The mean of a certain number of observations is 35. What is the new value of the mean if each observation is :

(i) increased by 7.

(ii) decreased by 5.

(iii) multiplied by 2.

(iv) divided by 5.

(v) increased by 20%.

(vi) decreased by 30%.

(i) If the same number is added to each value in a dataset, the mean will also increase by that same number.

Mean of a certain number of observations = 35

When each number is increased by 7.

New mean = 35 + 7 = 42

Hence, the mean = 42.

(ii) If the same number is subtracted from each value in a dataset, the mean will also decrease by that same number.

Mean of a certain number of observations = 35

When each number is decreased by 5.

New mean = 35 - 5 = 30

Hence, the mean = 30.

(iii) If each value in the dataset is multiplied by the same number, the mean will also be multiplied by that same number.

Mean of a certain number of observations = 35

When each number is multiplied by 2.

New mean = 35 x 2 = 70

Hence, the mean = 70.

(iv) If each value in the dataset is divided by the same number, the mean will also be divided by that same number.

Mean of a certain number of observations = 35

When each number is divide by 5.

New mean = 35 ÷ 5 = 7

Hence, the mean = 7.

(v) If each value in the dataset is increased by 20%, the mean will also increase by 20%.

Mean of a certain number of observations = 35

When each number is increased by 20%.

New mean = 35 x (100 + 20)%

= 35 x $\dfrac{120}{100}$

= 42

Hence, the mean = 42.

(vi) If each value in the dataset is decreased by 30%, the mean will also decrease by 30%.

Mean of a certain number of observations = 35

When each number is decreased by 30%.

New mean = 35 x (100 - 30)%

= 35 x $\dfrac{70}{100}$

= 24.5

Hence, the mean = 24.5.