Q. 103.7( 3 Votes )

The following distribution shows the number of out door patients in 64 hospitals as follows. If the mean is 18, find the missing frequencies f1 and f2 :


Answer :

This is a grouped frequency distribution.


To find f1 and f2, we’ll need to find mean of the following distribution by direct method and equate it to the given mean of the following distribution, 18.


This given data is exclusive, grouped frequency distribution.


So, let’s construct a table finding midpoints and stating frequencies.



So now, we have


xifi = 608 + 16f1 + 20f2


And fi = 35 + f1 + f2


Mean is given by



[given, mean = 18 and using the values from the table]


18 × (35 + f1 + f2) = 608 + 16f1 + 20f2


630 + 18f1 + 18f2 = 608 + 16f1 + 20f2


20f2 – 18f2 + 16f1 – 18f1 = 630 – 608


2f2 – 2f1 = 22


2(f2 – f1) = 22


f2 – f1 = 11 …(i)


Since, there are 64 hospitals.


Number of hospitals = 64


Frequency = 64


fi = 64


35 + f1 + f2 = 64


f1 + f2 = 64 – 35


f1 + f2 = 29 …(ii)


Solving equations (i) and (ii), we get


f2 – f1 = 11


f2 + f1 = 29


2f2 + 0 = 40


2f2 = 40



f2 = 20


Putting f2 = 20 in equation (ii), we get


f1 + 20 = 29


f1 = 29 – 20


f1 = 9


Thus, the missing frequencies are f1 = 9 and f2 = 20.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses