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

36, 64, 48, 52, 57, 73, 26, 39, 78, 67

31. The mean marks of the whole class is :

(a) 49.1
(b) 53.7
(c) 54
(d) 60

32. If the maximum marks in the test were 80, the mean percentage of marks obtained by the students is :

(a) 65%
(b) 67.5%
(c) 68%
(d) 72%

33. The mean marks of the top 5 scorers in the class is :

(a) 65.4
(b) 66.8
(c) 67.2
(d) 67.8

34. As per the Board’s instruction each student who obtained less than 50 marks was awarded 3 grace marks. The new mean of the marks thus obtained increases by :

(a) 0.9
(b) 1.2
(c) 1.5
(d) 1.8

31. By formula,

$\text{Mean} = \dfrac{\text{ Sum of all observations}}{\text{ Number of observations}} \\[1em] = \dfrac{36 + 64 + 48 + 52 + 57 + 73 + 26 + 39 + 78 + 67}{10} \\[1em] = \dfrac{540}{10} \\[1em] = 54.$

Hence, option (c) is the correct option.

32. By formula,

$\text{Percentage of marks} = \dfrac{\text{Mean of marks obtained}}{\text{Maximum marks}} \times 100 \\[1em] = \dfrac{54}{80} \times 100 \\[1em] = 0.675 \times 100 \\[1em] = 67.5 \%$

Hence, option (b) is the correct option.

33. Top five marks in class are 78, 73, 67, 64, 57.

By formula,

$\text{Mean} = \dfrac{\text{ Sum of all observations}}{\text{ Number of observations}} \\[1em] = \dfrac{78 + 73 + 67 + 64 + 57}{5} \\[1em] = \dfrac{339}{5} \\[1em] = 67.8$

Hence, option (d) is the correct option.

34. The students who scored less than 50 are: 36, 48, 26, 39

Since each of these 4 students gets 3 marks,

Total marks increased = 4(3) = 12 marks

The new mean of the marks thus obtained increases by :

$\dfrac{\text{Total marks increased}}{\text{Number of students}} \\[1em] = \dfrac{12}{10} \\[1em] = 1.2$

Hence, option (b) is the correct option.