Question

The frequency distribution of the age of students in a class of 40 students is given below:

\(Age\)	15	16	17	18	19	20
No. of Students	5	8	5	12	x	y

If the mean deviation about the median is 1.25, then \(4x + 5y\) is equal to:

• A. 43
• B. 44
• C. 47
• D. 46

Answer 1

The Correct Option is B

We are given:
x + y = 10 $\quad \cdots \text{(1)}$

The median is:
M = 18

The formula for the Mean Deviation (M.D.) is:

$\text{M.D.} = \frac{\sum f_i |x_i - M|}{\sum f_i}$

Substituting the given values:

1.25 = $\frac{36 + x + 2y}{40}$

Simplifying:

x + 2y = 14 $\quad \cdots \text{(2)}$

From equations (1) and (2), solving simultaneously:

x + y = 10

x + 2y = 14

Subtracting (1) from (2):

y = 4

Substituting y = 4 into (1):

x = 6

Now, substituting x = 6 and y = 4 into 4x + 5y:

4x + 5y = 4(6) + 5(4) = 24 + 20 = 44

Final Answer: 44

The table values are as follows:
 

Age \(x_i\)	f	\(|x_i - M|\)	\(f_i|x_i - M|\)
15	3	3	15
16	8	2	16
17	5	1	5
18	12	0	0
19	x	1	x
20	y	2	2y