The marks obtained by 10 students in a class-test were as follows :

38, 41, 36, 31, 45, 38, 27, 32, 29, 39

Find :

(i) the mean of their marks;

(ii) the mean of their marks, when the marks of each student are increased by 2;

(iii) the mean of their marks, when 1 mark is deducted from the marks of each student;

(iv) the mean of their marks, when the marks of each student are halved.

(i) We know that,

Mean = $\dfrac{\sum x_i}{n}$

We have,

$\Rightarrow \text{Mean of marks} = \dfrac{\text{Sum of marks}}{\text{Number of students}} \\[1em] = \dfrac{38 + 41 + 36 + 31 + 45 + 38 + 27 + 32 + 29 + 39}{10} \\[1em] = \dfrac{356}{10} \\[1em] = 35.6$

Hence, mean of marks = 35.6.

(ii) If 2 marks are added to each student, the mean also increases by 2.

New mean = 35.6 + 2 = 37.6

Hence, mean when marks are increased by 2 = 37.6

(iii) If 1 mark is deducted to each student, the mean also decreases by 1.

New mean = 35.6 - 1 = 34.6

Hence, mean when 1 mark is deducted = 34.6

(iv) If the marks of each student are halved, the mean is also halved.

New mean = $\dfrac{35.6}{2}$ = 17.8

Hence, mean when marks are halved = 17.8