## Standard deviation

The formula above will give the standard deviation of a set of numbers and saves one column (or one subtraction per data item) compared to the usual one. A disadvantage becomes apparent if you look at a worked example…

Suppose we have a set of 5 heights in centimetres: 160, 158, 162, 169, 155. According to my reckoning, the sum of these heights is 804 cm and the sum of the squares of each height is 129,394 cm^{2}. If I have got those numbers right (it *is* the morning of a General Election here in the UK) the rest of the calculation follows…

All fine and dandy, but did you notice the part of the calculation that looks like 25878.8 – 25856.64 ? That is two large numbers of similar size, and you are subtracting them. It is really important that **you don’t round the mean** using this formula.

Now try doing the calculation for *this* data set: 100160, 100158, 100162, 100169, 100155.

This formula is numerically unstable for data with low percentage variation. Of course, you could always subtract a constant to bring the data back into a range that a 10 digit calculator can cope with. This procedure is called using a ‘false mean’.