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anonymous

  • one year ago

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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  1. welshfella
    • one year ago
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    first find the mean of these numbers can you do that?

  2. anonymous
    • one year ago
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    no

  3. welshfella
    • one year ago
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    add them all up and divide by 10

  4. anonymous
    • one year ago
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    82 is what I got

  5. welshfella
    • one year ago
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    yes you are right

  6. welshfella
    • one year ago
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    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

  7. welshfella
    • one year ago
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    90 - 82 = 8 and so on

  8. anonymous
    • one year ago
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    75=7 80=2 90=8 95=13 75=7 85=3 55=27 80=2 90=8 95=13

  9. welshfella
    • one year ago
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    right strictly it should have been 80 - 82 = -2 but its not that important because we square each of those results

  10. welshfella
    • one year ago
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    so now we square ach of the 10 results 7^2 = 49 2^2 = 4 and so on

  11. welshfella
    • one year ago
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    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

  12. welshfella
    • one year ago
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    use your calculator - it would be a bit long winded otherwise. It a bit long winded anyway!

  13. welshfella
    • one year ago
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    in the formula x is a number , mu is the mean and N is the total numbers.

  14. anonymous
    • one year ago
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    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

  15. welshfella
    • one year ago
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    the biig 'E' means 'the sum of'.

  16. welshfella
    • one year ago
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    right i got that too so std dev = sqrt 131

  17. anonymous
    • one year ago
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    I'm confused on how to do the equation

  18. welshfella
    • one year ago
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    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

  19. welshfella
    • one year ago
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    correct is |dw:1438979612906:dw|

  20. welshfella
    • one year ago
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    the STd dev comes to 11.45 correct to decimal places

  21. anonymous
    • one year ago
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    Is that the answer? Sorry, math is my weakest subject.

  22. welshfella
    • one year ago
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    yes the variance is 131 the standard deviation is the square root of the variance

  23. welshfella
    • one year ago
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    standard deviation gives a measure of the spread of the data

  24. anonymous
    • one year ago
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    Oh, ok that makes sense

  25. welshfella
    • one year ago
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    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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