Solve problems using the z-scores and the 68–95–99.7% rule (VCE Unit 3 Further Maths)
LO: To calculate the z-score for a value given the data set.
Know:
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How to calculate the mean of a data set.
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How to calculate the standard deviation of a data set and what that represents.
Understand:
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that z-scores helps us to locate a data point within a standard distribution curve and what percentile that score could correspond to.
Do:
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I can calculate the z-score for a given data point.
Visual Representations
Teaching Notes
A z-score is the number of standard deviations away from the mean of a data set. It can positive or negative depending on whether the data point is above or below the mean respectively. Z-scores can only be applied to data which fits into a normal distribution curve.
Z-scores range from -3 to +3.
This histogram is normally distributed. It is also known as a “bell curve“.
This histogram is not normally distributed and you can not find a Z-score of a data point when the histogram is not a normally distributed curve.
The Z-Score Formula
To find the Z-score of a data point, you just have to use the data point then subtract the mean and then divide it by the standard deviation.
Z-Table
