If the mean of the data 7, 8, 9, 7, 8, 7, lam | vedclass

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

Question

(D) Given the mean of the data $7, 8, 9, 7, 8, 7, \lambda, 8$ is $8$.Mean $= \frac{7+8+9+7+8+7+\lambda+8}{8} = 8$$\Rightarrow \frac{54+\lambda}{8} = 8

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(D) Given the mean of the data $7, 8, 9, 7, 8, 7, \lambda, 8$ is $8$.Mean $= \frac{7+8+9+7+8+7+\lambda+8}{8} = 8$$\Rightarrow \frac{54+\lambda}{8} = 8$$\Rightarrow 54+\lambda = 64$$\Rightarrow \lambda = 10$Now,the data set is $7, 8, 9, 7, 8, 7, 10, 8$.Variance $(\sigma^2) = \frac{1}{n} \sum (x_i - \bar{x})^2$Variance $= \frac{(7-8)^2 + (8-8)^2 + (9-8)^2 + (7-8)^2 + (8-8)^2 + (7-8)^2 + (10-8)^2 + (8-8)^2}{8}$Variance $= \frac{(-1)^2 + 0^2 + 1^2 + (-1)^2 + 0^2 + (-1)^2 + 2^2 + 0^2}{8}$Variance $= \frac{1 + 0 + 1 + 1 + 0 + 1 + 4 + 0}{8} = \frac{8}{8} = 1$.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$2$	$3$	$x$	$5$	$4$

If the mean of the data $7, 8, 9, 7, 8, 7, \lambda, 8$ is $8$,then the variance of the data is:

Similar Questions

If each of the observations $x_{1}, x_{2}, \ldots, x_{n}$ is increased by $a$,where $a$ is a positive or negative number,show that the variance remains unchanged.

The variance of the variates $112, 116, 120, 125, 132$ about their $A.M.$ is

If the mean of $100$ observations is $50$ and their standard deviation is $5$,then the sum of squares of all observations is

If $X$ is a random variable such that $\sigma(X) = 2.6$, then $\sigma(1 - 4X)$ is equal to:

If the mean of the frequency distribution is $28$,then its variance is $........$.

Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$

Frequency $2$ $3$ $x$ $5$ $4$

Vedclass Test Series

Exam Paper Generator

Online Exam Module