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# How do you find the median of 6 numbers with 2 of those numbers being the same?

You find the median like normal:

1) list ALL the numbers in order from least to greatest putting any repeated numbers next to each other;

2) if there is an odd number of numbers the median is the middle one - to find which one it is add one to the number of numbers and divide by 2, eg if there are 11 numbers: (11+1)/2 = 6, so it is the 6th number;

3) otherwise there is an even number of numbers and the median is the mean average of the middle two - to find which ones divide the number of numbers by 2 and then find the mean average of that one and the next one, eg if there are 12 numbers 12/2 = 6, so find the mean average of the 6th and 7th numbers.

examples:

find the median of {1, 5, 2, 4, 6, 2}

{1, 5, 2, 4, 6, 2} → {1, 2, 2, 4, 5, 6} → 6 numbers, therefore mean of middle two (6/3 = 3 → 3rd and 4th) = (2 + 4)/2 = 3

find the median of {1, 5, 2, 4, 6, 4}

{1, 5, 2, 4, 6, 4} → {1, 2, 4, 4, 5, 6} → 6 numbers, therefore mean of middle two (6/3 = 3 → 3rd and 4th) = (4 + 4)/2 = 4

find the median of {1, 5, 2, 3, 6, 2}

{1, 5, 2, 3, 6, 2} → {1, 2, 2, 3, 5, 6} → 6 numbers, therefore mean of middle two (6/3 = 3 → 3rd and 4th) = (2 + 3)/2 = 2.5

If there is an even number of numbers in the set, the median does not have to be (and usually isn't) one of the numbers in the set.

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