The sum of the deviations of a set of n numbers x_1, x_2, x_3, \dots, x_n measured from 15 is -90 and the sum of the deviations of the same numbers measured from -3 is 54. What is the arithmetic mean ?

Explanation

We have \sum x_i - 15n = -90 and \sum x_i + 3n = 54. Subtracting the first equation from the second gives 18n = 144, yielding n = 8. Substituting n back into the second equation: \sum x_i + 24 = 54, which means \sum x_i = 30. The mean is 30 / 8 = 3.75.

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