Calculating the median (basic)
25
The Median (conceptual explanation)
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Transcript of Calculating the median (basic)
The Median
(conceptual explanation)
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
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
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
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
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
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
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
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
The Advantage of using the Median
Calculating the Median
Advantages of Using the Median
Here’s an example:
5
6
4 83 10
Here’s an example:
5
6
4 83 10
283 54
13
25
Advantages of Using the Median
Here’s an example:
5
6
4 83 10
283 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
Here’s an example:
5
6
8 10
283 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
Here’s an example:
5
6
43
283 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
Here’s an example:
5
6
4 83 10
283 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
Here’s an example:
5
6
4 83 10
285
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
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
Here’s an example:
6
4 83 10
283 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
Here’s an example:
54 83 10
283 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
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
283 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
Here’s an example:
5
6
4 83 10
283 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
5
6
4 83 10
Here’s an example:
283 54
13
25
Extremely low or high scores are treated the
same as moderate scores.
Advantages of Using the Median
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.
328
Advantages of Using the Median
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
