Standard Deviation (Leaving Cert Mathematics): Flashcards

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Standard Deviation
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What does standard deviation measure?

Spread/variation in data from the mean

Small standard deviation means

Data clustered close to the mean

Large standard deviation means

Data spread out over wider range

Symbol for standard deviation

σ\sigma (sigma)

Empirical Rule: % within 1 SD

68%

Empirical Rule: % within 2 SDs

95%

Empirical Rule: % within 3 SDs

99.7%

SD formula (simple data)

σ=Σ(x−xˉ)2n\sigma = \sqrt{\frac{\Sigma(x - \bar{x})^2}{n}}

SD formula (frequency data)

σ=Σf(x−xˉ)2Σf\sigma = \sqrt{\frac{\Sigma f(x - \bar{x})^2}{\Sigma f}}

First step to calculate SD

Calculate the mean (xˉ)(\bar{x})

After finding deviations, what's next?

Square each deviation

Can standard deviation be negative?

No, it cannot be negative

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