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
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