Standardisation and the 68–95–99.7% Rule (VCE SSCE Mathematical Methods): Flashcards

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Standardisation and the 68–95–99.7% Rule
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Other name for 68-95-99.7% rule

Empirical rule

% of values within 1 SD of mean (normal distribution)

68%

% of values within 2 SD of mean (normal distribution)

95%

% of values within 3 SD of mean (normal distribution)

99.7%

Formula for z-value

z=xμσz = \frac{x - \mu}{\sigma}

Meaning of positive z-value

Data value lies above the mean

Meaning of negative z-value

Data value lies below the mean

Mean of standard normal distribution

μ=0\mu = 0

SD of standard normal distribution

σ=1\sigma = 1

% in each tail beyond 2 SD from mean

2.5%

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