a normal distribution and you can see the mean is the average of the scores
of distribution and then we are going to use the standard aviation units so
the standard aviation unit is 1 standard deviation away from the mean and
so that would be 1 z-score,
2 standard deviations away with the mean would be 2 z-score.
And we know from our distribution that in one center deviation from the mean,
from 1 standard deviation to below 1 standard deviation,
there is 68% of all the variability in that distribution.
Knowing that allows us to compute the z-score.
For example, Z again, is the score minus the mean,
divided by the standard deviation.
So, if we had a score of 70 on some particular scale, the mean would be 60 and
the standard deviation is 15.
Then we compute the z-score which is simply the score minus the mean, which
would then be 10 divided by the standard aviation which is 15 which would be .667.
So, the standard score or the z-score is .667 for
this particular measure Let me show that again.
We have a mean, an average of 60.
The score is 70 in the distribution, which means that
the z-score is .667, which is simply the score minus the mean,
divided by the standard deviation, which is .667.
So then we can compute knowing the amount of the distribution which falls between
the mean in one standard deviation, and we can compute the probability that any
score is above or below the z-score that we're using.