What is the Median?

1. Median
(conceptual explanation)
What is the Median?

2. Median
What is the Median?

3. Median
Here is a technical definition of the “median”:
What is the Median?

4. Median
Here is a technical definition of the “median”:
“The median represents the observation that
divides the sample into halves regardless of the
weight of the observations”.
What is the Median?

5. Median
Here is a technical definition of the “median”:
“The median represents the observation that
divides the sample into halves regardless of the
weight of the observations”.
What does this
phrase mean?
What is the Median?

6. “The median represents the observation that divides the sample
into halves regardless of the weight of the observations”.
Here’s an example:
What is the Median?

7. “The median represents the observation that divides the sample
into halves regardless of the weight of the observations”.
Here’s an example:
5
6
4 83 10
What is the Median?

8. “The median represents the observation that divides the sample
into halves regardless of the weight of the observations”.
28
54 8
3 54
13
3
25
10
Here’s an example:
6
What is the Median?

9. “The median represents the observation that divides the sample
into halves regardless of the weight of the observations”.
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.
What is the Median?

10. “The median represents the observation that divides the sample
into halves regardless of the weight of the observations”.
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
What is the Median?

11. “The median represents the observation that divides the sample
into halves regardless of the weight of the observations”.
Here’s an example:
5
6
43
28
3 54
13
25
8 10
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.
What is the Median?

12. “The median represents the observation that divides the sample
into halves regardless of the weight of the observations”.
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.
What is the Median?

13. “The median represents the observation that divides the sample
into halves regardless of the weight of the observations”.
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
What is the Median?

14. “The median represents the observation that divides the sample
into halves regardless of the weight of the observations”.
Here’s an example:
5
6
4 83 10
3 54
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.
2825
What is the Median?

15. “The median represents the observation that divides the sample
into halves regardless of the weight of the observations”.
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.
Here’s an example:
5
6
4 83 10
28
3 54
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.
What is the Median?

16. “The median represents the observation that divides the sample
into halves regardless of the weight of the observations”.
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.
Here’s an example:
5
6
4 83 10
28
3 54
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.
What is the Median?

17. “The median represents the observation that divides the sample
into halves regardless of the weight of the observations”.
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:
5
6
4 83 10
28
3 54
13
25
Both data sets have the
same median, even
though the mean is “6”
in the first and “13” in
the second data set.
What is the Median?

18. “The median represents the observation that divides the sample
into halves regardless of the weight of the observations”.
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
Both data sets have the
same median, even
though the mean is “6”
in the first and “13” in
the second data set.
6
13
What is the Median?

19. “The median represents the observation that divides the sample
into halves regardless of the weight of the observations”.
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.
What is the Median?

20. “The median represents the observation that divides the sample
into halves regardless of the weight of the observations”.
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.
What is the Median?

21. “The median represents the observation that divides the sample
into halves regardless of the weight of the observations”.
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
What is the Median?

22. “The median represents the observation that divides the sample
into halves regardless of the weight of the observations”.
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
What is the Median?

23. Note
Addition or removal of extreme scores changes
the median very little.
What is the Median?

24. Note
In contrast, the mean is a less stable estimate of
the central tendency because it is based on
weighted scores.
What is the Median?

25. Note
In contrast, the mean is a less stable estimate of
the central tendency because it is based on
weighted scores.
The Mean
Weighted Scores
What is the Median?

26. Note
Where as the Median does not weight the
scores and therefore is not influenced by
extreme scores.
What is the Median?

27. Note
Where as the Median does not weight the
scores and therefore is not influenced by
extreme scores.
The Median
Unweighted Scores
Not as influenced by extreme
scores
What is the Median?

28. Note
Where as the Median does not weight the
scores and therefore is not influenced by
extreme scores.
The Median
Unweighted Scores
Because they all have the same weight
What is the Median?