# Useful Formulae

Statistical analysis allows us to process samples of observed data in order to reveal trends and make predictions. If x1, x2,..., xnis a set of values of some measurable phenomenon,the average or meanvalue is given by x x1xn. The standard deviationof the sample then gauges the extent to which the data deviate from this mean The most commonly occurring form of statistical distributionis the normal or Gaussian. Its general form produces a bellshaped curve centred at xwhose widthis dependent on . In data which is normally distributed the probability of a value occurring in the range between aand bis equal to the area under the curve between these values as shown opposite. The total area under the curve all possibilities is equal to one. The Poissondistributiontells us that if the mean number of events of a particular type in a fixed time interval is ,then the probability of nevents occurring in one interval is given by pn where e 2.718...see page 18. x12xn2 24 STATISTICS distribution and deviation 2 x12x2xn2x2 n n n fx e 1 xx 2 22 n e n x2 25