First slide

Introduction to statistics

Question

$The mean of n items is \bar{X} .If the first term, second term, third term \dots . is increased by$ $1,2,3… and so on. Then new mean is$

Moderate

A

$\bar{X} + \frac{n}{2}$
B

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

$\bar{X} + n$
D

$\bar{X} + \frac{n - 1}{2}$

Solution

$\begin{array}{l} W e h a v e a_{1} + 1, a_{2} + 2, a_{3} + 3, \dots . a_{n} + n \\ ∴ Mean = \frac{(a_{1} + a_{2} + \dots . + a_{n}) + (1 + 2 + + \dots n)}{n} \\ = \bar{X} + \frac{1 + 2 + 3 + \dots . + n}{n} \\ = \bar{X} + \frac{n (n + 1)}{2 n} \end{array}$

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