Choosing an Average
Mean, median and mode answer different questions. The best choice depends on the data and on what the conclusion must describe.
mean = 22.0·median = 20
Match the average to the purpose
| Situation | Usually prefer |
|---|---|
| categorical data or most popular category | mode |
| strong skew or an extreme outlier | median |
| roughly symmetric numerical data | mean |
| later calculations need every value | mean |
An outlier is a value far from most of the data. Skew means one tail of a distribution stretches farther than the other: positive skew has the long tail on the right; negative skew has the long tail on the left. A roughly symmetric distribution balances in a similar way on both sides of its centre.
- The mean uses every magnitude, so one extreme value can move it a long way.
- The median uses order, so changing the size of an extreme value may not change it at all.
- In a positively skewed distribution, the long right tail usually pulls the mean to the right of the median. Negative skew reverses the direction.
Key idea
Examiner note
Common mistake
Now you try
Four houses sold for $220 000, $236 000, $242 000 and $3 500 000. Calculate the mean and median selling prices. Which measure better describes a typical sale? Justify your choice.
Show worked answer
The total is $4 198 000, so the mean is $1 049 500. The median is the mean of $236 000 and $242 000, which is $239 000.
The $3.5 million sale is an extreme value and pulls the mean far above the other three prices.