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Statistics Questions

1. How do you solve for median if the given data is even? For example: 3,1,2,3,1,1 (these given data is even.)
2. When do you use the formula n+1/2 (for odd number) and n+2/2 (for even numbers)? NOTE: My teacher said that the formula that I gave, is only applicable on finding the median. Can you give one example to prove your answer?
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1 Answer

1) Average the two middle numbers after arranging in sequence; e.g.,
 
1, 1, 1, 2, 3, 3
Median is (1+2)/2 = 3/2 = 1.5
 
2) The Median value should have the same number of numbers to the left and to the right of it.
 
Assuming an ordered list with n numbers:
 
If n is odd there will be (n-1)/2 numbers to the left of the Median, so the Median is the (n-1)/2 + 1 = (n-1)/2 + 2/2 = (n+1)/2 number in the list.
 
If n is even the Median will be between the two middle values and there will be n/2 numbers to the left and right of the Median. The Median is not one of the n numbers, so the formula (n+2)/2 will not locate it.