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, ….,n in a distribution, then the mean is

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

Answer 1

Answer: (D)

$\frac{2}{n + 1}$

Answer 2

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

$= \frac{1 + 1 + 1 + 1 + ..... + 1}{\frac{n(n + 1)}{2}} = \frac{n}{\frac{n(n + 1)}{2}} = \frac{2}{n + 1}$.