UPSC 2014 CDS I Math Paper

The arithmetic mean uses all the data and is always uniquely defined.
Hence, statement A is correct
The median uses only one or two numbers from the data and is not always uniquely defined.
As when the number of observation given in data are odd in number, then
median is the middle term (unique) when arrangement is in descending or ascending order.
But when the number of observation given in data are even in number,
then the median is two middle terms (not unique) when arrangement is in descending or ascending order.
Hence, statement B is correct.