A set of 8 numbers has a mean of 16.8 and a standard deviation of 2.5.If every number of the set of data is multiplied by 2 and then add by 3,find
a)the new mean
b)the standard deviation of the set of data
Look at just 2 numbers and suppose the numbers are just "a" and "b". Then the mean is (a+ b)/2. If you multiply every number in the set by m and add n they become ma+ n and mb+ n and the mean is ((ma+n)+ (mb+ m))/2= (m(a+ b)+ 2n)/2= m(a+b)/2+ n. That is, the new mean is m times the old mean+ 3. What you do to the numbers, you do to the mean.