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  4. If the data x1, x2, ...., x10 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 :

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Q. 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 :

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Solution:

$x_{1} + .... +x_{4} =44 $
$ x_{5} + .... + x_{10} = 96 $
$ \bar{x} = 14, \sum x_{i} = 140 $
Variance $ = \frac{\sum x_{1}^{2}}{n} - \bar{x}^{2} = 4 $
Standard deviation = $2$