Basic Statistics

AREAS UNDER THE NORMAL CURVE 69

Table 6.1 Numerical Example of Interpolation

Smaller tabled .[A] value ,1.300 ,9032

Computed z 1.304?

Larger tabled .[A] value 1.310 ,9049

Table 6.2 Symbols for Interpolation Formula

4x1 x

Smaller tabled .[A] value z1 = 1.300 XI = ,9032

Larger tabled z[X] value z2 = 1.310 A2 = ,9049

Computed z z = 1.304 x =?

' 1.3 1.304 1.310 2

Figure 6.7 Example of graphical interpolation

Usually, this computation is performed with the following formula:

Table 6.2 shows the relationship between the symbols in the formula for the interpo-
lated X and numbers in Table 6.1. For men's heights, we have

X = ,9032 + "04' - '9032 (1.304 - 1.300) = .9039

1.310 - 1.300

The percentage of men's heights < 71 in. can be rounded off to 90.4%.

Figure 6.7 illustrates a simple graphical method of approximately the area X cor-

responding to z = 1.304. When drawn on ordinary graph paper, X is read from the

vertical scale and can be used either as a check on the .9039 obtained from linear

interpolation or as an approximation when not much accuracy is needed.