Answer :

Given: The mean and standard deviation of a set of n1 observations are and s1, respectively while the mean and standard deviation of another set of n2 observations are and s2, respectively


To show: the standard deviation of the combined set of (n1 + n2) observations is given by


As per given criteria,


For first set


Let xi where i=1, 2, 3,4 , …, n1


For second set


And yj where j=1, 2, 3, 4, …, n2


And the means are



Now mean of the combined series is given by



And the corresponding square of standard deviation is



Therefore, square of standard deviation becomes,



Now,




But the algebraic sum of the deviation of values of first series from their mean is zero.



Also,



But



Substituting value from equation (i), we get







Substituting this value in equation (iii), we get




Similarly, we have




But the algebraic sum of the deviation of values of second series from their mean is zero.



Also,



But


Substituting value from equation (i), we get







Substituting this value in equation (v), we get




Substituting equation (iv) and (vi) in equation (ii), we get









So the combined standard deviation



Hence proved


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
RELATED QUESTIONS :

The sum and the sRS Aggarwal - Mathematics

If x1,RD Sharma - Mathematics

The mean and variRS Aggarwal - Mathematics

If the sum of theRD Sharma - Mathematics

The mean and stanRS Aggarwal - Mathematics

Following are theRD Sharma - Mathematics

The mean and variRS Aggarwal - Mathematics

The following resRS Aggarwal - Mathematics

Coefficient of vaRS Aggarwal - Mathematics

The following resRS Aggarwal - Mathematics