Question

If each observation of the data is decreased by 8 then their mean
(a) remains the same
(b) is decreased by 8
(c) is increased by 5
(d) becomes 8 times the original mean

Answer 1

ANSWER:
(b) is decreased by 8
Let the numbers be x 1 , x 2, ...x n.
Hence, mean = $\frac{(x1+x2+....+xn)}{n}$
Now the new numbers after decreasing every number by 8 : (x 1 −8) , (x 2 −8)...,(x n −8)1

New Mean =$\frac{(x1-8+x2-8+....+xn-8)}{n}$
=$\frac{(x1+x2+....+xn-8)}{n}$
= $\frac{(x1+x2+....+xn)}{n}$-8∴New mean = mean - 8
Hence, mean is decreased by 8.