Transcript Slide 1

General Mathematics
HSC
z-scores
Stage 6 - Year 12
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©G Dear 2009 – Not to be sold/Free to use
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Z Scores – Basics (1/3)
• Measures the distance of raw scores from the mean.
• It’s unit of measure is in standard deviations.
• Z scores equal zero at the mean.
• Z scores only apply to normal distributions.
•Normal distributions are always bell shaped.
Bell Shaped
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Z Scores – Calculations (2/3)
So how do we calculate the z score for a data item?
x–x
Z=
s
•Z is the z score.
•x is the raw score.
•x is the mean of the scores.
•s is the standard deviation.
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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 = 1.4 standard deviations
above the mean.
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