Let μ be mean and sigma be standard deviation of distribution Xᵢ 0 1 2 3 4 5 fᵢ k+2 2k K^

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13.Statistics

hard

Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution

$X_i$ $0$ $1$ $2$ $3$ $4$ $5$

$f_i$ $k+2$ $2k$ $K^{2}-1$ $K^{2}-1$ $K^{2}-1$ $k-3$

where $\sum f_i=62$. if $[x]$ denotes the greatest integer $\leq x$, then $\left[\mu^2+\sigma^2\right]$ is equal $.........$.

$8$

$7$

$6$

$9$

(JEE MAIN-2023)

Solution

$\sum f _{ i }=62$

$3 k ^2+16 k -12 k -64=0$

$k =\text { or }-\frac{16}{3}(\text { rejected) }$

$\mu=\frac{\sum f _{ i } x _{ i }}{\sum f _{ i }}$

$\mu=\frac{8+2(15)+3(15)+4(17)+5}{62}=\frac{156}{62}$

$\sigma^2=\sum f _{ i } x _{ i }^2-\left(\sum f _{ i } x _{ i }\right)^2$

$=\frac{8 \times 1^2+15 \times 13+17 \times 16+25}{62}-\left(\frac{156}{62}\right)^2$

$\sigma^2=\frac{500}{62}-\left(\frac{156}{62}\right)^2$

$\sigma^2+\mu^2=\frac{500}{62}$

${\left[\sigma^2+\mu^2\right]=8}$

Standard 11

Mathematics

The frequency distribution:

$\begin{array}{|l|l|l|l|l|l|l|} \hline X & A & 2 A & 3 A & 4 A & 5 A & 6 A \\ \hline f & 2 & 1 & 1 & 1 & 1 & 1 \\ \hline \end{array}$

where $A$ is a positive integer, has a variance of $160 .$ Determine the value of $A$.

medium

Mean and standard deviation of 100 observations were found to be 40 and 10 , respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively, find the correct standard deviation.

hard

If the mean of the frequency distribution

Class: $0-10$ $10-20$ $20-30$ $30-40$ $40-50$

Frequency $2$ $3$ $x$ $5$ $4$

is $28$ , then its variance is $……..$.

hard

(JEE MAIN-2023)

The mean and standard deviation of $20$ observations are found to be $10$ and $2$ respectively. On rechecking, it was found that an observation $8$ was incorrect. Calculate the correct mean and standard deviation in each of the following cases:

If wrong item is omitted.

hard

The sum of squares of deviations for $10$ observations taken from mean $50$ is $250$. The co-efficient of variation is…..$\%$

easy

$X_i$	$0$	$1$	$2$	$3$	$4$	$5$
$f_i$	$k+2$	$2k$	$K^{2}-1$	$K^{2}-1$	$K^{2}-1$	$k-3$

Class:	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$2$	$3$	$x$	$5$	$4$

Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution $X_i$ $0$ $1$ $2$ $3$ $4$ $5$ $f_i$ $k+2$ $2k$ $K^{2}-1$ $K^{2}-1$ $K^{2}-1$ $k-3$ where $\sum f_i=62$. if $[x]$ denotes the greatest integer $\leq x$, then $\left[\mu^2+\sigma^2\right]$ is equal $.........$.

Solution

Similar Questions

The frequency distribution: $\begin{array}{|l|l|l|l|l|l|l|} \hline X & A & 2 A & 3 A & 4 A & 5 A & 6 A \\ \hline f & 2 & 1 & 1 & 1 & 1 & 1 \\ \hline \end{array}$ where $A$ is a positive integer, has a variance of $160 .$ Determine the value of $A$.

Mean and standard deviation of 100 observations were found to be 40 and 10 , respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively, find the correct standard deviation.

If the mean of the frequency distribution Class: $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ Frequency $2$ $3$ $x$ $5$ $4$ is $28$ , then its variance is $……..$.

The mean and standard deviation of $20$ observations are found to be $10$ and $2$ respectively. On rechecking, it was found that an observation $8$ was incorrect. Calculate the correct mean and standard deviation in each of the following cases: If wrong item is omitted.

The sum of squares of deviations for $10$ observations taken from mean $50$ is $250$. The co-efficient of variation is…..$\%$

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Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution

$X_i$ $0$ $1$ $2$ $3$ $4$ $5$

$f_i$ $k+2$ $2k$ $K^{2}-1$ $K^{2}-1$ $K^{2}-1$ $k-3$

where $\sum f_i=62$. if $[x]$ denotes the greatest integer $\leq x$, then $\left[\mu^2+\sigma^2\right]$ is equal $.........$.

The frequency distribution:

$\begin{array}{|l|l|l|l|l|l|l|} \hline X & A & 2 A & 3 A & 4 A & 5 A & 6 A \\ \hline f & 2 & 1 & 1 & 1 & 1 & 1 \\ \hline \end{array}$

where $A$ is a positive integer, has a variance of $160 .$ Determine the value of $A$.

If the mean of the frequency distribution

Class: $0-10$ $10-20$ $20-30$ $30-40$ $40-50$

Frequency $2$ $3$ $x$ $5$ $4$

is $28$ , then its variance is $……..$.

The mean and standard deviation of $20$ observations are found to be $10$ and $2$ respectively. On rechecking, it was found that an observation $8$ was incorrect. Calculate the correct mean and standard deviation in each of the following cases:

If wrong item is omitted.