stats

discrete variable

• distinct number of values

• countable

continuous variable

• any value between intervals

• usually measurement

• e.g. temperature

population data

• all elements from a data set

• all values the random variable takes

population mean (μ)

deviation from mean

average deviation

population variance

population standard deviation (σ)

sample data

one or more observations drawn from population

sample mean (x̄)

sample standard deviation (s)

mean and sd rounding rules

one more decimal place than occurs in raw data

intermediate calculations rounding rules

3 extra decimal places than occurs in raw data

linear transformation

the “a” effect

the “b” effect

mean for linear transformation

ȳ = a . x̄ + b

deviation for linear transformation

Sy = a . Sx

variance for linear transformation

S²y = a² . S²x

probability (P)

• probability of event (X) describes the mathematical likelihood of the event occurring

• 0 ≤ P(X) ≤ 1

sum of all probabilities

1

PDF property 1

• value of PDF is never negative

• f(x) ≥ 0

PDF property 2

the area under full PDF is always 1

a PDF is assumed to be zero where…

it is not defined

PDF for a continuous uniform variable is given as