Grade 10

Data Handling

Collect, organise, summarise and display data — and understand what the numbers are really telling you.

Measures of Central Tendency

A "measure of central tendency" is one number that tries to represent the middle or typical value of a dataset. There are three:

Theorem
Mean=xˉ=sum of all valuesnumber of values=∑xnMedian=middle value when data is sortedMode=value that appears most often\begin{aligned} \text{Mean} &= \bar{x} = \frac{\text{sum of all values}}{\text{number of values}} = \frac{\sum x}{n} \\[8pt] \text{Median} &= \text{middle value when data is sorted} \\[8pt] \text{Mode} &= \text{value that appears most often} \end{aligned}
When there is an even number of values, the median is the average of the two middle values.
Worked Example

For the dataset: 3, 7, 7, 9, 12, 15, 15, 15, 20 — find the mean, median and mode.

Tip
Use the median rather than the mean when the data has extreme outliers — for example, house prices in a suburb where one mansion skews the average.
Worked Example

The mean of five numbers is 14. Four of the numbers are 10, 12, 16, 18. Find the fifth number.