The sum of the deviations of a set of `n` values `x_1, x_2 ,.........x_n` measured from 50 is-10 and the sum of deviations of the values from 46 is 70.Find the values of `n` and the mean.

Explanation

Solution:
Sum of deviations from `50` is `−10`
`=> sum (x_i−50) = −10`
`sum (x_i - 50) = - 10`
`sum x_i - 50n = −10`​
y−50n=−10.....(1)
Sum of deviations from `46` is `70`
`=> sum(x_i - 46) = 70`
`sum x_i −46 sum 1 = 70`
`sum x_i −46n=70`
`:.y−46n=70.....(2)`Solving `(1)` and `(2)`, we get
`4n=80` i.e. `n=20`
Putting value of `n` in `(1)`, we get
`y=990`
Mean `=sum x_i/ n = y/n = 990/20 =49.5`