The algebraic sum of the deviations of a set of values x₁ , x₂, x₃, x_n measured from 100 is -20 and the algebriac sum of the deviations of the same set of values measured from 92 is 140 . What is the mean of the values?

Step-by-step solution

Here, ( x ₁-100 )+ ( x ₂-100 )+ . .+ ( x _ n -100 )=-20 hence (x₁+x₂+x₃+ . . x_n )-100 x=-20 Or x ₁+ x ₂+ x ₃+ x _ n =100 n -20 and accoding to question for same set x ₁+ x ₂+ x ₃+ . . x _ n =92 n +1408 n =160 n =20 aligned & from ( i ) x ₁+ x ₂+ x ₃ . .+ x _ n =1980 & Mean == 100 20-20 20 =99 aligned