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Grain Science and Industry

Common Statistical Equations

In statistics, a variable distribution is used to calculate helpful quantities, such as mean, variance, and standard deviation. However, when the distribution of a sample set is unknown, a sample mean and variation can be calculated based directly on the values of the number of samples taken, n. The following equations show how to calculate some helpful statistical values when a distribution model is not available.



(1) Sample Meanx =
x 1 + x 2 + ... +x n
n
= n
Σ i=0 x in


(2) VarianceS 2 =
1 n -1
[n
Σ i=0 x i2
n
( Σ i=0 x i ) 2n
]


(3) Standard Deviation S = √S2= square root of Variance


(4) Coefficient of Variation (%)c v = S x x 100


(5) Confidence IntervalCI = x ± Z S √ n