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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

  1. $Rs. 20,000$
  2. $Rs. 30,000$
  3. $Rs. 32,300$
  4. $Rs. 40,000$
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Migrated from GO Mechanical 4 years ago by Arjun

1 Answer

Best answer
7 votes
7 votes

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 $(B).$

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