Statistics Formulas Statistics Formulas Statistics is used very widely in the mathematics. The statistical approaches are used effectively numerical data. In the statistics we study of gathering data, ordering the data into a proper manner and checking the data line by line. For this we used many formulas. Below is the list of various Statistics Formulas. Parameters: Population mean = μ = (Σ Xi) / N Population standard deviation = σ = √[Σ ( Xi - μ )2 / N], Population variance = σ2 = Σ ( Xi - μ )2 / N, Variance of population proportion = σP2 = PQ / n, Standardized score = Z = (X - μ) / σ, Population correlation coefficient = ρ = [ 1 / N ] * Σ [ (Xi- μX) / σx ] * [ (Yi - μY) / σy ].
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Statistics: - The all methods that are listed below are assumed as random sampling. Sample mean = x' = ( Σ xi) / n, Sample standard deviation = s = sqrt [ Σ ( xi - x' )2 / ( n - 1 ) ] Sample variance = s2 = Σ ( xi - x' ) 2 / ( n - 1 ), Variance of sample proportion = sp2 = pq / (n 1), Pooled sample proportion = p = (p1 * n1 + p2 * n2) / (n1 + n2), Pooled sample standard deviation = sp = sqrt [ (n1 - 1) * s12 + (n2 - 1) * s22 ] / (n1 + n2 - 2)], Sample correlation coefficient = r = [ 1 / (n - 1) ] * Σ [ (xi - x') / sx ] * [ (yi - y') / sy ]. Simple Linear Regression Simple Linear regression line: ? = b0 + b1x, Regression coefficient = b1 = Σ [(xi - x') (yi - y')] / Σ [(xi – x')2], Regression slope intercept = b0 = y' - b1 * x, Regression coefficient = b1 = r * (sy / sx), Standard error of regression slope = sb1 = sqrt [Σ(yi – ?i )2 / (n - 2) ] / sqrt [ Σ(xi - x')2], Counting : n factorial: n! = n * (n-1) * (n - 2) * . . . * 3 * 2 * 1. By the convention, 0 ! = 1. Permutations of n things, taken ‘r’ at a time: nPr = n! / (n - r)!, Combinations of ‘n’ things, taken ‘r’ at a time: nCr = n! / r!(n - r)! = nPr / r! Probability: Rule of addition: P (A ∪ B) = P(A) + P(B) - P(A ∩ B),
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Rule of multiplication: P (A ∊ B) = P (A) P (B|A), Rule of subtraction: P (A') = 1 – P (A). Other statistical formulas that are not described above are : - Correlation, random variables, Sampling distribution, standard error, discrete probability distribution, linear transformation, estimation, hypothesis testing formulas. They are also the formulas that comers under the statistical formulas. The overall purpose of the statistics is that it is used to summarize data. Problem 1: Find the mean of given data. The data is 2,4,6,8,0,1. Solution: Given data is 2,4,6,8,0,1. The formula for mean = (sum of data) / ( total number of the data). mean = (2+4+6+8+0+1 / 6) = 21 / 6. So, the mean value is = 3.5.
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