Sample VarianceDate: 08/08/97 at 21:12:31 From: craig murray Subject: Sample variance 4,5,2,6,4,3,4 Could you please help me understand the sample variance using the data above? n = 7 X = 3.52 I am having a hard time understanding the problem. Thank you for any help. Craig Date: 08/09/97 at 07:29:35 From: Doctor Anthony Subject: Re: Sample variance The most convenient formula for calculating variance, (s^2), is SUM(x^2) s^2 = -------- - MEAN^2 n Lay out the working in tabular form: x f f.x f.x^2 ------------------------------- 2 1 2 4 3 1 3 9 4 3 12 48 5 1 5 25 6 1 6 36 ------------------------------- 7 28 122 MEAN = 28/7 = 4 Variance = 122/7 - 4^2 s^2 = 1.42857 and standard deviation = s = 1.19523 Note that this is SAMPLE variance and s.d. If you wish to estimate population variance from the sample, then you multiply sample variance by n/(n-1), in this case by 7/6. Population variance = (7/6)(1.42857) = 1.66667 -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994-2015 The Math Forum
http://mathforum.org/dr.math/