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

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Standard Deviation & Variance
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Standard deviation measures

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

Variance is also called

Mean square deviation

Formula for variance σ2\sigma^2

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

Relationship between σ\sigma and σ2\sigma^2

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

Alternative formula for σ2\sigma^2

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

What is x2\overline{x^2}?

Mean of all squared data

What is (xˉ)2(\bar{x})^2?

Mean of all data then squared

How many data points does σ\sigma use?

All data

Does IQR include outliers?

No, it ignores outliers

Hardest to calculate: range, IQR, or σ\sigma?

σ\sigma (standard deviation)

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