Question

If the values $1\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},......\frac{1}{n}$ occur at frequencies $1,2,3,4,5,\dots \dots ..,$ n in a distribution, then the mean is

• A. $1$
• B. $n$
• C. $\frac{1}{n}$
• D. $\frac{2}{n+1}$

Answer 1

The correct option is D $\frac{2}{n+1}$

$Mean=\frac{1.1+\frac{1}{2}.2+\frac{1}{3}.3+\frac{1}{4}.4+\frac{1}{5}.5+...+\frac{1}{n}n}{1+2+3+....+n}$
$=\frac{1+1+1+1+...+1}{\frac{n(n+1)}{2}}=\frac{n}{\frac{n(n+1)}{2}}=\frac{2}{n+1}.$