anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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welshfella
  • welshfella
first find the mean of these numbers can you do that?
anonymous
  • anonymous
no
welshfella
  • welshfella
add them all up and divide by 10

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anonymous
  • anonymous
82 is what I got
welshfella
  • welshfella
yes you are right
welshfella
  • 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
  • welshfella
90 - 82 = 8 and so on
anonymous
  • anonymous
75=7 80=2 90=8 95=13 75=7 85=3 55=27 80=2 90=8 95=13
welshfella
  • welshfella
right strictly it should have been 80 - 82 = -2 but its not that important because we square each of those results
welshfella
  • welshfella
so now we square ach of the 10 results 7^2 = 49 2^2 = 4 and so on
welshfella
  • 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
  • welshfella
use your calculator - it would be a bit long winded otherwise. It a bit long winded anyway!
welshfella
  • welshfella
in the formula x is a number , mu is the mean and N is the total numbers.
anonymous
  • 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
  • welshfella
the biig 'E' means 'the sum of'.
welshfella
  • welshfella
right i got that too so std dev = sqrt 131
anonymous
  • anonymous
I'm confused on how to do the equation
welshfella
  • 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
  • welshfella
correct is |dw:1438979612906:dw|
welshfella
  • welshfella
the STd dev comes to 11.45 correct to decimal places
anonymous
  • anonymous
Is that the answer? Sorry, math is my weakest subject.
welshfella
  • welshfella
yes the variance is 131 the standard deviation is the square root of the variance
welshfella
  • welshfella
standard deviation gives a measure of the spread of the data
anonymous
  • anonymous
Oh, ok that makes sense
welshfella
  • 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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