CAT Practice : Averages, Ratios, Mixtures

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.

Averages - Mean Median

    Q.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?


  • Correct Answer
    Median is 4, average is 3.875.

Detailed Solution

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.

Correct Answer: Median is 4, average is 3.875.

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