Converting to Percentiles and Back (2 of 4)
What about a person scoring
75 on the test? The proportion of the area below 75 is the same as the proportion
of scores below 75.
A score of 75 is one standard deviation below the mean because the mean
is 80 and the standard deviation is 5. Mathematical statisticians have
determined that 15.9% of the scores in a normal distribution are lower
than a score one standard deviation below the mean. Therefore, the proportion
of the scores below 75 is 0.159 and a person scoring 75 would have a percentile
rank score of 15.9.
The table below page gives the proportion of the scores below various
values of z; z is computed with the formula:
where z is the
number of standard deviations (σ) X is
above the mean (μ).
Naturally, it is more conventient to use a z calculator