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,$\bar x_{new} = \frac{1}{n} \sum_{i=1}^{n} x_i - \frac{n\lambda}{n} = \bar x - \lambda$.

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 $\mu$ is the mean of a distribution $(y_i, f_i)$,then $\sum f_i(y_i - \mu) = $

What is the value of $x$ if the mean of $8, 6, 7, 5, x,$ and $4$ is $7$?

Which of the following averages is most affected by extreme observations?

The average age of a teacher and three students is $20$ years. If all the students are of the same age and the difference between the teacher's age and the age of one of the students is $20$ years,find the teacher's age in years.

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