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# What is the median of 100 80 80 80 95 80 95 100?

The median for this set of numbers is 87.5.

The median of a set of numbers is the number that falls in the middle of all the numbers when they have been arranged in ranking order.

To make this easier one needs to arrange the set of numbers from smallest to largest (rank-order)
80 80 80 80 95 95 100 100.
Since this group of numbers has an even number of sets we have to take the two middle sets of numbers (80 and 95) and add them together and then divide by two (80+95)/2= 87.5. This gives us the median for this set of numbers of 87.5.

As many might already know to find the median for an old set of numbers, one would arrange (rank-order) the set of numbers from the smallest to largest. Next, you would locate the position of the middle score; this number is the median. There is a small Formula One can use if your working with a "large" set of numbers for find out exactly where the middle position is at (n+1)/2 (note: this formula works for an even set of numbers as well but you will get a decimal point number, which will fall in between the two sets of numbers that need to be added together). The letter "n" represent the total set of numbers that we are currently looking at. So for example, if we if we were to take

80 80 80 80 95 95 100 (notice I left out the other 100 from the original set of numbers in the question and I already arranged them in ranking order) now we are only working with seven sets of numbers instead of eight.
Now to figure out the median for these sets of numbers we would take (n+1)/2 and plug in the number 7 for (n). (7+1)/2= 8/2=4. The number 4 now tells us exactly what position in the group of numbers we will find the median in; the 4th number in line from the left. In the 4th position we find the number 80; so for my example the median would be 80.

Reference: Discovering Statistics by Andy Fields

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