FRAME 51.

The sixth characteristic relates horizontal distances on the base line to areas under the

normal curve.

Thus far we have measured the horizontal base line in terms of the unit of measure we are

dealing with in the specific problem: dollars, inches, etc. It would be more convenient if we could

use the same unit of measure for all problems. Our unit of measure for dispersion, the standard

deviation, is used to measure this horizontal distance. When using standard deviations, we

always measure from the mean of the distribution. Thus we can find a relationship between the

area under the normal curve and the number of standard deviations measured from the mean.

Suppose we collected data about the number of meals served per day in the fort Flatland

Consolidated Mess for the last 6 months. The mean was computed to be 2000 and the standard

deviation was 100.

The normal curve for the population would appear as:

1700

1800

1900

2000

2100

2200

2300

Meals/day

u-3σ

u-2σ

u-1σ

u+1σ

u+2σ

u+3σ

u

Standard

Deviations