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

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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