Average and median

[kulksnikhil]

I have a general mathematic question.

If Averge of three numbers is say 80 and one of the numbers is 80.. does it mean the median of the three numbers is 80 ???

[aim-wsc]

yes.

take a case of
60, 80, 100===>
arithmatic mean =80
&
median =80 too.

but
case 2
75, 80, 100
ave= 85
median= 80

i hope that helps.

Median number has to be in the set

[rnschmidt]

what if the set is even? For example:

3,4,5,6


wouldn't the median be 4.5?

[aim-wsc]

what if the set is even? For example:

3,4,5,6


wouldn't the median be 4.5?

the value of the median is always there in set of numbers.
4.5 is not in the list so it cannot be. 4.5 is an arithmetic mean average.

[Stacey Koprince]

Actually, the median is only in the set if there is an odd number of terms. If there is an even number of terms, we take the two middle numbers and average them to find the median - so, in this case, the median may not be one of the numbers in the set.

So, for example: 60, 80, 100 has an odd number of terms, so 80 is the median.

1, 4, 6, 7 on the other hand has an even number of terms, so we take the middle two (4 and 6) and average them to get 5 - this is the median even though it is not in the original set of numbers.

So for the original question, 80 is the median because we have an odd number of terms. Our two options are either 80, 80, 80 or something like 78, 80, 82 (the first and third numbers can be anything as long as they average to 80).

If we had an even number of integer terms, which average to 80 and which also include 80, then we could have 80, 80, 80, 80 OR something like 78, 80, 80, 82 OR something like 78, 79, 80, 83. In all 3 cases, the numbers average to 80 but only the first two also have 80 as the median. In the third case, the median is 79.5.

[aim-wsc]

In all 3 cases, the numbers average to 80 but only the first two also have 80 as the median. In the third case, the median is 79.5.

Oops i have to brush up some quant skills now :roll: