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STATISTICAL ANALYSIS
To separate as far as possible the truth from errors by measuring and define the region of doubt.
A large number of measurement is usually required to make statistical method and interpretations meaningful.
ARITHMETIC MEANS
The sum of a set numbers of n, divided by the total number of data.
x̄ = ( Σ xi ) / n
Σ is summation notation, which means “add up”
xi “all of the x-values”
n means “the number of items in the sample”
DEVIATION, d
The difference between each piece of test data and the arithmetic mean.
d1= x1- x̄n
AVERAGE DEVIATION, D
A low value for average deviation indicates a precise instrument.
D = (|d1|+ |d2|+....|dn|) / (n-1)
STANDARD DEVIATION
The degree to which the value vary about the average value.
σ = √ ∑(X-μ)^2 / (N)
σ = population standard deviation
∑ = sum of…
X = each value
μ = population mean
N = number of values in the population
PROBABLE ERROR
If coordinate are created as deviation of ± r = 0.6745σ , half of the area under the curve is enclosed between these limits.
There are two cases;
Probable error of one reading:
r = 0.6745σ (σ = standard deviation)
Probable error of mean:
Standard Error = (1-r2)/√N (N = no. of data)
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