If you like mathematical puzzles or love algebra, try this! Otherwise, just trust that the computational formula for the sum of squares is correct. We have a sample of x values. The sample size is n. Fill in the details for the following steps. Σ(x - x)2 = Σ(   2 - 2xx + x2) by binomial expansion   = Σx2 - 2xΣ   + Σx2 by distributive property   = Σx2 - 2xΣx +   x2 adding the same quantity, x, n times, is in fact multiplying it by n   = Σx2 - 2x(   x) + nx2 by substitution, since (Σx)/n = x, hence Σx = nx   = Σx2 -   x2 + nx2 by multiplication, and expansion   = Σx2 -   x2 by addition, combination of alike terms   = Σx2 - n ( Σ   n )2 by substitution, since (Σx)/n = x   = Σx2 - n ( (Σ   )2 n2 ) by distributive property   = Σx2 - (Σx)2   by multiplication, cancellation

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.