Question

Let the six numbers $a_1, a_2, a_3, a_4, a_5, a_6$, be in AP and $a_1+a_3=10$ If the mean of these six numbers is $\frac{19}{2}$ and their variance is $\sigma^2$, then $8 \sigma^2$ is equal to :

• A. 105
• B. 210
• C. 200
• D. 220

Answer 1

Answer: (B)

210

Answer 2

The correct answer is (C) : 210
a1​+a3​=10=a1​+d⇒5
a1​+a2​+a3​+a4​+a5​+a6​=57
⇒26​[a1​+a6​]=57
⇒a1​+a6​=19
⇒2a1​+5d=19 and a1​+d=5
⇒a1​=2,d=3
Numbers : 2,5,8,11,14,17
Variance =σ2= mean of squares-square of mean
=622+52+82+(11)2+(14)2+(17)2​−(219​)2
=6699​−4361​=4105​
8σ2=210