Calculating the median (basic)

1. The Median
(conceptual explanation)

2. The median is
estimated by
ordering the
observations from
lowest to highest.
Students Exam Scores
Bantam 30
Bella 42
Benton 40
Birch 28
Bork 37
Brenda 35
Bubba 33
Calculating the Median

3. The median is
estimated by
ordering the
observations from
lowest to highest.
Students Exam Scores
Birch 28
Bantam 30
Bubba 33
Brenda 35
Bork 37
Benton 40
Bella 42
Calculating the Median

4. Counting from the
lowest up to the
score that divides
the data set in half.
Students Exam Scores
Birch 28
Bantam 30
Bubba 33
Brenda 35
Bork 37
Benton 40
Bella 42
Calculating the Median

5. Counting from the
lowest up to the
score that divides
the data set in half.
Students Exam Scores
Birch 28
Bantam 30
Bubba 33
Brenda 35
Bork 37
Benton 40
Bella 42
Calculating the Median

6. The median
represents the 50th
percentile of a
distribution of
observations
Students Exam Scores
Birch 28
Bantam 30
Bubba 33
Brenda 35
Bork 37
Benton 40
Bella 42
Calculating the Median

7. The median
represents the 50th
percentile of a
distribution of
observations
Students Exam Scores
Birch 28
Bantam 30
Bubba 33
Brenda 35
Bork 37
Benton 40
Bella 42
Therefore the Median of this
data set is 35
Calculating the Median

8. In data sets with
even number of
cases (students), the
median is calculated
by summing the two
middle scores and
dividing the result by
2.
Students Exam Scores
Birch 28
Bantam 30
Bubba 33
Brenda 35
Bork 37
Benton 40
Bella 42
Boston 44
Calculating the Median

9. In data sets with
even number of
cases (students), the
median is calculated
by summing the two
middle scores and
dividing the result by
2.
Students Exam Scores
Birch 28
Bantam 30
Bubba 33
Brenda 35
Bork 37
Benton 40
Bella 42
Boston 44
35
+37
=72
72/2
Median = 36
Calculating the Median

10. The Advantage of using the Median
Calculating the Median

11. Advantages of Using the Median
Here’s an example:
5
6
4 83 10

12. Here’s an example:
5
6
4 83 10
28
3 54
13
25
Advantages of Using the Median

13. Here’s an example:
5
6
4 83 10
28
3 54
13
25
In the first data set,
there are two
observations to the left
of the MEDIAN “5”
and two observations to
the right of the MEDIAN.
Advantages of Using the Median

14. Here’s an example:
5
6
8 10
28
3 54
13
25
In the first data set,
there are two
observations to the left
of the MEDIAN “5”
and two observations to
the right of the MEDIAN.
43
Advantages of Using the Median

15. Here’s an example:
5
6
43
28
3 54
13
25
In the first data set,
there are two
observations to the left
of the MEDIAN “5”
and two observations to
the right of the MEDIAN.
8 10
Advantages of Using the Median

16. Here’s an example:
5
6
4 83 10
28
3 54
13
25
In the second data set,
there are also two
observations to the left
of “5” of the MEDIAN
and two observations to
the right of the MEDIAN.
Advantages of Using the Median

17. Here’s an example:
5
6
4 83 10
28
5
13
25
In the second data set,
there are also two
observations to the left
of “5” of the MEDIAN
and two observations to
the right of the MEDIAN.
3 4
Advantages of Using the Median

18. 3 4
Here’s an example:
5
6
4 83 10
5
13
In the second data set,
there are also two
observations to the left
of “5” of the MEDIAN
and two observations to
the right of the MEDIAN.
25 28
Advantages of Using the Median

19. Here’s an example:
6
4 83 10
28
3 4
13
25
Therefore, “5” is the
median for both data
sets because the same
number of observations
that are above BOTH
MEDIANS are also below
BOTH MEDIANS.
Advantages of Using the Median
5
5

20. Here’s an example:
54 83 10
28
3 54 25
Both data sets have the
same median, even
though the mean is “6”
in the first and “13” in
the second data set.
Advantages of Using the Median
6
13

21. In the first data set,
there are two
observations to the left
of the MEDIAN “5”
and two observations to
the right of the MEDIAN.
In the second data set,
there are two
observations to the left
of “5” of the MEDIAN
and two observations to
the right of the MEDIAN.
Therefore, “5” is the
median for both data
sets because the same
number of observations
that are above BOTH
MEDIANS are also below
BOTH MEDIANS.
Here’s an example:
54 83 10
28
3 54 25
6
13
Both data sets have the
same median, even
though the mean is “6”
in the first and “13” in
the second data set.
Advantages of Using the Median

22. Here’s an example:
5
6
4 83 10
28
3 54
13
25
Hence, the median is a
most stable estimate of
the central tendency
because it is based on the
unweighted scores.
Advantages of Using the Median

23. 5
6
4 83 10
Here’s an example:
28
3 54
13
25
Extremely low or high
scores are treated the
same as moderate
scores.
Advantages of Using the Median

24. 5
6
4 8
54
13
3
25
10
Here’s an example:
Extremely low or high
scores are treated the
same as moderate
scores.
3 28
Advantages of Using the Median

25. 28
5
6
4 8
3 54
13
25
Here’s an example:
Extremely low or high
scores are treated the
same as moderate
scores.
3 10
Advantages of Using the Median