Z-Scores (HSC SSCE Mathematics Standard): Flashcards

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Z-Scores
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What a z-score measures

How far a score is from the mean in standard deviations

Z-score formula

z=x−xˉsz = \frac{x - \bar{x}}{s}

Meaning of a positive z-score

The score is above the mean

Meaning of a negative z-score

The score is below the mean

Meaning of a z-score of 0

The score equals the mean

Meaning of a z-score of 1

One standard deviation above the mean

Meaning of a z-score of -1

One standard deviation below the mean

Mean and SD of a set of z-scores

Mean = 0, Standard deviation = 1

Purpose of z-scores

Standardise and compare scores from different distributions

What a larger absolute z-score indicates

The score is further from the centre of the data

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