+ Reply to Thread
Results 1 to 2 of 2

Thread: Mathematical intuition for variance

  1. #1
    Points: 4, Level: 1
    Level completed: 7%, Points required for next Level: 46

    Posts
    1
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Mathematical intuition for variance




    One explanation to "Why do we square the deviations" is..

    "The sum of the square deviations of any set of observations from their mean is the smallest that the sum of squared deviations from any number can possibly be. This is not true of the unsquared distances. So squared deviations point to the mean as center in a way that distances do not."

    I do not understand this explanation. Could you provide an example and break down the explanation?

  2. #2
    Dark Knight
    Points: 6,762, Level: 54
    Level completed: 6%, Points required for next Level: 188
    vinux's Avatar
    Posts
    2,011
    Thanks
    52
    Thanked 241 Times in 205 Posts

    Re: Mathematical intuition for variance


    Variance is one of the measures of dispersion. You could take mean deviation or range or IQR to represent dispersion.

    The sum of the square deviation from a point A is minimized when A is the mean. I.e. \sum (x_i -A) ^2 is minimized when A = \bar x. But when you take other deviation (other than squared), then the minimum value may not correspond to the mean. For example, mean deviation from point A is minimized when A is the median.
    In the long run, we're all dead.

+ Reply to Thread

           




Tags for this Thread

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts






Advertise on Talk Stats