Multiple choice

The mean of four observations is $3$. If the sum of the squares of these observations is $48$ then their standard deviation is

  1. $\sqrt{7}$
  2. $\sqrt{2}$
  3. $\sqrt{3}$
  4. $\sqrt{5}$
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C Correct answer
Explanation

Mean = 3, so sum of observations = 12. Sum of squares = 48. Variance = (Sum of squares / n) - (Mean)^2 = 48/4 - 3^2 = 12 - 9 = 3. Standard deviation = sqrt(3).

AI explanation

Using the formula for standard deviation, we find the variance by subtracting the square of the mean from the mean of the squares. The sum of the four observations is 3 multiplied by 4, giving 12, so the mean is 3. The mean of the squares is 48 divided by 4, which is 12. The variance is 12 minus 3 squared, or 12 minus 9, resulting in a variance of 3. The standard deviation is the square root of 3.

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