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.

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- welshfella

first find the mean of these numbers can you do that?

- anonymous

no

- welshfella

add them all up and divide by 10

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## More answers

- anonymous

82 is what I got

- welshfella

yes you are right

- welshfella

now you need to find the difference between each number in the list and 82
so for first number 75 it is 82 - 75 = 7
for 80 it is 82 - 80 = 2
do this for all the other numbers

- welshfella

90 - 82 = 8
and so on

- anonymous

75=7
80=2
90=8
95=13
75=7
85=3
55=27
80=2
90=8
95=13

- welshfella

right strictly it should have been 80 - 82 = -2 but its not that important because we square each of those results

- welshfella

so now we square ach of the 10 results
7^2 = 49
2^2 = 4
and so on

- welshfella

when you have done that add them all up
then divide the answer by the number of values (10)
this result is called the variance
find the square root of the variance to get the standard deviation

- welshfella

use your calculator - it would be a bit long winded otherwise. It a bit long winded anyway!

- welshfella

in the formula x is a number , mu is the mean and N is the total numbers.

- anonymous

75=7^2=49
80=2^2=4
90=8^2=64
95=13^2=169
75=7^2=49
85=3^2=9
55=27^2=729
80=2^2=4
90=8^2=64
95=13^2=169
1310 divided by 10=131

- welshfella

the biig 'E' means 'the sum of'.

- welshfella

right i got that too
so std dev = sqrt 131

- anonymous

I'm confused on how to do the equation

- welshfella

mu is the mean
x - mu is the differences
oops sorry i made a mistake with that
- the formula is just a summary of the process
you have to go through the procedure as we did

- welshfella

correct is
|dw:1438979612906:dw|

- welshfella

the STd dev comes to 11.45 correct to decimal places

- anonymous

Is that the answer? Sorry, math is my weakest subject.

- welshfella

yes the variance is 131
the standard deviation is the square root of the variance

- welshfella

standard deviation gives a measure of the spread of the data

- anonymous

Oh, ok that makes sense

- welshfella

good
the lower the standard deviation the closer the data is the mean . If the Std dev is high it means there is a lot of values far away from the mean

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