Multiple choice

The algebraic sum of the deviations of $5$ observations measured from $15$ is $10$. Therefore the mean of this observation is _____.

  1. $15$
  2. $14.2$
  3. $17$
  4. $16.1$
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C Correct answer
Explanation

Sum of deviations = Sum(x_i - 15) = 10. Sum(x_i) - 5*15 = 10. Sum(x_i) = 75 + 10 = 85. Mean = 85 / 5 = 17.

AI explanation

Let the observations be denoted by x. Using the property of arithmetic mean, the algebraic sum of deviations from the mean equals zero. We calculate the sum of deviations from 15 as the sum of (x - 15) across 5 observations, which equals the sum of x minus 15 times 5. Since this sum is given as 10, the sum of x is 85. The mean is calculated by dividing the sum of observations by the number of observations, which gives 85 divided by 5 equal to 17.

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