GMAT Statistics Practice – Median

Descriptive Statistics that includes mean, weighted mean, median, standard deviation and range is a GMAT favorite. At times it becomes “virulent” in its data sufficiency avatar.

Here is a medium difficulty DS question from Descriptive Statistics:

Directions
This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwise), you must indicate whether –

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Question
What is the median of five integers 20, 22, 26, 30 and ‘a’?
1. The mean of the 5 integers is equal to the median of the 5 integers.
2. The range of the 5 integers is greater than ‘a’.

The correct answer to this question is B – Statement 2 alone is sufficient to answer this question.

Explanation

From the question stem we know that ‘a’ is an integer and the median is one of the following 3 values : 22 or 26 or a.

Statement 1 : The mean of the 5 integers is equal to the median of the 5 integers.

The mean of the 5 integers is (20 + 22 + 26 + 30 + a)/5 = (98 + a)/5
As the mean and median are same from statement 1,
When the median is 22, we have 22 = (98 + a)/5 or a = 12.
When the median is 26, we have 26 = (98 + a)/5 or a = 32
When the median is a, we have a = (98 + a)/5 or a = 24.5

However, as ‘a’ is an integer, it can be either 12 or 32 and hence the median is either 22 or 26.

Statement 1 is NOT sufficient as we get 2 values for the median.

Statement 2: The range of the 5 integers is greater than ‘a’.

If ‘a’ is less than 15, ‘a’ will always be less than the range. The median will be
22 for all values of ‘a’ less than 15.

Hence, statement 2 alone is SUFFICIENT to answer the question.

Choice B is the answer.

You can access additional questions on Descriptive Statistics on the GMAT question bank.

If you want a comprehensive material to crack this topic, you can download our GMAT Descriptive Statistics eBook.