Arithmetic Mean - Data Sufficiency

Here is an easy Descriptive Statistics Data Sufficiency Question

What is the median of a set of 10 positive integers?
1. The numbers are in an AP with the first term being 10
2. The arithmetic mean of these 10 numbers is 55

Answer - Choice C

Explanatory Answer

Break down the process of solving any DS question into 3 mandatory steps and 1 optional step.

Step 1 : Get an idea about the answer : Answering this question is providing with one single value for the median of 10 positive integers. This number will be a positive number - may or may not be an integer.

Step 2 : Evaluate Statement 1 alone. 

The numbers are in an AP with the first term being 10.

If there are 10 terms, then the median is the arithmetic mean of the 5th and the 6th term.

From statement 1 we know that the first term is 10. However, there is no information about the subsequent terms - information about the common difference is missing.

Hence, we will not be able to find the 5th and the 6th term. 

Data is Not Sufficient.

Step 3 : Evaluate Statement 2 alone.

The arithmetic mean of these 10 numbers is 55.

The arithmetic mean of the numbers may or may not be equal to the median. 

The arithmetic mean will be the median too if the distribution is symmetric about the mean.

Statement 2 alone is Not Sufficient.

Step 4 : Combine statement 1 and statement 2.

The necessity to combine the two statements arises only when the two statements independently do not provide you with an answer.

Step 4, therefore, is not mandatory for all questions. In fact, do not combine the two statements if you get an answer from these statements independently.

Combining the statements, we can deduce that the terms are in an AP and their mean is 55. 

If terms are in an AP, the mean and the median are the same.

Hence, we can deduce the median to be 55.

Statements 1 and 2 together are sufficient to answer the question.

Choice C is the answer.

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