Mean, median and mode defined
These are the three classic measures of central tendency — different ways to describe the "middle" of a data set:
mean: add all values, divide by how many there are
median: sort the values, take the middle one
mode: the value (or values) that appears most often
range: largest value − smallest value
When there's an even number of values, the median is the average of the two middle ones. A data set can have one mode, several modes, or no mode at all if every value is unique.
Worked example
For 4, 8, 15, 16, 16, 23, 42:
Mean: 124 ÷ 7 ≈ 17.71.
Median: sorted, the 4th of 7 values is 16.
Mode: 16 appears twice, so the mode is 16.
Range: 42 − 4 = 38.
Which average should you use?
The mean is the everyday average but is pulled around by outliers. The median is more robust — it's why incomes and house prices are usually reported as medians. The mode is the only one that works for categories (the most common shoe size, say).
Tip: if the mean and median are far apart, your data is skewed — a few very large or very small values are dragging the mean.