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Math Help - Frequency Table Standard Deviation

  1. #1
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    Frequency Table Standard Deviation

    Okay I need help. I'm studying for a test, and I keep trying to do this problem over and overrr.

    This is the table.

    Classes ---- Frequency
    10-13 ---- 1
    14-17 ---- 0
    18-21 ---- 15
    22-25 ---- 7
    26-29 ---- 2

    I keep getting 7.93 but my answer sheet says it's supposed to be 3.2!

    What am I doing wrong?
    I would post my work but I don't know how to .

    Thanks in advance!
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  2. #2
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    Quote Originally Posted by hellotarina View Post
    Okay I need help. I'm studying for a test, and I keep trying to do this problem over and overrr.

    This is the table.

    Classes ---- Frequency
    10-13 ---- 1
    14-17 ---- 0
    18-21 ---- 15
    22-25 ---- 7
    26-29 ---- 2

    I keep getting 7.93 but my answer sheet says it's supposed to be 3.2!

    What am I doing wrong?
    I would post my work but I don't know how to .

    Thanks in advance!
    It would help if you said what the actual question was.
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  3. #3
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    The question just tells me to find The Standard Deviation of the frequency table posted above. It is to compare standard deviation done by raw data (3.2) and standard deviation done by a grouped data. I know the answer is meant to be 3.2 as well but I don't know how they get this.
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  4. #4
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    Quote Originally Posted by hellotarina View Post
    The question just tells me to find The Standard Deviation of the frequency table posted above. It is to compare standard deviation done by raw data (3.2) and standard deviation done by a grouped data. I know the answer is meant to be 3.2 as well but I don't know how they get this.
    Please show the details of your calculation. You might want to read this first and then re-do your calculations: http://www.indiana.edu/~econstat/pdf...pendix%20C.pdf

    I get 3.24.
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  5. #5
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    √n[Sigma(f * x^2)] - [Sigma(f*x]^2
    _____________________________ = s
    n(n-1)

    I get

    √ [29(11213.9)] - (523.5)^2
    ______________________
    29(28)

    So,

    325203.1 - 274052.25
    ___________________
    812

    51151
    _____ = √62.99
    812

    And then I get 7.93

    I got all the results from:

    Classes----Frequency ---- Midpoint (x) ---- x^2
    10-13 ---- 1 -----11.5------132.25
    14-17 ---- 0 -----15.5 ----- 240.25
    18-21 ---- 15-----19.5-----380.25
    22-25 ---- 7------23.5-----552.25
    26-29 ---- 2------27.5-----756.25

    And then of course:

    x^2*f
    132.25
    0
    5703.75
    3865.4
    1512.5
    Sigma=11213.9

    The 523.5 I got from Sigmaf*x
    Last edited by hellotarina; December 12th 2009 at 04:40 AM.
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  6. #6
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    Quote Originally Posted by hellotarina View Post
    √n[Sigma(f * x^2)] - [Sigma(f*x]^2
    _____________________________ = s
    n(n-1)

    I get

    √ [29(11213.9)] - (523.5)^2
    ______________________
    29(28)

    So,

    325203.1 - 274052.25
    ___________________
    812

    51151
    _____ = √62.99
    812

    And then I get 7.93

    I got all the results from:

    Classes----Frequency ---- Midpoint (x) ---- x^2
    10-13 ---- 1 -----11.5------132.25
    14-17 ---- 0 -----15.5 ----- 240.25
    18-21 ---- 15-----19.5-----380.25
    22-25 ---- 7------23.5-----552.25
    26-29 ---- 2------27.5-----756.25

    And then of course:

    x^2*f
    132.25
    0
    5703.75
    3865.4
    1512.5
    Sigma=11213.9

    The 523.5 I got from Sigmaf*x
    There are several mistakes (although some might just be typos). But the fact that your value for n is wrong is a very bad mistake, one that you should have realised yourself.
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  7. #7
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    Quote Originally Posted by mr fantastic View Post
    There are several mistakes (although some might just be typos). But the fact that your value for n is wrong is a very bad mistake, one that you should have realised yourself.
    I'm a noob at this. It's my first stats class. And I just realised what you mean. I confused the classes with the n. However, I get 600 when I do n(n-1) and that only makes the standard deviation higher...

    Farther from the answer I'm supposed to be getting.

    51151
    _____= 85.3
    600

    √85.3 = 9.24
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  8. #8
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    Holy...

    I just got the answer!!! Hehe.

    3.23

    You're a genius, sir!
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  9. #9
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    Quote Originally Posted by hellotarina View Post
    I'm a noob at this. It's my first stats class. And I just realised what you mean. I confused the classes with the n. However, I get 600 when I do n(n-1) and that only makes the standard deviation higher...

    Farther from the answer I'm supposed to be getting.

    51151
    _____= 85.3
    600

    √85.3 = 9.24
    I have given you a link with the formula and which shows how to set things out. It's now nothing more than arithmetic.

    Following the link - carefully - I got  s^2 = \frac{1}{24} \left( 11214.25 - \frac{523.5^2}{25}\right) = 10.5067 \Rightarrow s = 3.24.

    I cannot push the buttons on the calculator for you. And I should not have to be telling you the value of n. It's not a matter of being a 'noob'. It's simply a matter of doing things carefully.
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  10. #10
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    Quote Originally Posted by hellotarina View Post
    Holy...

    I just got the answer!!! Hehe.

    3.23

    You're a genius, sir!
    See ....! I told you so. Simply arithmetic. A matter of taking care. Being a noob does not matter.

    (And yes, I am, aren't I!)
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