Friday, April 6, 2012

XAT 2012 Q59 : Mean, Median, Mode

This is a 1 - Mark question that appeared in XAT 2012 from Statistics. This is an interesting question that tests your basic understanding of how Mean, Median and Mode can be interpreted.

Question

Ramesh analysed the monthly salary figures of five vice presidents of his company. All the salary figures are in integer lakhs. The mean and the median salary figures are Rs. 5 lakhs, and the only mode is Rs. 8 lakhs. Which of the options below is the sum (in Rs. lakhs) of the highest and the lowest salaries?
A.    9
B.    10
C.    11
D.    12
E.    None of the above

Correct Answer – Choice A. Rs. 9 lakhs

Explanatory Answer

The mean salary of the five vice presidents is Rs.5 lakhs.
So, the sum of their salaries = 5 * 5 = 25 lakhs.

Let their salaries in ascending order be a, b, c, d and e.
So, a + b + c + d + e = 25.
The median salary is Rs.5 lakhs. So, C’s salary is Rs.5 lakhs.

The only  mode is Rs.8 lakhs.
So,  Rs.8 lakhs salary is drawn by the maximum number of VPs.
C’s salary is Rs.5 lakhs. So, d and e have to draw Rs. 8 lakhs each.

Therefore, a + b + 5 + 8 + 8 = 21
or a + b = 4

Their salaries are in integer lakhs.
Therefore, a can draw Rs.1 lakh and b can draw Rs.3 lakhs or a and b can both draw Rs. 2 lakhs each.

However, there is only one mode. So, a and b cannot draw Rs.2 lakhs each.
So, a draws Rs.1 lakh (the least salary) and e draws Rs.8 lakhs (the highest salary).

So, a + e = Rs.9 lakhs

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