Commonly Used Symbols

• The symbol ΣΣ means to add or to find the sum.
• nn = the number of data values in a sample
• NN = the number of people, things, etc. in the population
• x¯x¯ size 12{ {overline {x}} } {} = the sample mean
• ss = the sample standard deviation
• μμ = the population mean
• σσ = the population standard deviation
• ff = frequency
• xx = numerical value

Commonly Used Expressions

• x*fx*f = A value multiplied by its respective frequency
• ∑x∑x size 12{ Sum {x} } {} = The sum of the values
• ∑x*f∑x*f size 12{ Sum {x} times f} {} = The sum of values multiplied by their respective frequencies
• ( x − x ¯ ) (x− x ¯ ) or ( x − μ ) (x−μ) = Deviations from the mean (how far a value is from the mean)
• ( x − x ¯ ) 2 ( x − x ¯ ) 2 or ( x − μ ) 2 ( x − μ ) 2 = Deviations squared
• f ( x − x ¯ ) 2 f ( x − x ¯ ) 2 or f ( x − μ ) 2 f ( x − μ ) 2 = The deviations squared and multiplied by their frequencies

• x¯=x¯= size 12{ {overline {x}} ={}} {}∑xn∑xn size 12{ { { Sum {x} } over {n} } } {} or x¯=x¯= size 12{ {overline {x}} ={}} {}∑f· xn∑f· xn size 12{ { { Sum {f times x} } over {n} } } {}
• μ=μ= size 12{μ={}} {}∑xN∑xN size 12{ { { Sum {x} } over {N} } } {} or μμ size 12{μ} {}= ∑f·xN∑f·xN size 12{ { { Sum {f times x} } over {N} } } {}

• s=s= size 12{s={}} {} Σ ( x − x ¯ ) 2 n − 1 Σ ( x − x ¯ ) 2 n − 1 or s=s= size 12{s={}} {} Σ f · ( x − x ¯ ) 2 n − 1 Σ f · ( x − x ¯ ) 2 n − 1
• σ=σ= size 12{σ={}} {} Σ ( x − μ ¯ ) 2 N Σ ( x − μ ¯ ) 2 N or σ=σ= size 12{σ={}} {} Σ f · ( x − μ ¯ ) 2 N Σ f · ( x − μ ¯ ) 2 N

• value = mean + (#ofSTDEVs)(standard deviation), where #ofSTDEVs = the number of standard deviations
• xx size 12{x} {} = x¯ x + (#ofSTDEVs)(ss)
• xx size 12{x} {} = μμ size 12{μ} {} + (#ofSTDEVs)(σσ)