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1 Press Ctrl-A ©G Dear 2009 – Not to be sold/Free to use z-scores Stage 6 - Year 12 General Mathematics HSC

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2 Z Scores – Basics (1/3) scoresmean Measures the distance of raw scores from the mean. unitstandard deviations It’s unit of measure is in standard deviations. zeromean Z scores equal zero at the mean. normal distributions Z scores only apply to normal distributions. bell shaped.Normal distributions are always bell shaped. Bell Shaped

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3 Z Scores – Calculations (2/3) z scoredata So how do we calculate the z score for a data item? Z = x – x s Zz scoreZ is the z score. xraw scorex is the raw score. xmeanx is the mean of the scores. sstandard deviations is the standard deviation.

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4 Z Scores – Calculations (3/3) In the last test one student got a score of 84. If the mean was 70 and the standard deviation was 10. then calculate the z score of the score. z = x – x s z = 84- 70 10 z = 1.4standard deviations above the mean.

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A standardized value A number of standard deviations a given value, x, is above or below the mean z = (score (x) – mean)/s (standard deviation)

A standardized value A number of standard deviations a given value, x, is above or below the mean z = (score (x) – mean)/s (standard deviation)

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