Results 1 to 6 of 6

Math Help - Find the variance and standard deviation of this set of data?

  1. #1
    Member princess_anna57's Avatar
    Joined
    Jul 2007
    Posts
    78

    Find the variance and standard deviation of this set of data?

    16, 21, 21, 22, 22, 23, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 28, 20, 29, 29, 31, 32, 33, 33, 35, 35, 36, 37
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,664
    Thanks
    298
    Awards
    1
    Quote Originally Posted by princess_anna57 View Post
    16, 21, 21, 22, 22, 23, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 28, 20, 29, 29, 31, 32, 33, 33, 35, 35, 36, 37
    \sigma ^2 = \frac{1}{N} \sum_{n = 1}^N (\bar{x} - x_n)^2 <-- variance
    where \bar{x} = \frac{1}{N} \sum_{n = 1}^Nx_n

    and

    \sigma = \sqrt{\frac{1}{N} \sum_{n = 1}^N (\bar{x} - x_n)^2} <-- standard deviation

    Depending on the kind of statistic you are trying to work with the \frac{1}{N} might be a \frac{1}{N - 1}. You'll have to check your text or your notes to make sure.

    So the first thing to is to calculate the average, \bar{x}, then use that to find the variance.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member princess_anna57's Avatar
    Joined
    Jul 2007
    Posts
    78
    The mean is 26.73. Now what do I do? ^_^

    It's 1/N by the way.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,664
    Thanks
    298
    Awards
    1
    Quote Originally Posted by princess_anna57 View Post
    16, 21, 21, 22, 22, 23, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 28, 20, 29, 29, 31, 32, 33, 33, 35, 35, 36, 37
    Quote Originally Posted by princess_anna57 View Post
    The mean is 26.73. Now what do I do? ^_^

    It's 1/N by the way.
    Now tabulate (\bar{x} - x_n)^2 for all the data points, then add them. Then divide by N and you have the variance.

    This is where something like Excel comes in handy...

    -Dan
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member princess_anna57's Avatar
    Joined
    Jul 2007
    Posts
    78
    Cool beans. How about the standard deviation?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,664
    Thanks
    298
    Awards
    1
    Quote Originally Posted by princess_anna57 View Post
    Cool beans. How about the standard deviation?
    Take a look at the symbol I used for the variance, \sigma ^2. (This may not be a Universal notation, but it is standard in the two books I own.)

    So to get the standard deviation \sigma from the variance, just take the square root.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Mean, Variance, and Standard Deviation
    Posted in the Statistics Forum
    Replies: 1
    Last Post: May 10th 2011, 09:34 AM
  2. Replies: 3
    Last Post: September 25th 2010, 11:35 AM
  3. Variance, and Standard Deviation
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: November 11th 2009, 08:13 PM
  4. Find the mean, variance, and standard deviation
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: August 27th 2009, 06:24 AM
  5. variance and standard deviation
    Posted in the Statistics Forum
    Replies: 3
    Last Post: August 7th 2007, 12:03 PM

Search Tags


/mathhelpforum @mathhelpforum