Given a table showing grouped data and the frequency of each class, find the median Q2

Step 1: Add a cumulative frequency column to the table

Step2: Use the formula n/2 (where n is the final total in the cumulative frequency column) to find the class the median, Q₂, is in.

Let n/2= a, so that Q₂  is in the class d<=y<e

because in the cumulative frequency column , b<a<c where b is the cumulative frequency of the class before d<=y<e and c the cumulative frequency of the class after

 

Step 3: Find the lower and upper class boundaries of the class that Q₂ is in.

Q₂ is the class d<=y<e.

Let class before d<=y<e  with cumulative frequency b be f<=y<g

Let the class after d<=y<e  with cumulative frequency c be  h<=y<i

Lower class boundary= l = (g+d)/2

Upper class boundary = u= (e+h)/2

 

 

Step 4: Interpolate to find Q₂ 

Using the following formula, the value of Q₂ can be found:

(Q₂-l) / (u-l) = (n/2-b) / (c-b)

 

We know from step 2

Q₂  is in the class d<=y<e

b<a<c with n/2=a

b= the cumulative frequency of the class before the class Q₂  is in

c= cumulative frequency of the class after the class Q₂  is in

 

We know from step 3

 l=lower class boundary of the class d<=y<e

u= upper class boundary of the class d<=y<e