For a sample $x_1,\ldots,x_n\,$ with mean $xˉ\bar x$ , a researcher proposes using $∑(xi−c)2\sum(x_i-c)^2$ as a measure of spread about a chosen centre $c$ .

Show that $∑(xi−c)2=∑(xi−xˉ)2+n(xˉ−c)2\sum(x_i-c)^2=\sum(x_i-\bar x)^2+n(\bar x-c)^2$ .

Hence state which value of $c\,$ minimises the sum.

For a sample $x_1,\ldots,x_n\,$ with mean $xˉ\bar x$ , a researcher proposes using $∑(xi−c)2\sum(x_i-c)^2$ as a measure of spread about a chosen centre $c$ .

Show that $∑(xi−c)2=∑(xi−xˉ)2+n(xˉ−c)2\sum(x_i-c)^2=\sum(x_i-\bar x)^2+n(\bar x-c)^2$ .

Hence state which value of $c\,$ minimises the sum.

2 Statistics

Question 144

Markscheme

2 Statistics

Question 144

Markscheme

2 Statistics

Question 144

2 Statistics Questions

2 Statistics

Question 144

2 Statistics Questions