Standard Deviation

The Standard Deviation of a set of values is calculated as:

((x - m_a)²/n)

Where:

x = an individual value

n = the number of test values

m_n = the mean of n values

The Standard Deviation of two independent sets of values is calculated as:

((n₁ - 1) x s₁² + (n₂ - 1) x s₂²)/(n₁ + n₂ - 2))

Where:

n₁ = the number of values in the first set

s₁ = the Standard Deviation of the first set of values

n₂ = the number of values in the second set

s₂ = the Standard Deviation of the second set of values

ACI 301-96 (References 1) stipulates that if the test strengths under consideration are for two sets of consecutive tests, the expression given above should be used to obtain the overall standard deviation from the standard deviations of the two sets of test strengths.