mean vs median

gmattarget2009 wrote:QUE ON DS

PETER , PAUL AND MARY EACH RECEIVED A PASSING SCORE ON HIS / HER HISTORY MIDTERM. THE ARITHMETIC MEAN OF THE THREE SCORES WAS 78. WHAT WAS THE MEDIAN OF THE THREE SCORE.

1. PETER SCORED A 73 ON THIS EXAM
2. MARRY SCORED A 78 ON HER EXAM

answer is b.

median is middle number in set.

statement 1)

(73+paul+mary)/3=78
73+Paul+Mary=234
Paul+Mary=161
Paul's and Mary's are variable and we don't know if P>M or P<M or if P=M.
Insufficient

Statement 2)

Mary=78 which is average as well. This has to be the median, because there are only three values. Thus, Paul and Peter cannot both be less than Mary or both be greater than Mary with out moving the average. Mary has to be in the middle.

Please provide OA.

Answer should be B

As 78 is the mean, therefore three scores will be

78 - x, 78, 78 + x

where x can be 0. But the median will be 78 in every case.

Statement 1 gives us more than 1 value for the median