The mean of a set of 15 data items is 600 and the standard d

The mean of a set of 15 data items is 600 and the standard deviation is 12. Another piece of data is discovered and the new mean is 600.25. Find the new standard deviation.

Solution

M = (X) / N

where X=individual data points N=number of data points, M=Mean
In first case , 600*15 =(X)
                  now, 600.25 *16 = (X+1)
implies new data set = 600.25*16-66*15=604

S2 = underroot of [(X-M) 2 / N - 1]

In first case , S2=12*12= underroot of [(X-M) 2 / 14]
                  now, S2\'= underroot of [(X+1-M) 2 / 15] =underroot of [144*underroot(14) +604]2 / 15]
                                  =295.06917

so,new standard deviation =17.177 equivalent to 17.2