Why 70 is 2 Standard Deviations Below the Mean.
The mean is 80 and the standard deviation is 5. Since 70 is 10
points below the mean (80-70 = 10) and since a standard deviation is
5 points, there is a distance of 2 standard deviations between the 80
and 70 (10/5=2). In general, the number of standard deviations a
score is from the mean can be computed using the formula
where z is the number of standard deviations above the mean (μ) the
score X is. The standard deviation is (σ) . When z is negative it
means that X is below the mean. For this example,
z = (70 - 80)/5 = -2.
, only 2.3% of the population
scores below a score two standard deviations below the mean.