The variance of the data 2, 4, 6, 8, 10 is | vedclass

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

Question

(C) Step $1$: Calculate the mean $(\bar{x})$ of the data.$\bar{x} = \frac{2 + 4 + 6 + 8 + 10}{5} = \frac{30}{5} = 6$.Step $2$: Calculate the variance

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(C) Step $1$: Calculate the mean $(\bar{x})$ of the data.$\bar{x} = \frac{2 + 4 + 6 + 8 + 10}{5} = \frac{30}{5} = 6$.Step $2$: Calculate the variance using the formula $	ext{Variance} = \frac{1}{n} \sum (x_i - \bar{x})^2$.$	ext{Variance} = \frac{1}{5} \{(2 - 6)^2 + (4 - 6)^2 + (6 - 6)^2 + (8 - 6)^2 + (10 - 6)^2\}$.Step $3$: Simplify the expression.$	ext{Variance} = \frac{1}{5} \{(-4)^2 + (-2)^2 + (0)^2 + (2)^2 + (4)^2\}$.$	ext{Variance} = \frac{1}{5} \{16 + 4 + 0 + 4 + 16\}$.$	ext{Variance} = \frac{1}{5} \{40\} = 8$.Thus,the correct option is $C$.

The variance of the data $2, 4, 6, 8, 10$ is

Similar Questions

Suppose values taken by a variable $x$ are such that $a \le x_i \le b$,where $x_i$ denotes the value of $x$ in the $i^{th}$ case for $i = 1, 2, ..., n$. Then:

If the mean of $10$ observations is $50$ and the sum of the squares of the deviations of the observations from the mean is $250$,then the coefficient of variation of those observations is

The mean of $5$ observations is $15$ and variance is $9$. If two observations having values $-5$ and $13$ are combined with these observations,then what will be the new variance?

The variance of $20$ observations is $5$. If each observation is multiplied by $2$,find the new variance of the resulting observations.

The variance of the observations $8, 12, 13, 15, 22$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module