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Tricks for Calculating Median Easily

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Tricks for Calculating Median Easily  [#permalink]

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New post Updated on: 17 Mar 2017, 17:49


EVEN NUMBERS OF TERMS: Even numbers of terms have no “true median” (i.e, one of the numbers already in the list) so you will have to take the average of “half” and “half plus one.”

For example, the median of 102 terms is the average of the \(\frac{102}{2}\)= 51st and 52nd terms.

ODD NUMBERS OF TERMS: Odd numbers of terms are easier. Just divide by 2--you will get a decimal (.5) answer--and then it’s the next integer term.

For example the median of 1,003 terms is the \(\frac{1003}{2}\)= 501.5 --> 502nd term.

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Originally posted by mcelroytutoring on 13 Apr 2016, 17:31.
Last edited by mcelroytutoring on 17 Mar 2017, 17:49, edited 2 times in total.
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Re: Tricks for Calculating Median Easily  [#permalink]

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New post 15 Apr 2016, 20:43
Here is a slightly different way of doing the same thing.

Case of odd number of terms: Let's say we need to find the position of the median term when we have say 93 elements in a list. I take out 1 from 93, which leaves me with 92, split that into two, or 46 each. And I visualize that there are 46 elements to the right and left of the median, which means the median is at the 47th position.

Case of even number of terms: In this case the median is the average of the middle two terms. If we have say 98 terms, then take the two out of that total, which leaves us with 96. Divide that into equal parts, 48 each. This means there are 48 elements to the left and right of the middle two numbers. Therefore, the we are looking for the 49th and 50th element counting from either left or right.

I used to have trouble with this and by doing it this way I find it much easier to visualize the arrangement of the elements.

Also, Brian you may want to edit the typo on the 3rd line, it should be 51st and 52nd term.

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Re: Tricks for Calculating Median Easily  [#permalink]

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New post 15 Apr 2016, 21:26
The concepts are the same, It is what suits you OR what strikes you easily..
In case of ODD terms, another way is
ADD 1 to the number and divide by 2, and the answer is the median..

The logic is ofcourse that we can pair each number except the middle, so the median is always there in the ODD number of integers..

Applying the same logic, the MEDIAN is never there in the set if set contains EVEN number of integers/fractions, as its position is in the center of the middle two numbers. Divide the number by 2 , the answer you get and one more than the answer are the two middle numbers. Their average will give you the value of median
Ofcourse the value of MEDIAN can be in the set if middle numbers are SAME

1) Absolute modulus :
2)Combination of similar and dissimilar things :
3) effects of arithmetic operations :

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Re: Tricks for Calculating Median Easily  [#permalink]

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