Q136 / 225 · JEE Main 2003 · Mathematics

In an experiment with 15 observations on $x$, the following results were available: $\Sigma x^2=2830, \Sigma x=170$ One observation that was 20 was found to be wrong and was replaced by the correct value 30 . The corrected variance is

  • A
    $8.33$
  • Correct answer
    B
    $78.00$
  • C
    $188.66$
  • D
    $177.33$

Solution

$\Sigma x=170, \Sigma x^2=2830$ increase in $\Sigma x=10$, then $\Sigma x^{\prime}=170+10=180$ Increase in $\Sigma \mathrm{x}^2=900-400=500$ then $\Sigma x^{\prime 2}=2830+500=3330$ Variance $=\frac{1}{n} \Sigma x^{\prime 2}-\left(\frac{1}{n} \Sigma x^{\prime}\right)^2$ $=\frac{1}{15} \times 3330-\left(\frac{1}{15} \times 180\right)^2=222-144=78$

Hence, the correct answer is option: 'B'.

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