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