If data x₁, x₂, ...., x_{10} is such that mean of first four of these is 11 , mean of remaining

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13.Statistics

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If the data $x_1, x_2, ...., x_{10}$ is such that the mean of first four of these is $11$, the mean of the remaining six is $16$ and the sum of squares of all of these is $2,000$; then the standard deviation of this data is

A

$2\sqrt 2 $

B

$2$

C

$4$

D

$\sqrt 2 $

(JEE MAIN-2019)

Solution

${x_1} + … + {x_4} = 44$

${x_5} + … + {x_{10}} = 96$

$\bar x = 14,\sum {{x_i} = 140} $

Variance $ = \frac{{\sum {x_i^2} }}{n} – {{\bar x}^2} = 4$

Standard deviation $=2$

Standard 11

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