Multiple choice

If the sum and sum of squares of $10$ observations are $12$ and $18$ resp., then, The $S.D$ of observations is :-

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

Sum of observations = 12, n = 10. Mean = 1.2. Sum of squares = 18. Variance = (Sum of squares / n) - (Mean)^2 = 18/10 - (1.2)^2 = 1.8 - 1.44 = 0.36. Standard deviation = sqrt(0.36) = 0.6 = 3/5.

AI explanation

Using the standard deviation formula, the variance equals the sum of squares divided by the number of observations, minus the square of the mean. The mean is 12 divided by 10, which is 1.2, so the variance equals 18 divided by 10 minus 1.44, giving 0.36. The standard deviation is the square root of 0.36, which equals 3/5.

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