JAMIA 2022 — Mathematics PYQ

1. Set Up the Frequency Table

First, we list the values ($x_i$) and their corresponding frequencies ($f_i$):

Value (xi​)	Frequency (fi​)	Product (fi​xi​)
3	$x$	$3x$
5	$x+4$	$5(x+4)=5x+20$
7	$x-3$	$7(x-3)=7x-21$
4	$x+8$	$4(x+8)=4x+32$

2. Calculate the Total Frequency ($\sum f_i$)

Sum all the frequency terms:

3. Calculate the Sum of Products ($\sum f_i{x}_i$)

Sum the products calculated in the table:

4. Use the Arithmetic Mean Formula

The arithmetic mean ($\bar{x}$) is given as 4. The formula is:

Substitute the values:

5. Solve for $x$

Cross-multiply to solve the equation:

Rearrange the terms (bring $x$ terms to one side and constants to the other):

Final Answer

The value of $x$ is $\frac{5}{3}$.