Handbook of Civil Engineering Calculations

Project time, days

FIGURE 19. Workforce requirements based on project schedule.

Statistics, Probability, and Their Applications

Basic Statistics

If the value assumed by a variable on a given occasion cannot be predicted because it is
influenced by chance, the variable is known as a random, or stochastic, variable. The
number of times the variable assumes a given value is called the frequency of that value.
A number that may be considered representative of all values of the variable is called an
average. There are several types of averages, such as arithmetic mean, geometric mean,
harmonic mean, median, mode, etc. Each is used for a specific purpose. The standard de-
viation is a measure of the dispersion, or scatter, of the values of the random variable; it is
approximately equal to the amount by which a given value of the variable may be expect-
ed to differ from the arithmetic mean, in either direction. The variance is the square of the
standard deviation. Where no mention of frequency appears, it is understood that all fre-
quencies are 1.

Notational System

Here X= random variable; X 1 = ith value assumed by X\ft - frequency of X 1 ; n = sum of
frequencies; X = arithmeticmean of values of X\ Xmed = median of these values; dt = devi-
ation of Xb from X = Xi-X\ A = an assumed arithmetic mean; dA>i = deviation of X 1 from
A=X 1 -A', s = standard deviation; s^2 = variance. In the following material, the subscript /
will be omitted.

DETERMINATIONOFARITHMETICMEAN,

MEDIAN, AND STANDARD DEVIATION

Column 2 of Table 22 presents the number of units of a commodity that were sold month-
ly by a firm for 7 consecutive months. Find the arithmetic mean, median, and standard de-
viation of the number of units sold monthly.

Workforce