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

  • [JEE MAIN 2019]
  • A

    $\frac {2}{3}$

  • B

    $2$

  • C

    $\frac {\sqrt 5}{2}$

  • D

    $\sqrt 2$

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