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:

  • How to calculate the mean of a data set.

  • How to calculate the standard deviation of a data set and what that represents.

Understand:

  • that z-scores helps us to locate a data point within a standard distribution curve and what percentile that score could correspond to.

Do:

  • 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

A z-table tells me what percentage of data points fit under the distribution curve.

Z-Score Videos

Practise Questions

My Maths 10/10A

Exercise 10C pg. 495 Q. 1-13