Statistics-And-Probability Question 590
Question: The mean of the numbers a, b, 8, 5, 10, is 6 and the variance is 6.80. The which one of the following gives possible values of a and b?
Options:
A) $ a=0,b=7 $
B) $ a=5,b=2 $
C) $ a=1,b=6 $
D) $ a=3,b=4 $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Mean of $ a,b,8,5,10 $ is 6
$ \Rightarrow \frac{a+b+8+5+10}{5}=6\Rightarrow a+b=7 $ ?. (i) Variance of $ a,b,8,5,10 $ is $ 6.80 $
$ \Rightarrow \frac{{{(a-6)}^{2}}+{{(b-6)}^{2}}+{{(8-6)}^{2}}+{{(5-6)}^{2}}+{{(10-6)}^{2}}}{5} $ $ =6.80 $
$ \Rightarrow a^{2}-12a+36+{{(1-a)}^{2}}+21=34 $ [Using eq. (i)]
$ \Rightarrow 2a^{2}-14a+24=0\Rightarrow a^{2}-7a+12=0 $
$ \Rightarrow a=3or\Rightarrow b=4or3 $
$ \therefore $ The possible values of a and b are a=3 and b= 4 or, a = 4 and b = 3
BETA
