Let us suppose that for the
20 values
1st
15 terms are equal to
80, and the
5 of the rest are equal to
100this 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.
76Let 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
72Hence we do not have a fixed median
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