Question

What are the formulas of statistics

Answer 1

Parameters

Population mean = μ = ( Σ Xi ) / NPopulation standard deviation = σ = sqrt [ Σ ( Xi - μ )2 / N ]Population variance = σ2 = Σ ( Xi - μ )2 / NVariance of population proportion = σP2 = PQ / nStandardized score = Z = (X - μ) / σPopulation correlation coefficient = ρ = [ 1 / N ] * Σ { [ (Xi - μX) / σx ] * [ (Yi - μY) / σy ] }

Statistics

Unless otherwise noted, these formulas assume simple random sampling.

Sample mean = x = ( Σ xi ) / nSample 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 ] }

Correlation

Pearson product-moment correlation = r = Σ (xy) / sqrt [ ( Σ x2 ) * ( Σ y2 ) ]Linear correlation (sample data) = r = [ 1 / (n - 1) ] * Σ { [ (xi - x) / sx ] * [ (yi - y) / sy ] }Linear correlation (population data) = ρ = [ 1 / N ] * Σ { [ (Xi - μX) / σx ] * [ (Yi - μY) / σy ] }

Simple Linear Regression

Simple linear regression line: ŷ = b0 + b1xRegression coefficient = b1 = Σ [ (xi - x) (yi - y) ] / Σ [ (xi -x)2]Regression slope intercept = b0 = y - b1 * xRegression coefficient = b1 = r * (sy / sx)Standard error of regression slope = sb1 = sqrt [ Σ(yi - ŷi)2 / (n - 2) ] / sqrt [ Σ(xi - x)2 ]

Answer 2

The formula of mean is, Mean <x> = ∑x/N 
where 
∑ represents the summation
x represents scores
N represents number of scores.

The formula of median is,
Median = (n+1)/2 th term    ; when n is a odd number
Median: [(n/2) th term + {(n/2)+1} th term ] / 2  ; when n is an even number

And, Mode is the most frequently occurring value.

Let us have an example.

Given sequence :18, 21, 7, 4, 18, 14, 9
Total number of numbers in the sequence(N) = 7

So, Mean = (18+21+7+4+18+14+9)/7 = 13

Now, To calculate the median, first we need to arrange the sequence in the ascending order
Ascending order of the sequence = 4, 7, 9, 14, 18, 18, 21
Total number of numbers in the sequence = 7 = odd
So, Median = (n+1)/2 th term = (7+1)/2 th term = 4th term i.e 14.

MARK BRAINLIEST..