Results 1 to 13 of 13

Math Help - standard deviation question

  1. #1
    Newbie
    Joined
    Aug 2009
    Posts
    7

    standard deviation question

    hi all.

    i have a problem. i am trying to figure out the SD for a data set where the largest value is 5 (it's a data set of customer service ratings from 1 - 5) My mean is 4 and my standard deviation is 2. How is this possible if my largest possible rating can only be 5?

    Thanks for the help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    I may try to construct a sample to see if I can recreate this, do you know the number of observations, i.e., sample size?

    I played around with a sample of {2,5,5}.
    I got the sample mean to be 4 and the st deviation to be \sqrt 3 which is close.
    That's about the highest st deviation I can get with a mean of 4 and a small sample.
    Maybe with 2 observations I might get a st deviation of 2, but 2 is high.
    Last edited by matheagle; August 5th 2009 at 10:20 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2009
    Posts
    7
    Thanks for your help, matheagle, i do appreciate it.

    size is 85 data points, mean is 4, data points are:

    1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    Quote Originally Posted by fiurik View Post
    Thanks for your help, matheagle, i do appreciate it.

    size is 85 data points, mean is 4, data points are:

    1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
    Please fill in...
    how many
    1's=
    2's=
    3's=
    4's=
    5's=
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Aug 2009
    Posts
    7
    1 = 13
    2 = 5
    3 = 7
    4 = 11
    5 = 49
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    so \sum x^2=(13)(1)+(5)(4)+(7)(9)+(11)(16)+(49)(25)=1497

    check my work

    \sum x=(13)(1)+(5)(2)+(7)(3)+(11)(4)+(49)(5)=333

    sample mean is 333/85=3.917647..............

    so one thing is, we have a round off error, which is making things worse as I calculate the variance

    sample VARIANCE is

    {1497-{(333)^2\over 85}\over 84}=2.290756....

    some use 85 in the denomiator, but both are fine, then square root this to get the st deviation.

    .... 1.5135244...
    Last edited by matheagle; August 5th 2009 at 10:21 PM.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Aug 2009
    Posts
    7
    ok
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Aug 2009
    Posts
    7
    sorry, the message truncated the first time and all I saw was this part of your first sentence. I refreshed the screen just now and got full explanation.

    do, if i follow your steps, doesn't the SD still come to 2 (after rounding)?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    Quote Originally Posted by fiurik View Post
    sorry, the message truncated the first time and all I saw was this part of your first sentence. I refreshed the screen just now and got full explanation.

    do, if i follow your steps, doesn't the SD still come to 2 (after rounding)?

    barely, 1.51
    Last edited by matheagle; August 6th 2009 at 06:11 AM.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Newbie
    Joined
    Aug 2009
    Posts
    7
    right, so if my maximum rating is a 5 and my mean is 4 (or 3.9...) how can my SD be 2

    2 points away from four puts me beyond me max rating? is this ok?
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    Let's see if I understand the question...

    Sample Data Set
    1
    5
    5
    5

    Mean = 4
    Sample Standard Deviation = 2

    4 + 2 = 6 > 5 and this gives you pause. How can a mere one standard deviation exceed the greatest possible value?!

    This is a reasonable question.

    Try to remember that the Mean and Standard Devaition are measures of Central Tendency and Variability, respectively. They are NOT population restrictions.

    This does give cause for additional consideration when constructing confidence intervals. The task of using "truncated" distributions is a matter of much conversation.

    Note: This is just the sort of thing that gives Tchebychev's Inequality its power. Tchebychev's Inequality Truly amazing stuff!
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Newbie
    Joined
    Aug 2009
    Posts
    7
    wow, thanks for your answer. it sounds great, but i wasn't kidding when I said I was a novice. that was way over my head!
    Follow Math Help Forum on Facebook and Google+

  13. #13
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    You don't need to worry about the awesome ineauality. For now, just get the hang of the arithmetic. Try to recall that some measures of Central Tendency are better than others. There are also various measures of variability. Some work better in some situations. Always keep your eye out for results that don't make sense - like your observation that motivated this question. Good work.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A standard deviation question
    Posted in the Statistics Forum
    Replies: 4
    Last Post: February 16th 2011, 04:59 AM
  2. Help with mean and standard deviation question.
    Posted in the Statistics Forum
    Replies: 2
    Last Post: November 18th 2009, 10:53 PM
  3. Standard deviation and mean question
    Posted in the Statistics Forum
    Replies: 3
    Last Post: November 13th 2009, 11:18 AM
  4. Mean/Standard Deviation question
    Posted in the Statistics Forum
    Replies: 3
    Last Post: May 25th 2009, 07:18 PM
  5. Standard Deviation question?
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 8th 2007, 08:45 PM

Search Tags


/mathhelpforum @mathhelpforum