Calculating the Median

Calculating 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



The median is estimated by ordering the observations from lowest to highest.


Birch 28

Bantam 30

Bubba 33

Brenda 35

Bork 37

Benton 40

Bella 42



Counting from the lowest up to the score that divides the data set in half.


Birch 28

Bantam 30

Bubba 33

Brenda 35

Bork 37

Benton 40

Bella 42



Counting from the lowest up to the score that divides the data set in half.


Birch 28

Bantam 30

Bubba 33

Brenda 35

Bork 37

Benton 40

Bella 42



The median represents the 50th percentile of a distribution of observations


Birch 28

Bantam 30

Bubba 33

Brenda 35

Bork 37

Benton 40

Bella 42



The median represents the 50th percentile of a distribution of observations


Birch 28

Bantam 30

Bubba 33

Brenda 35

Bork 37

Benton 40

Bella 42

Therefore the Median of this data set is 35



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.


Birch 28

Bantam 30

Bubba 33

Brenda 35

Bork 37

Benton 40

Bella 42

Boston 44



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.


Birch 28

Bantam 30

Bubba 33

Brenda 35

Bork 37

Benton 40

Bella 42

Boston 44

35+37=72

72/2 Median = 36


Here is the formula

*


Data Set 7654321

The Formula


Data Set 7654321

Here is the Median calculated in Excel using

the Median Function

Calculated Median using Excel function =MEDIAN(N3:N9) 4


Data Set 7654321

L = lower real limit of the interval containing the .5 times the Nth score (.5*7)

Calculated Median using Excel function =MEDIAN(N3:N9) 43.5

Step 1 – calculate “L” by doing the following


Data Set 7654321

L = lower real limit of the interval containing the .5 times the Nth score (.5*7)N = total number of observations in the distribution


7

Step 2 – calculate “N” by counting the number of

observations.


Data Set 7654321

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


7

0.5

Step 3 - .5 represents the 50% of the data.


Data Set 7654321


.5 = percentage as proportion cf = cumulative frequency of the interval containing the .5 times the Nth score


7

0.5

3

Step 4 – calculate “cf” by doing the following


Data Set 7654321



f = frequency of scores in the interval containing the .5 times Nth score


7

0.5

3

1

Step 5 – calculate “f” by doing the following:


Data Set 7654321



f = frequency of scores in the interval containing the .5 times Nth score W = width or size of interval


7

0.5

3

1

1

Step 6 – calculate “f” by determining the value of each interval “1” in this

case.


Data Set 7654321



f = frequency of scores in the interval containing the .5 times Nth score W = width or size of interval


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


Education

Calculating the Median