The mean of 15 observations is 32. Find the resulting mean, if each observation is :

(i) increased by 3

(ii) decreased by 7

(iii) multiplied by 2

(iv) divided by 0.5

(v) increased by 60%

(vi) decreased by 20%

(i) According to property 2, if each observation is increased by quantity a, then the mean is also increased by the same quantity a.

The mean of 15 observations is 32.

If each observation is increased by 3, then the mean increases by 3 ( 32 + 3 = 35).

Hence, the mean of the new observations = 35.

(ii) According to property 3, if each observation is decreased by a quantity a, then the mean is also decreased by the same quantity a.

The mean of 15 observations is 32.

If each observation is decreased by 7, then the mean is decreased by 7 ( 32 - 7 = 25).

Hence, the mean of the new observations = 25.

(iii) According to property 4, if each observation is multiplied by a quantity a, then the mean is also multiplied by the same quantity a.

The mean of 15 observations is 32.

If each observation is multiplied by 2, then the mean is multiplied by 2 ( 32 x 2 = 64).

Hence, the mean of the new observations = 64.

(iv) According to property 5, if each observation is divided by a quantity a, then the mean is also divided by the same quantity a.

The mean of 15 observations is 32.

If each observation of the data is divided by 0.5, then the mean is divided by 0.5 $\Big(\dfrac{32}{0.5} = 64\Big)$.

Hence, the mean of the new observations = 64.

(v) According to property 2, if each observation is increased by a quantity a, then the mean is also increased by the same quantity a.

The mean of 15 observations is 32.

If each observation is increased by 60%, then the mean is increased by 60% ( 32 + $\dfrac{60}{100} \times 32$ = 32 + 19.2 = 51.2).

Hence, the mean of the new observations = 51.2.

(vi) According to property 3, if each observation is decreased by a quantity a, then the mean is also decreased by the same quantity a.

The mean of 15 observations is 32.

If each observation is decreased by 20%; then the mean is decreased by 20% ( 32 - $\dfrac{20}{100} \times 32$ = 32 - 6.4 = 25.6).

Hence, the mean of the new observations = 25.6.