Multiple choice

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

  1. $78$
  2. $188.6666$
  3. $177.3333$
  4. $8.3333$
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A Correct answer
Explanation

Sum x = 170. Corrected sum x = 170 - 20 + 30 = 180. Sum x^2 = 2830. Corrected sum x^2 = 2830 - 20^2 + 30^2 = 2830 - 400 + 900 = 3330. Variance = (Sum x^2 / n) - (Mean)^2. Mean = 180/15 = 12. Variance = (3330 / 15) - 12^2 = 222 - 144 = 78.

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