The variance of the following data is: x_i | vedclass

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

Question

(C) To calculate the variance,we use the assumed mean method where $a = 18$. The calculations are as follows:   $x_i$ $f_i$ $d_i = x_i - 18$ $f_i d_i$

Vedclass · Accepted Answer

$43.4$

Vedclass · Answer

(C) To calculate the variance,we use the assumed mean method where $a = 18$. The calculations are as follows:   $x_i$ $f_i$ $d_i = x_i - 18$ $f_i d_i$ $f_i d_i^2$   $6$ $2$ $-12$ $-24$ $288$   $10$ $4$ $-8$ $-32$ $256$   $14$ $7$ $-4$ $-28$ $112$   $18$ $12$ $0$ $0$ $0$   $24$ $8$ $6$ $48$ $288$   $28$ $4$ $10$ $40$ $400$   $30$ $3$ $12$ $36$ $432$   Total $N = 40$ - $\sum f_i d_i = 40$ $\sum f_i d_i^2 = 1776$   The formula for variance is $\sigma^2 = \frac{\sum f_i d_i^2}{N} - \left(\frac{\sum f_i d_i}{N}\right)^2$. Substituting the values: $\sigma^2 = \frac{1776}{40} - \left(\frac{40}{40}\right)^2$ $\sigma^2 = 44.4 - (1)^2$ $\sigma^2 = 44.4 - 1 = 43.4$.

The variance of the following data is:

$x_i$ $6$ $10$ $14$ $18$ $24$ $28$ $30$

$f_i$ $2$ $4$ $7$ $12$ $8$ $4$ $3$

Similar Questions

If each of given $n$ observations is multiplied by a certain positive number $k$,then for the new set of observations -

Determine the mean and standard deviation of the first $n$ terms of an $A.P.$ whose first term is $a$ and common difference is $d$.

$A$ student scored the following marks in five tests: $45, 54, 41, 57, 43$. His score is not known for the sixth test. If the mean score is $48$ in the six tests,then the standard deviation of the marks in the six tests is:

The variance of $50$ observations is $7$. Suppose that each observation in this data is multiplied by $6$ and then $5$ is subtracted from it. Then the variance of that new data is

If the mean and variance of the data $65, 68, 58, 44, 48, 45, 60, \alpha, \beta, 60$ where $\alpha > \beta$ are $56$ and $66.2$ respectively,then $\alpha^2 + \beta^2$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module

The variance of the following data is: $x_i$ $6$ $10$ $14$ $18$ $24$ $28$ $30$ $f_i$ $2$ $4$ $7$ $12$ $8$ $4$ $3$