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

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Standard Deviation & Variance
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What does standard deviation measure?

Average deviation from the mean

What is variance represented by?

σ2\sigma^2 (mean square deviation)

How is standard deviation related to variance?

Standard deviation is square root of variance

Which formula correctly represents variance?

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

In the alternative formula, what does x2\overline{x^2} represent?

Mean of all squared data

Why are deviations squared in the calculation?

To make deviations positive

Which measure of spread uses all data points?

Standard deviation (σ\sigma)

Which measure of spread ignores outliers?

Interquartile range (IQR)

Which measure is easiest to calculate?

Range

Using σ2=x2(xˉ)2\sigma^2 = \overline{x^2} - (\bar{x})^2, if x2=12.5\overline{x^2} = 12.5 and xˉ=3\bar{x} = 3, what is σ2\sigma^2?

3.53.5

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