UPSC NDA Math Model Paper 8

Let, two sets of data containing n1 and n2 observations with means X1 and X2 and variances S12 and S22
Given data: n1=100 and n2=200
X1=30 and X2=60
S12=4 and S22=9
Combined mean =X=

n1X1+n2X2

n1+n2

=

100×30+200×60

100+200

=

3000+12000

300

=50
Now, Combined variance
=

100[4+(30−50)2]+200[9+(60−50)2

100+200

=

100×404+200×109

300

=

404+218

3

=

622

3

=207.3