First slide

Introduction to statistics

Question

The mean of variable $1, 2, \dots n$ whose corresponding frequencies are $1, 2, \dots n$ is given by

Easy

A

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

$\frac{2 n + 1}{6}$
C

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

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

Solution

Mean $= \frac{1.1 + 2.2 + \dots n . n}{1 + 2 \dots + n}$
$\begin{array}{l} = \frac{\sum_{K = 1}^{n} k^{2}}{\sum_{K = 1}^{n} k} = \frac{n (n + 1) (2 n + 1)}{6} \times \frac{2}{n (n + 1)} \\ = \frac{2 n + 1}{3} \end{array}$

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