Measures of Spread (VCE SSCE Mathematical Methods): Quizzes

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Measures of Spread
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What does variance quantify in a probability distribution?

How far values typically fall from mean

What symbol is typically used to denote variance?

σ2\sigma^2

If XX measures length in metres, what are the units of Var(X)\text{Var}(X)?

Square metres

How is standard deviation related to variance?

sd(X)=Var(X)\text{sd}(X) = \sqrt{\text{Var}(X)}

What symbol is typically used to denote standard deviation?

σ\sigma

What is the computational formula for variance?

Var(X)=E(X2)μ2\text{Var}(X) = E(X^2) - \mu^2

Which two measures of spread are most commonly used?

Variance and standard deviation

The interquartile range captures the spread of which portion of the distribution?

Middle 50%

What is the formula for interquartile range?

IQR=Q3Q1\text{IQR} = Q_3 - Q_1

What is an advantage of using the interquartile range?

Not affected by extreme values in tails

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