The S.D. provides information on the proportion of observations above or below the mean value. Suppose the average height of all adult men in a country is 70" and the S.D. is 3.

Assume the distribution is normal (i.e., bell-shaped).

This implies :

• The height of nearly 68% of men will be in the range
"Average ± 1σ"
which is 70 ± 1 × 3 = 67" to 73".
• The height of nearly 95% of men will be in the range
"Average ± 2σ"
which is 70 ± 2 × 3 = 64" to 76".
• The height of nearly 99.7% of men will be in the range
"Average ± 3σ"
which is 70 ± 3 × 3 = 61" to 79".

If the entire population of men were to be of the same height!