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

Directions :
At a courier company, a daily report of parcels received for dispatch is prepared every evening, which classifies the parcels on the basis of their weights. The report of a certain day is as under :

35.How many parcels have weights in the range of 300 – 400 grams?
(a) 4
(b) 12
(c) 13
(d) 19

36.How many parcels have weights in the range of 200 – 300 grams?
(a) 10
(b) 12
(c) 13
(d) 19

37.In which of the following weight ranges, the number of parcels is the lowest?
(a) 100 – 200
(b) 200 – 300
(c) 400 – 500
(d) 500 – 600

38.The mean weight of parcels received on that particular day is :
(a) 226.78 g
(b) 251.67 g
(c) 284.28 g
(d) 302.16 g

Assertion (A): If x_i’s are the mid-points of the class intervals of a grouped data, Σf_i’s are the corresponding frequencies and x̄ is the mean, then Σf_i(x_i − x̄) = 1.

Reason (R): The sum of the deviations from the mean is 0.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Assertion (A): Out of 25 numbers, the mean of 15 of them is 18. If the mean of the remaining numbers is 13, then the mean of the 25 numbers is 14.

Reason (R): Mean of the variates x₁, x₂, …, x_n having corresponding frequencies f₁, f₂, …, f_n is given by

x̄ = $\Big(\dfrac{f$1 x1 + f2 x2 + \dots + fn xn}{x1 + x2 + \dots + x_n}\Big).

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false