If the mean of the following frequency distribution is 2.6 then the value of x is ........

Variable	1	2	3	4	5
Frequency	4	5	x	1	2

Correct option is B

Step 1: Recall the formula for mean in frequency distribution:

$$\text{Mean} = \frac{\sum f_i x_i}{\sum f_i}$$​​

Where:
- $$f_i$$​ = frequency of the i -th variable
- $$x_i$$​ = value of the i -th variable

Step 2: Data from the table:

$$\sum f_i = 4 + 5 + x + 1 + 2 = 12 + x$$​​

$$\sum f_i x_i = (4 \cdot 1) + (5 \cdot 2) + (x \cdot 3) + (1 \cdot 4) + (2 \cdot 5)$$​​

$$\sum f_i x_i$$​ = 4 + 10 + 3x + 4 + 10 = 28 + 3x

Step 3: Use the mean formula:
The mean is given as 2.6 , so:

$$2.6 = \frac{28 + 3x}{12 + x}$$​​

Multiply both sides by 12 + x :

2.6 (12 + x) = 28 + 3x

31.2 + 2.6x = 28 + 3x

Simplify:

31.2 - 28 = 3x - 2.6x

3.2 = 0.4x

x = $$\frac{3.2}{0.4}$$​ = 8

Final Answer:
The value of x is 8.