Multiple choice

The mean of 100 observations is $50$ and their standard deviation is $5$. The sum of the squares of all the observations is

  1. $50000$
  2. $250000$
  3. $252500$
  4. $255000$
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C Correct answer
Explanation

Given mean = 50, standard deviation = 5, n = 100. Variance = 25. Variance = (Sum of squares / n) - (mean^2). So, 25 = (Sum of squares / 100) - 2500. Sum of squares = 2525 * 100 = 252500.

AI explanation

Using the formula relating variance, mean, and the sum of squares, the variance equals the sum of the squares divided by n, minus the square of the mean. We substitute the given values to get 5 equals the sum of the squares divided by 100, minus 50 squared. This simplifies to 5 equals the sum of the squares divided by 100, minus 2500. Adding 2500 to both sides gives 2505 equals the sum of the squares divided by 100. Multiplying by 100 gives the sum of the squares as 252500.

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