Of the 13 employees in a certain department, 1 has an annual salary of

Oh this is brutal. GMAT gives first two salaries in ascending order and so I assumed that all salaries are given in ascending order and got it wrong.

Since (13 + 1)/2 = 7, the median is the 7th value when the salaries are ordered from least to greatest.

The salaries from least to greatest are:

38,000 (1st)

40,000 (2nd to 4th)

42,500 (5th and 6th)

45,000 (7th and 8th)

Thus, the median salary is 45,000.

Answer: D

If the total observations is odd, then the median is the \(\frac{n \space + \space 1}{2}th\)

If the number of observations are odd, then the median is the average of the \(\frac{n}{2}th\) and the next number.


In the question above, the frequencies are small enough for us to list out the numbers. If the frequencies are large, then we would create a 3rd table which would list the cumulative frequency as shown in the figure.


The last value of the cumulative frequency table tells us the total number of observations.



First arrange the numbers and their corresponding frequencies in ascending order


Here n = 13. The median is the \(\frac{13 \space + \space 1}{2}\) = 7th number.

Looking at the cumulative frequency table, the 7th number is when when x = 45,000



Option D

Arun Kumar

Given: Of the 13 employees in a certain department, 1 has an annual salary of 38,000, 2 have an annual salary of 45,000 each, 2 have an annual salary of 42,500 each, 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each.
Asked: What is the median annual salary for the 13 employees?

Salaries of 13 employees = {38K, 40K,40K,40K, 42.5K, 42.5K, 45K, 45K,48.5K ,48.5K ,48.5K ,48.5K ,48.5K }
Median = 45000

IMO D

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