Mean of five observations is 5 and their variance is 9.20 . If three of given five observations are

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13.Statistics

hard

The mean of five observations is $5$ and their variance is $9.20$. If three of the given five observations are $1, 3$ and $8$, then a ratio of other two observations is

$10 : 3$

$4 : 9$

$5 : 8$

$6 : 7$

(JEE MAIN-2019)

Solution

$\mu = \frac{{1 + 3 + 8 + x + y}}{5}$

$25 = 12 + x + y \Rightarrow x + y = 13\,\,\,\,\,\,\,\,……..\left( 1 \right)$

${\sigma ^2} = \frac{{\sum {{{\left( {{x_i} – \mu } \right)}^2}} }}{N}$

$9.2 = \frac{{1 + 9 + 64 + {x^2} + {y^2}}}{5} – 25$

$34.2 \times 5 = 74 + {x^2} + {y^2}$

$171 = 74 + {x^2} + {y^2}$

$97 = {x^2} + {y^2}……….\left( 2 \right)$

${\left( {x + y} \right)^2} = {x^2} + {y^2} + 2xy$

$169 – 97 = 2xy \Rightarrow xy = 36$

$T = 4,9$

So, ratio is $\frac{4}{9}$ or $\frac{9}{4}$

Standard 11

Mathematics

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 :

hard

(JEE MAIN-2018)

Find the standard deviation for the following data:

${x_i}$ $3$ $8$ $13$ $18$ $25$

${f_i}$ $7$ $10$ $15$ $10$ $6$

medium

Find the mean and variance for the data

${x_i}$ $92$ $93$ $97$ $98$ $102$ $104$ $109$

${f_i}$ $3$ $2$ $3$ $2$ $6$ $3$ $3$

hard

The number of values of $a \in N$ such that the variance of $3,7,12 a, 43-a$ is a natural number is (Mean $=13$)

medium

(JEE MAIN-2022)

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 it is replaced by $12$

hard

${x_i}$	$92$	$93$	$97$	$98$	$102$	$104$	$109$
${f_i}$	$3$	$2$	$3$	$2$	$6$	$3$	$3$

The mean of five observations is $5$ and their variance is $9.20$. If three of the given five observations are $1, 3$ and $8$, then a ratio of other two observations is

Solution

Similar Questions

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Find the standard deviation for the following data:

${x_i}$ $3$ $8$ $13$ $18$ $25$

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Find the mean and variance for the data

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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 it is replaced by $12$