MEDIAN
Another well known central measure of tendency is the
median
which is the middle
value after the data elements are sorted from lowest to highest.
Example 1

Find the median of
3 4 1 2 9 2 8.
•
First, sort the data from lowest to highest:
1 2 2
3
4 8 9
•
Then, since 3 is the middle element, so the median of the set of data is
3
.
•
Notice that this is not an average, but just the number in the middle of the set.
Now we will add another element to our original set to give us an
even
number of points.
Example 2

Find the median of
3 4 1 2 9 2 8 5.
•
First we sort the data: 1 2 2
3 4
5 8 9.
•
Find the middle TWO values
3
4
•
Now, find the mean of those values.
x
= (3 + 4) / 2
= 7/2 = 3.5.
•
The median of the set of data is now
3.5
So, to find the median of a set of data with an
odd
number of elements, sort the data and
locate the middle number.
For data with an
even
number of elements, sort the data,
locate the two middle numbers, and then, find the mean of those two numbers.
325
Find the median of
53,52,75,62,68,58,49,49.
Reorder the data:
Median numbers:
Average of median numbers:
326
Find the median of 3,24,30,47,43,7,47,13,44,39.
Reorder the data: