Median by Sabir Chdhry

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                                                                           By: Sabir Chdhry

Median is one way of finding the measure of central tendency. By measure of central tendency, we mean the statistical average of the numbers given in a series or list.

How to calculate the median value?

To find out the median value, first of all we arrange the given numbers in ascending order (increasing order) or in descending order (decreasing order) in such a way that in this newly arranged number series whichever number comes in the middle or middle of the range, that number will be called the median value of that category.

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Example: If a number series is 15, 13, 17, 7, 9, 5, 11, then first of all we arrange these numbers in ascending or descending order like

after applying ascending order- 5, 7, 9, 11, 13, 15, 17 or

In descending order- 17, 15, 13, 11, 9, 7, 5

After arranging the numbers in ascending or descending order, we see that in both the cases the middle number of the series is 11, so the median value of this series will be 11.

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Formula to find median value if number in individual series is odd

An odd number means a number that is not exactly divisible by 2, such as 3, 5, 7, 9, 11, 13, 15, etc.

In this case, first all the numbers in the given series are arranged in ascending or descending order, then the following formula is used

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Here M = median,

N = total numbers in the series

Example: Find the median value with the help of the following data.

       5, 8, 4, 3, 6, 11, 7, 10, 9, 12, 15, 13, 16, 14, 2

after arranging in ascending order (can also arrange in descending order) –

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16

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Total numbers in this series is 15 i.e. N = 15 on putting in the formula

Therefore, according to the median formula, the answer is  8th term, and 8th tern of the series is 9. Therefore, the median value of this series is 9.

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Formula to find median value if numbers in individual category is Even

An even number means a number which is completely divisible by 2, such as 2, 4, 6, 8, 12, 14, 16, etc.

The problem that comes when number are even in the series -

Using the above formula (N+1) will be an odd number, when we divide the odd number by 2 then our answer will be 1.5th term or 2.5th term or 3.5th term etc., but no such term is  there in the series because there are complete terms in the series like second term or third term or fourth term  etc.

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Let us see how to solve this problem with the following example

Example: Find the median value with the help of the following data.

       4, 6, 8, 2, 5, 3, 1, 12, 18, 20, 19, 21,

On keeping in ascending order (can also keep in descending order) –

1, 2, 3, 4, 5, 6, 8, 12, 18, 19, 20, 21

Now the total numbers in this series are 12 i.e. putting N = 12 in the formula

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Now we have the problem when having an even number in the series, since there is no 6.5th term in the series, what will we do in such a situation, we will add the sixth term and the seventh term of the series and divide it by 2. That number will be our median value.

Note- Why did we take the 6th and 7th term? since 6.5 comes between 6 and 7, if the answer was 9.5 by using the formula of median, then we would have divided it by 2 by adding the 9th and 10th terms.

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 So, as explained above

Since the 6th term in the series in ascending order is 6 and the 7th term is 8, so Median value is 7.

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Author: Sabir Chdhry 

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