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The outcome of each of $30$ items was observed; $10$ items gave an outcome $\frac{1}{2} - d$ each, $10$ items gave outcome $\frac {1}{2}$ each and the remaining $10$ items gave outcome $\frac{1}{2} + d$ each. If the variance of this outcome data is $\frac {4}{3}$ then $\left| d \right|$ equals
$\frac {2}{3}$
$2$
$\frac {\sqrt 5}{2}$
$\sqrt 2$
Solution
Variance remains some if same number is subracted from each observation. (subtract $10$ from each observation)
$\therefore \frac{{1{{\left( { – d} \right)}^2} + 10{{\left( 0 \right)}^2} + 10{{\left( d \right)}^2}}}{{30}} – {\left( {\frac{{10\left( { – d} \right) + 10\left( 0 \right) + 10\left( d \right)}}{{30}}} \right)^2} = \frac{4}{3}$
$\frac{{20{d^2}}}{{30}} = \frac{4}{3}$
$ \Rightarrow {d^2} = 2$
$\left( d \right) = \sqrt 2 $
Similar Questions
If the variance of the frequency distribution is $160$ , then the value of $\mathrm{c} \in \mathrm{N}$ is
| $X$ | $c$ | $2c$ | $3c$ | $4c$ | $5c$ | $6c$ |
| $f$ | $2$ | $1$ | $1$ | $1$ | $1$ | $1$ |
