score.
Now, what a z-score basically is, is it tells you how many standard deviations either above
or below the mean a particular data value is.
Ok.
So the formula that you see for this involves a lot of different things, but it mainly involves
the mu, which stands for our mean, and this lower case sigma for our standard deviations.
Now sometimes the z-score may positive that tells you that our particular data value is
above the mean.
If its negative, it means our data value is below the mean.
Ok So let's go ahead and grab some numbers and
give this a try.
So suppose I know that my mean is 24.
And I know my standard deviation is 5.
So I might be curious, alright, what is the z-score for a value of say 20?
Well, we can figure this out.
We are going to plug in our data point for x, subtract our mean,
and divide by the standard deviation.
Alright, this will give us a -4 on top divided by 5.
Now sometimes its handy to express this as a decimal, so I'm going to write this as -0.8.
So what this z-score telling me is that since its negative our data point below the mean.
And sure enough we can see that, 20 is less than 24.
Now notice how its not quite -1.
This means that it is not quite 1 standard deviation from the mean.
We can see that as well, 1 standard deviation would be 5 away at 19.
So our z-score is just this -0.8.
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