Let be a set of performance scores. If
were to be added to each score, the mean would go up. For example,
if
then
mean (average) =
,
After each score increase of
average =
,
Thus the mean would go up by 5. Also the median would go up by
. In the example above, initially the median was
, and after the increase of each score of
the median was equal to
.
The standard deviation can be found by the formula:
where
.
After each score was increased by 5
So, the standard deviation would not change.
If you look at the figure, all points simultaneously lifted upwards by 5, but the spread of points around the new average (standard deviation) has not changed.
Let be a set of values.
The standard deviation
If then median
If then
median =