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 Qis 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 Q

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

Qis in the class d<=y<e

b<a<c with n/2=a

b= the cumulative frequency of the class before the class Qis in

c= cumulative frequency of the class after the class Qis 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

Answered by Lesedi S. Maths tutor

9061 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Use integration to find I = ∫ xsin3x dx


Expand and simplify (n + 2)^3 − n^3.


Solve simultaneously: x + y + 3 = 0 and y = 2x^2 +3x - 1


Consider the functions f and g where f (x) = 3x − 5 and g (x) = x − 2 . (a) Find the inverse function, f^−1 . (b) Given that g^−1(x) = x + 2 , find (g^−1 o f )(x) . (c) Given also that (f^−1 o g)(x) = (x + 3)/3 , solve (f^−1 o g)(x) = (g^−1 o f)(x)


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences