Statistics And Probability Question 418
Question: The means of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2 and 6, then the other two are
[AMU 1994]
Options:
A) 2 and 9
B) 3 and 8
C) 4 and 7
D) 5 and 6
Show Answer
Answer:
Correct Answer: C
Solution:
Let the two unknown items be x and y, then Mean $ =4\Rightarrow \frac{1+2+6+x+y}{5}=4 $
Þ $ x+y=11 $ …..(i) and variance = 5. 2
Þ $ \frac{1^{2}+2^{2}+6^{2}+x^{2}+y^{2}}{5}-{{(mean)}^{2}}=5.2 $ $ 41+x^{2}+y^{2}=5[5.2+{{(4)}^{2}}] $ $ 41+x^{2}+y^{2}=106 $ $ x^{2}+y^{2}=65 $ …..(ii) Solving (i) and (ii) for $ x $ and y, we get $ x=4,y=7 $ or $ x=7,y=4 $ .
BETA
