Question

Find the population standard deviation (σ not S) for the data set: {75,80,90,95,75,85,55,80,90,95}

Round your answer to the nearest 10th.

Answer 1

The steps to work out standard deviation is as follows

Step 1: Find the mean of the data


`(75+80+90+95+75+85+55+80+90+95)/(10)=82`

Step 2: Subtract the mean from each data value


`75-82=-7`

`80-82=-2`

`90-82=7`

`95-82=13`

`75-82=-7`

`85-82=3`

`55-82=-27`

`80-82=-2`

`90-82=8`

`95-82=13`

Step 3: Add up the answers from step 2
`√(2.9)=1.7`


`-2+(-2)+7+13+(-7)+3+(-2)+(-2)+8+13=29`

Step 4: Divide the answer is step 3 by the number of data


`(29)/(10)=2.9`

Step 5: Square root the answer in step 4


`√(2.9) =1.7`