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The question is from CAT Ratio, Mixtures and Averages. When the median is greater than the mean, what can we infer from that? CAT exam is known to test on basics rather than high funda ideas. A range of CAT questions can be asked from Ratios and Proportions, Mixtures, Alligations and Averages. Make sure you master the topics. 2IIMs CAT questions bank provides you with CAT questions that can help you gear for CAT Exam CAT 2019.

Question 6: The median of n distinct numbers is greater than the average, does this mean that there are more terms above the average than below it?


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Explanatory Answer

Method of solving this CAT Question from Ratio, Mixtures and Averages: A clear understanding of median and mean is essential to cracking these types of questions. Median refers to the middle-term, mean to the average.

If there are an odd number of terms, say, 2n + 1, then the median is the middle term. And if average is lesser than the middle term, there will at least be n + 1 terms greater than the average. So, there will be more terms above the average than below it.

However, this need not be the case when there are an even number of terms. When there are 2n distinct terms, n of them will be greater than the median and n will be lesser than the median. The average of these two terms can be such that there are n terms above the average and n below it.

For instance, if the numbers are 0, 1, 7, 7.5. The median is 4, average is 3.875. Average is less than the median. And there are more 2 numbers above the average and 2 below the average.

The question is "does this mean that there are more terms above the average than below it?"

Hence, the answer is "No, it doesn't mean that".

 


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