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JEE Main 2003
Exam
JEE Main
Year
2003
Subject
Mathematics
Chapter
Statistics

JEE Main 2003 · Mathematics · Statistics

In an experiment with 15 observations on x , the following results...

In an experiment with 15 observations on xx, the following results were available: Σx2=2830,Σx=170\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

Options

  1. A8.338.33
  2. B78.0078.00
  3. C188.66188.66
  4. D177.33177.33

Correct answer

B. 78.0078.00

Step-by-step solution

Σx=170,Σx2=2830\Sigma x=170, \Sigma x^2=2830 increase in Σx=10\Sigma x=10, then Σx′=170+10=180\Sigma x^{\prime}=170+10=180 Increase in Σx2=900−400=500\Sigma \mathrm{x}^2=900-400=500 then Σx′2=2830+500=3330\Sigma x^{\prime 2}=2830+500=3330 Variance =1nΣx′2−(1nΣx′)2=\frac{1}{n} \Sigma x^{\prime 2}-\left(\frac{1}{n} \Sigma x^{\prime}\right)^2 =115×3330−(115×180)2=222−144=78=\frac{1}{15} \times 3330-\left(\frac{1}{15} \times 180\right)^2=222-144=78
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