First slide

Introduction to statistics

Question

The weighted mean of first n natural numbers whose weights are equal is given by

Moderate

A

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

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

$\frac{2 n + 1}{3}$
D

$\frac{(2 n + 1) (n + 1)}{6}$

Solution

Let w be equal weight. Then
Required mean $\begin{array}{l} = \frac{1 \cdot w + 2 \cdot w + 3 \cdot w + \dots + n \cdot w}{w + w + w + \dots + w} \\ = \frac{\frac{n (n + 1)}{2} w}{n w} = \frac{n + 1}{2} \end{array}$

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