Question

If each observation of the data is decreased by 5 , then what is the effect on the mean ?

Answer 1

mean will be decrease by 5

Answer 2

The mean will also be decreased by 5.

• Given that if each observation is decreased by 5 then what will be the effect on the mean of the data.
• Let us assume the mean of n data items to be m.

m = $\frac{Sum \ of \ all \ the \ items}{n}$   (Equation 1)

• Now each data item is decreased by 5 then,

Sum of all the new items = Sum of all items - 5n

• Now,

Mean of new items = Sum of all the new items / n

Mean of new items = (Sum of all items - 5n )/ n

Mean of new items = (Sum of all items)/ 5n - (5n/ n)

Mean of new items = m - 5     (From equation 1)

• Therefore, if each observation of the data is decreased by 5 then the mean also gets decreased by 5.