Question

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

Answer 1

The steps to work out standard deviation is as follows

Step 1: Find the mean of the data

$\frac{75+80+90+95+75+85+55+80+90+95}{10}=82$

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$\sqrt{2.9}=1.7$

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

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

$\frac{29}{10}=2.9$

Step 5: Square root the answer in step 4

$\sqrt{2.9} =1.7$