If the mean and standard deviation of 10 observations x1,x2,…,x10 are 2 and 3 respectively, then mean of x1+12,x2+12,…,x10+12 is equal to

We have, Mean = 2 and S. D. = 3⇒ 110∑i=1010 xi=2 and 110∑i=110 xi2−22=32⇒ ∑i=110 xi=20 and   ∑i=110 xi2=130Let X¯ be the mean of x1+12,x2+12,…,x10+12. Then,X¯=110∑i=110 xi+12⇒ X¯=110∑i=110 xi2+210∑i=110 xi+110∑i=110 1⇒ X¯=110×130+210×20+1010=18