Why 70 is 2 Standard Deviations Below the Mean.

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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.

As stated, only 2.3% of the population scores below a score two standard deviations below the mean.