In the formula $\bar x = a + \Big(\dfrac{\sum f$i di}{\sum f_i}\Big) for finding the mean of grouped data, d_is are deviations from a, of :

1. lower limits of the classes

2. upper limits of the classes

3. mid-points of the classes

4. frequencies of the class marks

If x_i's are the class marks of the class-intervals of grouped data, f_i's are the corresponding frequencies and x̄ is the mean, then Σ f_i(x_i − x̄) is equal to :

1. −1

2. 0

3. 1

4. 2

In a class of 100 students, the mean marks obtained in a certain test is 30 and in another class of 50 students the mean marks obtained in the same test is 60. The mean marks obtained by the students of both the classes taken together is :

1. 40

2. 45

3. 48

4. 50

A distribution consists of three components with frequencies 45, 40 and 15 having their means 2, 2.5 and 2 respectively. The mean of the combined distribution is :

1. 2.1

2. 2.2

3. 2.3

4. 2.4