Re: A group of 20 values has a mean of 85 and a median of 80
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05 Nov 2018, 05:47
Let us suppose that for the 20 values
1st 15 terms are equal to 80, and the 5 of the rest are equal to 100
this gives a mean of 85 and median of 80
For the next 30 terms
21 of them are 72 and 9 of them are 82. This gives a mean of 72 and median of 75.
when we arrange them in ascending order we have
\(21 72's\) followed by \(15 80's\) followed by \(9 82's\) and then \(5 100's\)
the avg of \(25th\) and \(26th\) term is the median
In this case the median is the avg of 72 and 80 i.e. 76
Let us manipulate the data a bit
for the 1st 20 values
if 10 terms are equal to 70, 1 term is equal to 90. 7 terms are equal to 100 and 2 terms are equal to 105
we still have the required mean of 85 and median of 80 for the 20 terms
for the next 30 terms suppose
21 terms are 72 and the rest 9 of them 82 then we still have median as 72 and mean as 75
now arranging the terms in ascending order we get,
\(10 70's,21 72's, 9 82's, 1 90's, 7 100's, 2 105'\)
so the median is 72
Hence we do not have a fixed median