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

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Standard Deviation & Variance
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What does standard deviation measure?

Average deviation of data from the mean

What does variance measure?

Squared spread of data

What is the relationship between standard deviation σ\sigma and variance σ2\sigma^2?

σ=σ2\sigma = \sqrt{\sigma^2}

Which formula correctly represents variance?

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

Which alternative formula can be used to calculate variance?

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

What is x2\overline{x^2} in the variance formula?

The mean of all squared data

What is (xˉ)2(\bar{x})^2 in the variance formula?

The mean of all data then squared

Why are deviations squared in standard deviation calculations?

To make the deviations positive

Which measure of spread uses all data points?

Standard deviation

Which measure of spread is easiest to calculate but includes outliers?

Range

Which measure of spread ignores outliers?

Interquartile range

When is range not an appropriate measure?

When the highest value is unknown

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