Multiple choice

The algebraic sum of deviations of ten observations about 15 is 70.The mean is

  1. 22

  2. 25

  3. 20

  4. none of these
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A Correct answer
Explanation

Sum of deviations = sum(x_i - 15) = 70. sum(x_i) - 150 = 70. sum(x_i) = 220. Mean = sum(x_i) / 10 = 220 / 10 = 22.

AI explanation

The algebraic sum of deviations about a value A is equal to the sum of the observations minus n multiplied by A. Setting up the equation gives the sum of the observations minus 10 times 15 equal to 70, meaning the sum of the observations is 150 plus 70, which is 220. The mean is the sum of the observations divided by n, so 220 divided by 10 yields 22.

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