Multiple choice

The sum of deviations from 50 of n values x1, x2, ... xn is -10 and the sum of deviations from 46 of x1, x2, ... xn is 70. Then the deviation of the mean of the given values from 48 is

  1. 1.5

  2. -1.5

  3. 2

  4. -2.5
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A Correct answer
Explanation

Sum of deviations from A is sum(x_i - A) = sum(x_i) - nA. For A=50, sum(x_i) - 50n = -10. For A=46, sum(x_i) - 46n = 70. Subtracting equations: 4n = 80, so n = 20. Then sum(x_i) = 990. Mean = 990/20 = 49.5. Deviation from 48 = 49.5 - 48 = 1.5.

AI explanation

Let the number of values be n and their mean be m. The sum of deviations from 50 gives 50n minus the total sum, equaling 10, so the sum is 50n minus 10. The second condition gives 46n minus the sum, equaling 70, which means the sum is 46n minus 70. Equating the two expressions for the sum gives 50n minus 10 equals 46n minus 70, meaning 4n equals 80, so n is 20. The total sum is 990, making the mean 49.5. The deviation of this mean from 48 is 49.5 minus 48, which is 1.5.

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