If the data x_1, x_2, ...., x_ 10 is such that the mean of first … - Vidyadip

MCQ

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 $
✓
$2$
C
$4$
D
$\sqrt 2 $

✓

Answer

Correct option: B.

$2$

b
${x_1} + ... + {x_4} = 44$

${x_5} + ... + {x_{10}} = 96$

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

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

Standard deviation $=2$

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