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

Answer: (B)

44

Answer 2

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