For what value of x the mean of the given observations (2x − 5), (x + 3), (7 − x), (5 − x) and (x + 9) with frequencies 2, 3, 4, 6 and 1 respectively is 4?

1. 1

2. 2

3. 3

4. 4

The mean of n observations is $\bar x$. If the first observation is increased by 1, second by 2 and so on, then the new mean is :

1. $\bar x$ + n

2. $\bar x$ + $\Big(\dfrac{n}{2}\Big)$

3. $\bar x$ + $\Big(\dfrac{n + 1}{2}\Big)$

4. $\bar x$ + $\Big(\dfrac{n − 1}{2}\Big)$

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 the formula x̄ = a + h $\Big(\dfrac{\Sigma f$i ui}{\Sigma f_i}\Big) for finding the mean of grouped frequency distribution, u_i =

1. $\Big(\dfrac{x_i + a}{h}\Big)$

2. h (x_i − a)

3. $\Big(\dfrac{x_i − a}{h}\Big)$

4. $\Big(\dfrac{a − x_i}{h}\Big)$