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13.Statistics
hard
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
Mathematics
Similar Questions
The variance $\sigma^2$ of the data is $ . . . . . .$
$x_i$ | $0$ | $1$ | $5$ | $6$ | $10$ | $12$ | $17$ |
$f_i$ | $3$ | $2$ | $3$ | $2$ | $6$ | $3$ | $3$ |