Calculating Z-Scores (VCE)

Calculate and interpret the mean and standard deviation of data and use these to compare data sets. Investigate the effect of individual data values including outliers, on the standard deviation(VCMSP372)

LO: To calculate the Z-Score for a data set.
Know:

  • How to calculate the mean of a data set.
  • How to calculate the standard deviation of a data set.

Understand:
That Z-scores helps us to locate a data point within a standard distribution curve.

Do:

  • I can calculate the Z-score for a data point.

Visual Representations

Notes

A Z-score is the number of standard deviations from the mean a data point is. 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 with 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. You can not find a Z-score of a data point when the histogram is not a normally distributed curve.

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