Relative Frequency (HSC SSCE Mathematics Advanced): Flashcards

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Relative frequency
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Formula for relative frequency

fr=fnf_r = \frac{f}{n} where ff = frequency, nn = total trials

Another name for relative frequencies

Experimental probabilities

Formula for expected value E(X)E(X) of discrete random variable

E(X)=xp(x)E(X) = \sum x \cdot p(x)

Alternative variance formula (not using (Xμ)2(X-\mu)^2)

Var(X)=E(X2)μ2\text{Var}(X) = E(X^2) - \mu^2

Formula for standard deviation σ\sigma

σ=Var(X)\sigma = \sqrt{\text{Var}(X)}

Definition of cumulative distribution function F(x)F(x)

F(x)=P(Xx)F(x) = P(X \leq x)

Key property of all CDFs

Always increases from 0 to 1 (monotonic increase)

Total area of rel. freq. histogram (bar width = 1)

Equals 1

What deciles divide data into

Ten equal parts

How probability calculated for continuous distributions

Using area

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