Question

Can I get some help please? thanks!

Answer 1

`barx=16.1" (nearest tenth)"`

`sigma=3.6" (nearest tenth")`

Explanation:

The mean is the sum of the numbers divided by how many there are:

`barx=1/nsumx_i`

`barx=(20+16+18+14+9+20+16)/7`

`barx=113/7=16.1428....=16.1" (nearest tenth)"`

For the standard deviation, there are a several formulae one can use. Whichever one you use, there will be a lot of arithmetic to do!

We will use:

`sigma=sqrt(1/nsum(x_i-barx)^2`

We have to subtract the mean from each `x_i` value, square these differences, and then add:

`(20-113/7)^2=729/49`

`(16-113/7)^2=1/49`

`(18-113/7)^2=169/49`

`(14-113/7)^2=225/49`

`(9-113/7)^2=2500/49`

`(20-113/7)^2=729/49`

`(16-113/7)^2=1/49`

The sum is `(729+1+169+225+2500+729+1)/49=4354/49`

So

`sigma=sqrt(1/7xx(4354)/49)`

`sigma =sqrt622/7=3.56284.......`

`sigma=3.6" (nearest tenth")`