The mean of a set of numbers is bar x. If lam | vedclass

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

Question

(D) Let the set of $n$ numbers be $x_1, x_2, ..., x_n$. The mean is given by $\bar x = \frac{1}{n} \sum_{i=1}^{n} x_i$. If $\lambda$ is subtracted fro

Vedclass · Accepted Answer

$\bar x - \lambda$

Vedclass · Answer

(D) Let the set of $n$ numbers be $x_1, x_2, ..., x_n$. The mean is given by $\bar x = \frac{1}{n} \sum_{i=1}^{n} x_i$. If $\lambda$ is subtracted from each number,the new set becomes $(x_1 - \lambda), (x_2 - \lambda), ..., (x_n - \lambda)$. The new mean $\bar x_{new}$ is $\frac{1}{n} \sum_{i=1}^{n} (x_i - \lambda)$. This simplifies to $\frac{1}{n} (\sum_{i=1}^{n} x_i - \sum_{i=1}^{n} \lambda) = \frac{1}{n} (\sum_{i=1}^{n} x_i - n\lambda)$. Thus,$\bar x_{new} = \frac{1}{n} \sum_{i=1}^{n} x_i - \frac{n\lambda}{n} = \bar x - \lambda$.

$x_i$	$3$	$6$	$9$	$12$
$f_i$	$1$	$2$	$3$	$4$

The mean of a set of numbers is $\bar x$. If $\lambda$ is subtracted from each number,what will be the mean of the new set?

Similar Questions

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

In a data,if the number $i$ is repeated $i$ times for $i=1, 2, \ldots, n$,then the mean of the data is

Find the mean of the following frequency distribution:

$x_i$ $3$ $6$ $9$ $12$

$f_i$ $1$ $2$ $3$ $4$

If the mean of the first $n$ natural numbers is equal to $\frac{n + 7}{3}$,then what is the value of $n$?

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