Question

If $A$ and $B$ are the variances of the $1^{st}$ $n$ even numbers and $1^{st}$ ${}^{\prime }{n}^{\prime }$ odd numbers respectively then

• A. A = B
• B. A > B
• C. A < B
• D. A = B + 1

Answer 1

Answer: (A)

We know that variance of $n$ number which are in A.P. whose first terms is 'a' and common difference $d$ is
${\sigma }^2=\frac{d^2\left(n^2-1\right)}{12}$
$\therefore \mathrm{Var}\left({\sigma }_1\right)=\frac{2^2\left(n^2-1\right)}{12}=\frac{\left(n^2-1\right)}{3}=A$
$\mathrm{Var}\left({\sigma }_2\right)=\frac{2^2\left(n^2-1\right)}{12}-\frac{n^2-1}{3}=B$
$\therefore A=B$