Standard Deviation & Variance (Edexcel A-Level Mathematics): Flashcards

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Standard Deviation & Variance
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What standard deviation measures

On average, how far each data point deviates from the mean

Definition of variance

Mean square deviation

Relationship between σ\sigma and σ2\sigma^2

σ=σ2\sigma = \sqrt{\sigma^2} (SD is square root of variance)

Formula for variance σ2\sigma^2 (method 1)

σ2=Σ(xxˉ)2n\sigma^2 = \frac{\Sigma(x-\bar{x})^2}{n}

Alternative formula for σ2\sigma^2

σ2=x2(xˉ)2\sigma^2 = \overline{x^2} - (\bar{x})^2

Meaning of x2\overline{x^2}

Mean of all squared data

Meaning of (xˉ)2(\bar{x})^2

Mean of all data, then squared

Data points used by range

Two data points

Data points used by IQR

Two data points

Data points used by σ\sigma

All data

Range and outliers

Includes outliers

IQR and outliers

Ignores outliers

σ\sigma and outliers

Includes extreme outliers

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