GATE Mechanical 2017 Set 1 | GA | Question: 4

Question

In a company with $100$ employees, $45$ earn $Rs. 20,000$ per month, $25$ earn $Rs. 30000$, $20$ earn $Rs. 40000$, $8$ earn $Rs. 60000$, and $2$ earn $Rs. 150,000$. The median of the salaries is

• A. $Rs. 20,000$
• B. $Rs. 30,000$
• C. $Rs. 32,300$
• D. $Rs. 40,000$

Answer 1

Given that:

$$\begin{array}{|l|l|}\hline \textbf{Employees} & \textbf{Salaries}\\\hline 45 & 20,000 \\\hline 25 & 30,000 \\\hline 20 & 40,000 \\\hline 8 & 60,000 \\\hline 2 & 150,000\\\hline \end{array}$$

The Median 

$(1)$ If the total number of numbers$(n)$ is an odd number, then the formula is given below (the numbers are assumed to be in ascending order)$:$

$$\text{Median}=\left(\dfrac{n+1}{2}\right)^{th}\text{term}$$

$(2)$ If the total number of numbers(n) is an even number, then the formula is given below$:$

$$\text{Median}=\dfrac{\left(\dfrac{n}{2}\right)^{th}\text{term}+\left(\dfrac{n}{2}+1\right)^{th}\text{term}}{2}$$

Here, $n=100$

$\text{Median}=\dfrac{\left(\dfrac{100}{2}\right)^{th}\text{term}+\left(\dfrac{100}{2}+1\right)^{th}\text{term}}{2}$

$\text{Median}=\dfrac{\left(50\right)^{th} \ \text{term}+\left(51\right)^{th} \ \text{term}}{2}$

$\text{Median}=\dfrac{30,000+30,000}{2}=30,000 $

So, the correct answer is $(B).$

Comments

Why the formula of "3Median = 2Mode + Mean" doesn't work here?

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best soln lakshman bhaiya

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@Manan Sharma you don't required to do with that formula. Only Arrange the Persons in INC Order (According to Salary, Not with Number of Persons) then , find the Median 50th Person from left. 

Answer 2

my approach was arrange oin increasing order like 2,8,20,25,45

 

then here middle value is 20 which earn rs 40000 per month so dont do this mistake

Many people will think like this