(B) Given $n = 15, \Sigma x = 170, \Sigma x^2 = 2830$.When an incorrect observation $20$ is replaced by the correct value $30$:Correct sum of observat

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(B) Given $n = 15, \Sigma x = 170, \Sigma x^2 = 2830$.When an incorrect observation $20$ is replaced by the correct value $30$:Correct sum of observations $= 170 - 20 + 30 = 180$.Correct sum of squares of observations $= 2830 - 20^2 + 30^2 = 2830 - 400 + 900 = 3330$.Correct mean $\bar{x} = \frac{180}{15} = 12$.Correct variance $\sigma^2 = \frac{\Sigma x^2}{n} - (\bar{x})^2 = \frac{3330}{15} - (12)^2$.$\sigma^2 = 222 - 144 = 78$.

Class 11 Mathematics Statistics Variance and Standard Deviation

Difficult

In an experiment with $15$ observations of $x$,the results $\Sigma x^2 = 2830$ and $\Sigma x = 170$ are obtained. If one observation $20$ is found to be incorrect and is replaced by the correct observation $30$,what is the correct variance?

A
$8.33$
B
$78$
C
$188.66$
D
$177.33$

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Statistics

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Variance and Standard Deviation

Let $X = \{x \in \mathbb{N} : 1 \le x \le 19\}$ and for some $a, b \in \mathbb{R}$, $Y = \{ax + b : x \in X\}$. If the mean and variance of the elements of $Y$ are $30$ and $750$, respectively, then the sum of all possible values of $b$ is

DifficultJEE MAIN 2026

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For a frequency distribution,the standard deviation is computed by applying the formula:

Medium

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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

EasyTS EAMCET 2018

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$A$ data consists of $20$ observations $x_1, x_2, ..., x_{20}$. If $\sum_{i=1}^{20} (x_i + 5)^2 = 2500$ and $\sum_{i=1}^{20} (x_i - 5)^2 = 100$, then the ratio of mean to standard deviation of this data is:

DifficultJEE MAIN 2026

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If the variance of the first $n$ natural numbers is $10$ and the variance of the first $m$ even natural numbers is $16$,then $n: m=$

MediumAP EAMCET 2025

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In an experiment with $15$ observations of $x$,the results $\Sigma x^2 = 2830$ and $\Sigma x = 170$ are obtained. If one observation $20$ is found to be incorrect and is replaced by the correct observation $30$,what is the correct variance?

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Let $X = \{x \in \mathbb{N} : 1 \le x \le 19\}$ and for some $a, b \in \mathbb{R}$, $Y = \{ax + b : x \in X\}$. If the mean and variance of the elements of $Y$ are $30$ and $750$, respectively, then the sum of all possible values of $b$ is

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