Question

The mean of 100 observations is 24 if 6 is added to each of the observations and then each of them is multiplied by 2.5 find the new mean

Answer 1

We know, mean =∑x/total number of data(n)
so ∑x= mean* total number of data that is 100*24=2400

Now if 6 is added to each number  total of 100*6(i.e 600) is added to the ∑x while the total number of data (n) remains the same.

∑x= 2400+600

Again 2.5 is multiplied to each number so  the new ∑x= (2400+600)*2.5 i.e 7500
so now the mean is
mean=∑x/total number of data(n)
 mean  =7500/100   

Therefore the new mean is 750