Multiple choice

The mean of $100$ items is $50$ and their S.D. is $4$. The sum of the item and also the sum of the squares of the items is

  1. $5000,251600$
  2. $4000,251600$
  3. $5000,261600$

  4. None of these
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A Correct answer
Explanation

The mean is sum/n, so sum = 50 * 100 = 5000. Using the variance formula SD^2 = (sum of squares/n) - (mean^2), we get 16 = (sum of squares/100) - 2500, which leads to sum of squares = 251600.

AI explanation

The sum of the items is calculated as n multiplied by the mean, which gives 100 times 50 equal to 5000. The formula for variance is the sum of squared items divided by n minus the square of the mean, so the sum of squared items equals n multiplied by (variance plus the square of the mean). Substituting the values gives 100 times (16 plus 2500), which equals 100 times 2516 to yield 251600. The required sum and sum of squares are 5000 and 251600.

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