Question

Determine the value of k such that ∑(x-k)=0.

Answer 1

\[\Sigma(x-k)=0\]

Answer 2

\[\sum_{i=i}^n (x-\bar{x})=0\], where \[\bar{x}=\frac{1}{n}\sum_{i=1}^n x_i\]

Answer 3

are there indices on the summation?

Answer 4

i'm sorry, i wasn't told what indices means. that's all i have in a formula.

Answer 5

Is this related to statistics by any chance?

Answer 6

yes, it's statistics

Answer 7

Oh ok then yes it would make sense for \(k = \bar{x}\), then is k is the mean. Unfortunately the way your notation is presented is a bit sloppy/vague. With proper notation, you can prove that easily:

\[\sum_{i=1}^n(x_i-\bar{x})=\sum_{i=1}^nx_i-n\bar{x}=\sum_{i=1}^nx_i-n \left( \frac{1}{n}\sum_{i=1}^nx_i\right)=\sum_{i=1}^nx_i-\sum_{i=1}^nx_i=0 \]