Describing and Comparing Distributions (HSC SSCE Mathematics Standard): Flashcards

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Describing and Comparing Distributions
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3 characteristics describing distribution shapes

Smoothness, symmetry, number of modes

Mode definition

Value appearing most frequently (peak with highest frequency)

Unimodal distribution

Single peak or mode

Bimodal distribution

Two distinct peaks or modes

Positively skewed tail direction

Long tail extending toward right (positive side)

Negatively skewed tail direction

Long tail extending toward left (negative side)

Mean formula

xˉ=sum of scoresnumber of scores\bar{x} = \frac{\text{sum of scores}}{\text{number of scores}}

Median advantage regarding outliers

Not affected by outliers or extreme values

Range formula

Highest score - lowest score

IQR formula

Q3Q1Q_3 - Q_1

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