Mean of a certain number of observation is x If each observation is divided by m(m ≠ 0) and - Maths -

Question

Mean of a certain number of observation is x If each observation is
divided by m(m ≠ 0) and increased by
n, then the mean of new observation is

(a) x m + n
(b) x n + m
(c) x + n m
(d) x + m n

Global Expert · Accepted Answer

Let y1, y2, y3, , yk be k observations

Mean of the observations = x

⇒y1+y2+y3+ +ykk=x⇒y1+y2+y3+
+yk=kx        1

If each observation is divided by m and increased by
n, then the new observations are

y1m+n, y2m+n, y3m+n,   , ykm+n

∴ Mean of new observations

=y1m+n+ y2m+n+ +ykm+nk=y1m+y2m+ +ykm+ n+n+ +nk=y1+y2+
+ykmk+nkk=kxmk+nkk=xm+n

Hence, the correct option is (a)

Mean of a certain number of observation is x . If each observation is divided by m(m ≠ 0) and increased by n, then the mean of new observation is (a) x m + n (b) x n + m (c) x + n m (d) x + m n