A firm pays its five clerks Rs. 15,000 each, three assistants Rs. 40,000 each and its accountant Rs. 66,000. Then the mean salary in the firm comprising of these nine employees exceeds its median salary by rupees
There are 9 employees in the firm. Median of any set is the element which occurs in the middle of the set when the elements are positioned in increasing or decreasing order. The number of elements in this set = 5+3+1 = 9
Thus, the middle element will be in the position $$\frac {9+1}{2}$$ = 5th. Since we know that the clerks are paid the least so the clerk salaries would be in the beginning of the set if arranged in ascending order. Thus, the 5th element will be a clerk's salary as the number of clerks is 5.
Thus, median of the set = Rs 15,000.
To find the mean salary, we first need to find the sum total salary of the people involved.
Total salary = (Number of clerks*salary of 1 clerk) + (Number of assistants*salary of 1 assistant) + (Number of accountants*salary of 1 accountant)
$$ \Rightarrow$$ Total salary = (5*15,000)+(3*40,000)+(1*66,000)
$$ \Rightarrow$$ Total salary = 75,000+1,20,000+66,000
$$ \Rightarrow$$ Total salary = 2,61,000
Mean salary = $$\frac{\textrm{Total Salary}}{\textrm{Total number of employees}} $$
$$ \Rightarrow $$ Mean salary = $$ \frac{261000}{9} $$
$$ \Rightarrow $$ Mean salary = Rs 29,000 /-
Thus, difference between mean and median salary = 29,000-15,000 = Rs 14,000
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