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

1. Find the mean (arithmetic mean) of the numbers:


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

2. Find the differences of each number to the mean, and calculate the square of each of these differences :

82-75=7, 7^2=49
82-80=2 2^2=4
90-82=8 8^2=64
95-82=13 13^2=169
82-75=7 7^2=49
85-82=3 3^2=9
82-55=27 27^2=729
82-80=2 2^2=4
90-82=8 8^2=64
95-82=13 13^2=169

3. Calculate the mean of the differences (the Variance):


`(49+4+64+169+49+9+729+4+64+169)/(10)= 131.2`

4. Standart deviation is the root of the variance =
`√(131.2) =11.5`