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17 February, 13:40

The sum of deviations of a set of values x1, x2, x3, ..., xn, measured from 50 is - 10 and the sum of deviations of the values from 46 is 10. find the value of n and the mean

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  1. 17 February, 14:57
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    n = 5

    mean = 48

    Let's create a series of equations to express "sum of deviations of a set of values x1, x2, x3, ..., xn, measured from 50 is - 10"

    (x1 - 50) + (x2 - 50) + ... + (xn - 50) = - 10

    (x1 + x2 + ... + xn) - 50n = - 10

    x1 + x2 + ... + xn = 50n - 10

    And do the same for 46.

    (x1 - 46) + (x2 - 46) + ... + (xn - 46) = 10

    (x1 + x2 + ... + xn) - 46n = 10

    x1 + x2 + ... + xn = 46n + 10

    Both 50n - 10 and 46n + 10 is equal to the sum of x1, x2, ..., xn. So set them equal to each other and solve for n:

    50n - 10 = 46n + 10

    50n = 46n + 20

    4n = 20

    n = 5

    Now we can calculate the sum of x1, x2, ..., xn:

    50n - 10 = 50*5 - 10 = 250 - 10 = 240

    And the mean mean = 240/5 = 48
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