Question

Compute the standard deviation for the set of data.




2, 4, 6, 8, 10

Answer 1

`\sigma` - standard deviation
m - mean

`\sigma= \sqrt{ (1)/(n) \sum_(i=1)^(n) (x_i-m)^2} \\m= (2+4+6+8+10)/(5)= (30)/(5) =6 \\ \\ \sigma= \sqrt{ (1)/(5) \sum_(i=1)^(5) (x_i-6)^2} \\= \sqrt{ (1)/(5) [ (2-6)^2+(4-6)^2+(6-6)^2+(8-6)^2+(10-6)^2]} \\= \sqrt{ (1)/(5) [ 16+4+0+4+16]} \\= \sqrt{ (1)/(5) * 40} \\= \sqrt{ (1)/(5) * 40} \\=2√(2)`