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anonymous

  • one year ago

What is the standard deviation of the following data? If necessary, round your answer to two decimal places. 12, 13, 8, 13, 9, 11, 12, 9, 1

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  1. jtvatsim
    • one year ago
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    I don't think @heretohelpalways that we want the mean absolute deviation for this problem. We need the standard deviation.

  2. jtvatsim
    • one year ago
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    The steps to do this are: 1. Find the mean of the data. (Find the average) 2. Then find subtract each data point from the mean and square the result. 3. Find the mean of the "square differences" we found in step 2. 4. Take the square root of Step 3 and we are done. This is easier to see in a table. Which I will show below.

  3. jtvatsim
    • one year ago
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    Here's the start of my table.

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  4. jtvatsim
    • one year ago
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    Let's go ahead and do step 1. What is the mean of the data? To do this, just add up all the data and divided my how many we have.

  5. anonymous
    • one year ago
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    9.8?

  6. jtvatsim
    • one year ago
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    12 + 13 + 8 + 13 + 9 + 11 + 12 + 9 + 1 = 88 Then, divide this by 9 (that's how many we have), this gives us 88/9 = 9.8. You beat me! Good! :D

  7. jtvatsim
    • one year ago
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    Now, for the annoying part... we have to subtract the mean from each of our data points. So, for example, we do 12 - 9.8 = 2.2. Then we repeat this for all the other points... BORING! But, not that hard. :)

  8. jtvatsim
    • one year ago
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    When you are done, you will get something like this (I'm cheating since I have a computer that does this for me...)

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  9. jtvatsim
    • one year ago
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    Does that make sense so far?

  10. anonymous
    • one year ago
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    Yep! got it so far, thanks

  11. jtvatsim
    • one year ago
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    Great! Now, for the second part of Step 2. We need to "square" (multiply the number by itself) each of the differences we just found. What am I trying to say? For example, The first difference was 2.2. So find 2.2^2 = 2.2 * 2.2 = 4.84. And do this for each of the differences... BORING AGAIN! But not hard.

  12. jtvatsim
    • one year ago
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    You should get something that looks like this

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  13. jtvatsim
    • one year ago
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    Phew! Almost done! Now, we find the mean (average) of these crazy squared numbers. Add them up, divide by how many (9) and we get: 12.6 about.

  14. jtvatsim
    • one year ago
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    This number we just found is called the "variance" of the data. The standard deviation is the square root of this number. So just find sqrt(12.6) = 3.6 and we are done.

  15. anonymous
    • one year ago
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    Got it! Thank you so much, that was very well explained!

  16. jtvatsim
    • one year ago
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    Glad to help! No point to make it harder than it already is! :) Good luck!

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