(B) Given,$\sum x = 170$ and $\sum x^2 = 2830$ for $n = 15$. Replacing the wrong observation $20$ with the correct observation $30$: Corrected $\sum x

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(B) Given,$\sum x = 170$ and $\sum x^2 = 2830$ for $n = 15$. Replacing the wrong observation $20$ with the correct observation $30$: Corrected $\sum x = 170 - 20 + 30 = 180$. Corrected $\sum x^2 = 2830 - (20)^2 + (30)^2 = 2830 - 400 + 900 = 3330$. We know that,$\text{Variance} = \frac{\sum x^2}{n} - \left(\frac{\sum x}{n}\right)^2$. Substituting the values: $\text{Variance} = \frac{3330}{15} - \left(\frac{180}{15}\right)^2$. $\text{Variance} = 222 - (12)^2$. $\text{Variance} = 222 - 144 = 78$.

Class 11 Mathematics Statistics Variance and Standard Deviation

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For a data consisting of $15$ observations $x_i$,$i=1, 2, 3, \ldots, 15$,the following results are obtained: $\sum_{i=1}^{15} x_i = 170$ and $\sum_{i=1}^{15} x_i^2 = 2830$. If one of the observations,namely $20$,was found to be wrong and was replaced by its correct value $30$,then the corrected variance is:

AP EAMCET 2019 All AP EAMCET

A
$80$
B
$78$
C
$76$
D
$75$

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Statistics

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Variance and Standard Deviation

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AP EAMCET 2019 Paper All AP EAMCET years →

Two plants $A$ and $B$ of a factory show the following results regarding the number of workers and the wages paid to them:
\text{Parameter} \text{Plant } $A$ \text{ and } $B$ \text{ Data}
\text{No. of workers} $A: 500, B: 6000$
\text{Average monthly wages} $A: Rs. 2500, B: Rs. 2500$
\text{Variance of distribution of wages} $A: 81, B: 100$

In which plant,$A$ or $B$,is there greater variability in individual wages?

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Let the observations $x_{i} (1 \leq i \leq 10)$ satisfy the equations $\sum_{i=1}^{10}(x_{i}-5)=10$ and $\sum_{i=1}^{10}(x_{i}-5)^{2}=40$. If $\mu$ and $\lambda$ are the mean and the variance of the observations $x_{1}-3, x_{2}-3, \dots, x_{10}-3$,then the ordered pair $(\mu, \lambda)$ is equal to:

DifficultJEE MAIN 2020

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Find the variance of the following frequency distribution.

$Class$ $0-2$ $2-4$ $4-6$ $6-8$ $8-10$ $10-12$

$f_i$ $2$ $7$ $12$ $19$ $9$ $1$

$Class$	$0-2$	$2-4$	$4-6$	$6-8$	$8-10$	$10-12$
$f_i$	$2$	$7$	$12$	$19$	$9$	$1$

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The arithmetic mean of the observations $10, 8, 5, a, b$ is $6$ and their variance is $6.8$. Then $ab$ is equal to:

EasyAP EAMCET 2015

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The frequency distribution is given below:
$\begin{array}{|l|l|l|l|l|l|l|} \hline X & 2 & 3 & 4 & 5 & 6 & 7 \\ f & 4 & 9 & 16 & 14 & 11 & 6 \\ \hline \end{array}$
Find the standard deviation.

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\text{Parameter}	\text{Plant } $A$ \text{ and } $B$ \text{ Data}
\text{No. of workers}	$A: 500, B: 6000$
\text{Average monthly wages}	$A: Rs. 2500, B: Rs. 2500$
\text{Variance of distribution of wages}	$A: 81, B: 100$

Similar Questions

Let the observations $x_{i} (1 \leq i \leq 10)$ satisfy the equations $\sum_{i=1}^{10}(x_{i}-5)=10$ and $\sum_{i=1}^{10}(x_{i}-5)^{2}=40$. If $\mu$ and $\lambda$ are the mean and the variance of the observations $x_{1}-3, x_{2}-3, \dots, x_{10}-3$,then the ordered pair $(\mu, \lambda)$ is equal to:

Find the variance of the following frequency distribution. $Class$ $0-2$ $2-4$ $4-6$ $6-8$ $8-10$ $10-12$ $f_i$ $2$ $7$ $12$ $19$ $9$ $1$

The arithmetic mean of the observations $10, 8, 5, a, b$ is $6$ and their variance is $6.8$. Then $ab$ is equal to:

The frequency distribution is given below:$\begin{array}{|l|l|l|l|l|l|l|} \hline X & 2 & 3 & 4 & 5 & 6 & 7 \\ f & 4 & 9 & 16 & 14 & 11 & 6 \\ \hline \end{array}$Find the standard deviation.

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Find the variance of the following frequency distribution.

$Class$ $0-2$ $2-4$ $4-6$ $6-8$ $8-10$ $10-12$

$f_i$ $2$ $7$ $12$ $19$ $9$ $1$

The frequency distribution is given below:
$\begin{array}{|l|l|l|l|l|l|l|} \hline X & 2 & 3 & 4 & 5 & 6 & 7 \\ f & 4 & 9 & 16 & 14 & 11 & 6 \\ \hline \end{array}$
Find the standard deviation.