Multiple choice

The sum of $10$ observations is $110$ and the sum of squares of observations is $2900$, their standard deviation is ______.

  1. $13$
  2. $8$
  3. $10$
  4. $9$
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A Correct answer
Explanation

Variance = (Sum of squares / n) - (Mean)^2. Mean = 110/10 = 11. Variance = (2900/10) - 11^2 = 290 - 121 = 169. Standard deviation = sqrt(169) = 13.

AI explanation

The mean is 110 divided by 10, which equals 11. Using the standard deviation formula of the square root of the sum of squares divided by n minus the mean squared, we calculate the square root of (2900 divided by 10 minus 121), resulting in the square root of 169, which is 13.

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