The rule
mean = sum ÷ count · median = the middle value once sorted
Why it works
The mean balances the values, the median splits them in half, and the mode is whichever occurs most. They describe the centre in genuinely different ways, and which one to use depends on the shape of the data.
How to do it by hand
- Add the values and divide by how many there are for the mean
- Sort them and take the middle one for the median
- The most frequent value is the mode
- The standard deviation measures how spread out they are
What is worth knowing
The mean is the one to distrust with skewed data, because a single extreme value drags it. Household income is the standard case: the mean is far above the median because a small number of very high incomes pull it up, which is why the median is what gets reported. The mode is the only one that works on categories rather than numbers — you can have a most common colour but not an average one. As for standard deviation, this uses the sample version, dividing by n−1, which is the right choice whenever the data is a sample rather than the whole population.