If the mean of the series x_1, x_2, ......., | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given that the mean of $x_1, x_2, ......., x_n$ is $\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$.Let the new series be $y_i = x_i + 2i$ for $i = 1, 2,

Vedclass · Accepted Answer

$\bar{x} + n + 1$

Vedclass · Answer

(B) Given that the mean of $x_1, x_2, ......., x_n$ is $\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$.Let the new series be $y_i = x_i + 2i$ for $i = 1, 2, ......., n$.The mean of the new series is $\bar{y} = \frac{1}{n} \sum_{i=1}^{n} (x_i + 2i)$.$\bar{y} = \frac{1}{n} (\sum_{i=1}^{n} x_i + 2 \sum_{i=1}^{n} i)$.Using the sum of first $n$ natural numbers formula $\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$:$\bar{y} = \frac{\sum x_i}{n} + \frac{2}{n} 	imes \frac{n(n+1)}{2}$.$\bar{y} = \bar{x} + (n+1)$.

If the mean of the series $x_1, x_2, ......., x_n$ is $\bar{x}$,then what will be the mean of the series $x_i + 2i, (i = 1, 2, ......., n)$?

Similar Questions

If the mean of the numbers $27, 31, 89, 107, 156$ is $82$,what is the mean of the numbers $130, 126, 68, 50, 1$?

Which of the following,in the case of discrete data,is not equal to the median?

$A$ student scores $75\%, 80\%,$ and $85\%$ in three subjects. If the marks of a fourth subject are added,what is the minimum possible average percentage?

The mean weight per student in a group of seven students is $55 \ kg$. If the individual weights of $6$ students are $52, 58, 55, 53, 56$ and $54 \ kg$,then the weight of the seventh student is.....$kg$.

If the values $1, \frac{1}{2}, \frac{1}{3}, \dots, \frac{1}{n}$ have frequencies $1, 2, 3, \dots, n$ respectively,what is their mean?

Vedclass Test Series

Exam Paper Generator

Online Exam Module