In a company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 11% of the employees earn $43,000 a year and 5% of the employees earn $49,000 a year. What is the median salary for the company?Assume that there are 100 employees in the company.
60 % of the employees i.e 60 % of 100 = 60 employees earn less than $50,000 a year.
Similarly , 60 employees earn more than $40,000 a year.
11 employees earn $43,000 a year.
5 employees earn $49,000 a year.
If we arrange the salaries of the 100 employees in ascending order
\(S1, S2, S3...........S100\).
Where S1 is the lowest salary paid to the employee and S100 is the highest salary paid to the employee.
The median salary of the company would be average of \((S50 + S51)\) i.e \(\frac{(S50 + S51)}{2} \) as the no of employees in the company is even.
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From the above table we can conclude that the salary of S41-S60 lies between $40,000 and $50,000.
Also we need to find S50 and S51 in order to find the median.
Since its given that 11 employees earn $43,000 a year and 5 employees earn $49,000 a year. That means we have the salary details of 16 employees in the range S41-S60. But we are not aware of the salaries of the remaining 4 employees in range S41-S60.
The salary of these 4 employess could be in the range
$40,000 < S < $43,000 or
$43,000 < S < $49,000 or
$49,000 < S < $50,000.
Does it matter in which range it would be ? No, In all cases, the salary of S50 and S51 will be $43,000 each as there are 11 employees with a salary $43,000 a year
Median = (S50 + S51)/2 = ($43,000 + $43,000)/2 = $43,000.
Option A is the answer.Hope it helps,
Clifin J Francis,
GMAT SME _________________