Page 291 - Industrial Process Plant Construction Estimating and Man Hour Analysis

Appendix B

Statistical and mathematical

formulas

Statistical formulas for the mean, variance, and standard deviation
Mean: y¼y1+y2+⋯+yn; Σ y/n
2 2 2 2
Variance:S ¼(y1 Y) +(Y2+Y )+⋯ +(Yn Y) /n 1
2 2
ð
s ¼ Σ yi yð Þ = n 1Þ
2
2
Standard-deviation:S¼[(y1 Y) +Y2+Y )+⋯+(Yn Y) /n 1]½
2
h i
Þ = n 1Þ ½
2
s ¼ Σ yi yð ð
Straight line graph: handle and install large bore standard pipe
ð
ð
y ¼ a + bx; Y ¼ a+ y y1Þ= x x1Þ xðÞ
where
y¼dependent variable
a¼intercept value along the y-axis at x ¼ 0
b¼slope or the length of the rise divided by the length of the run;
b¼(y y1)/(x x1)
x¼independent or control variable
P
Mathematical expectation: E(X)¼p1X1+p2X2+⋯+ρkXk¼ ρX
Normal distribution:Y¼1/(σ(2pi) 1/2)e 1/2(X μ) /σ 2
2
^
^
where μ¼mean, σ¼standard deviation, pi¼3.1416…, and e¼2.71828….
2
Standard form: Y¼1/(2pi 1/2)e 1/2(z )
^
^
z is normally distributed with mean 0 and variance 1
Central limit theorem:W i ¼((x) i μ)/(σ/k 1/2)
^
N(0,1) in the limit as k approaches infinity

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