NDA Math Statistics

Let x and y be the remaining two observations
Then X = mean =4.4
⇒

1+2+6+x+y

5

=4.4
⇒9+x+y=22
⇒x+y=22−9=13....(i)
and variance =8.24
⇒

1

5

(41+x2+y2)−19.36=8.24
⇒41+x2+y2=27.60×5=138
⇒x2+y2=138−41=97
Now, (x+y)2+(x–y)2=2(x2+y2)
⇒169+(x−y)2=2(97)
⇒(x−y)2=194−169=25
⇒x−y=±5....(ii)
from (i) and (ii), we get, if x−y=5
Then,2x=18⇒x=9
and 2y=8⇒y=4
If x−y=−5∴2x=8⇒x=4
and 2y=18⇒y=9
Hence, the remaining two observations are 9 and 4
or 4 and 9