Calculating the Median

1. Calculating the Median
(conceptual explanation)
Calculating the Median

2. Calculating the Median
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. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. Here is the formula
*
Calculating the Median

11. Data Set
7
6
5
4
3
2
1
The Formula
Calculating the Median

12. Data Set
7
6
5
4
3
2
1
Here is the Median
calculated in Excel using
the Median Function
Calculated Median using Excel function =MEDIAN(N3:N9) 4
Calculating the Median

13. Data Set
7
6
5
4
3
2
1
L = lower real limit of the interval containing the .5 times the Nth score (.5*7)
Calculated Median using Excel function =MEDIAN(N3:N9) 4
3.5
Step 1 – calculate “L” by
doing the following
Calculating the Median

14. Data Set
7
6
5
4
3
2
1
L = lower real limit of the interval containing the .5 times the Nth score (.5*7)
N = total number of observations in the distribution
Calculated Median using Excel function =MEDIAN(N3:N9) 4
3.5
7
Step 2 – calculate “N” by
counting the number of
observations.
Calculating the Median

15. Data Set
7
6
5
4
3
2
1
L = lower real limit of the interval containing the .5 times the Nth score (.5*7)
N = total number of observations in the distribution
.5 = percentage as proportion
Calculated Median using Excel function =MEDIAN(N3:N9) 4
3.5
7
0.5
Step 3 - .5 represents the
50% of the data.
Calculating the Median

16. Data Set
7
6
5
4
3
2
1
L = lower real limit of the interval containing the .5 times the Nth score (.5*7)
N = total number of observations in the distribution
.5 = percentage as proportion
cf = cumulative frequency of the interval containing the .5 times the Nth score
Calculated Median using Excel function =MEDIAN(N3:N9) 4
3.5
7
0.5
3
Step 4 – calculate “cf” by
doing the following
Calculating the Median

17. Data Set
7
6
5
4
3
2
1
L = lower real limit of the interval containing the .5 times the Nth score (.5*7)
N = total number of observations in the distribution
.5 = percentage as proportion
cf = cumulative frequency of the interval containing the .5 times the Nth score
f = frequency of scores in the interval containing the .5 times Nth score
Calculated Median using Excel function =MEDIAN(N3:N9) 4
3.5
7
0.5
3
1
Step 5 – calculate “f” by
doing the following:
Calculating the Median

18. Data Set
7
6
5
4
3
2
1
L = lower real limit of the interval containing the .5 times the Nth score (.5*7)
N = total number of observations in the distribution
.5 = percentage as proportion
cf = cumulative frequency of the interval containing the .5 times the Nth score
f = frequency of scores in the interval containing the .5 times Nth score
W = width or size of interval
Calculated Median using Excel function =MEDIAN(N3:N9) 4
3.5
7
0.5
3
1
1
Step 6 – calculate “f” by
determining the value of
each interval “1” in this
case.
Calculating the Median

19. Data Set
7
6
5
4
3
2
1
L = lower real limit of the interval containing the .5 times the Nth score (.5*7)
N = total number of observations in the distribution
.5 = percentage as proportion
cf = cumulative frequency of the interval containing the .5 times the Nth score
f = frequency of scores in the interval containing the .5 times Nth score
W = width or size of interval
Calculated Median using Excel function =MEDIAN(N3:N9) 4
3.5
7
0.5
3
1
1
Calculated Median using the formula 4
Now you have all of the
terms you need to
calculate the Median
Calculating the Median