Averages and spread

Mean, median, mode, range, variance and standard deviation, worked on real data. About 11 minutes, KS3 / A-level.

What you will do

1. Three averages. The mean adds up and shares out. The median is the middle value once sorted. The mode is the most common. Each answers "what is typical?" in a different way.
2. Mean, median and mode. Watch every measure worked out for one data set, including the table of deviations from the mean.
3. When there is no mode. If every value appears once there is no mode, and that is a perfectly good answer.
4. Measuring spread. The range is the biggest minus the smallest. Variance is the average squared distance from the mean, and the standard deviation is its square root: back in the units of the data.
5. A common slip. Dividing by n gives the population variance; dividing by n - 1 gives the sample variance, used when the data is only a sample of a bigger group. The engine shows both.