Standard Deviation

Two datasets share the same mean of 50. The first is {50, 50, 50, 50, 50} — every value sits exactly on the centre. The second is {10, 30, 50, 70, 90} — values flung far to either side. The mean insists they're identical; your eyes insist they're nothing alike. We need a single number that measures how far the data strays from its centre on average — a number for SPREAD. That number is the standard deviation.