If mathop sum limits_{i = 1}^9 left( {{x_i} - | vedclass

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

Question

Given $\sum\limits_{i = 1}^9 {\left( {{x_i} - 5} \right)}  = 9 \Rightarrow \sum\limits_{i = 1}^9 {{x_i} = 54\,\,\,.....\left( i \right)} $

Vedclass · Accepted Answer

$2$

Vedclass · Answer

Given $\sum\limits_{i = 1}^9 {\left( {{x_i} - 5} \right)}  = 9 \Rightarrow \sum\limits_{i = 1}^9 {{x_i} = 54\,\,\,.....\left( i \right)} $

Also, $\sum\limits_{i = 1}^9 {{{\left( {{x_i} - 5} \right)}^2}}  = 45$

$\sum\limits_{i = 1}^9 {x_i^2}  - 10\sum\limits_{i = 1}^9 {{x_i} + 9\left( {25} \right)}  = 45\,\,\,\,\,...\left( {ii} \right)$

From $(i)$ and $(ii)$ we get,

$\sum\limits_{i = 1}^9 {x_i^2}  = 360$

Since, variance $ = \frac{{\sum {x_i^2} }}{9} - {\left( {\frac{{\sum {{x_i}} }}{9}} \right)^2}$

$ = \frac{{360}}{9} - {\left( {\frac{{54}}{9}} \right)^2} = 40 - 36 = 4$

Standared deviation $ = \sqrt {Variance}  = 2$

class	0-10	10-20	20-30	30-40
Freq	1	3	4	2

If $\mathop \sum \limits_{i = 1}^9 \left( {{x_i} - 5} \right) = 9$ and $\mathop \sum \limits_{i = 1}^9 {\left( {{x_i} - 5} \right)^2} = 45,$ then the standard deviation of the $9$ items ${x_1},{x_2},\;.\;.\;.\;,{x_9}$ is :

Similar Questions

The mean and variance of the marks obtained by the students in a test are $10$ and $4$ respectively. Later, the marks of one of the students is increased from $8$ to $12$ . If the new mean of the marks is $10.2.$ then their new variance is equal to :

What is the standard deviation of the following series

class

0-10

10-20

20-30

30-40

Freq

1

3

4

2

If the standard deviation of the numbers $-1, 0, 1, k$ is $\sqrt 5$ where $k > 0,$ then $k$ is equal to

The variance of the first $n$ natural numbers is

Statement $1$ : The variance of first $n$ odd natural numbers is $\frac{{{n^2} - 1}}{3}$
Statement $2$ : The sum of first $n$ odd natural number is $n^2$ and the sum of square of first $n$ odd natural numbers is $\frac{{n\left( {4{n^2} + 1} \right)}}{3}$