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From |
Jeph Herrin <junk@spandrel.net> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Average of Sample vesus Sub-Samples |

Date |
Fri, 19 Mar 2010 11:59:05 -0400 |

The original question was not whether these two numbers could differ, but whether the average of the larger group could be greater than the mean of the two sub averages. In your case they differ, but the average of the larger group is smaller. I think you have to have negative numbers to reverse the inequality. cheers, Jeph Tim Scharks wrote:

but what about A = 1, 1, 1 B = 3 m(A) = 1 m(B) = 3 (m(A)+m(B))/2=2 mean (A+B) =1.5 uh oh... The problem is not negative numbers--it is your failure to weight the subsample means according to their relative size: (m(A)*3+m(B)*1)/4 =1.5 m(A+B) = 1.5 On Fri, Mar 19, 2010 at 6:49 AM, Jeph Herrin <junk@spandrel.net> wrote:Yes, if they are negative. A = -1,-1,-1 B = -3 then mean(A) = -1 mean(B) = -3 (mean(A)+mean(B))/2 = -2 mean(A+B)= -6/4 = -1.5 -1.5 > -2 So the average of all 4 numbers is larger than the average of the means of the two subsamples. hth, Jeph Erasmo Giambona wrote:Dear Statalisters, Is it possible that the arithmetic average of a sample is larger than the averages of two sub-samples containing overall all the observations of the full samples? Any thoughts would be appreciated, Erasmo * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/* * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/* * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

* * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Average of Sample vesus Sub-Samples***From:*Tim Scharks <tim.scharks@gmail.com>

**References**:**st: Average of Sample vesus Sub-Samples***From:*Erasmo Giambona <e.giambona@gmail.com>

**Re: st: Average of Sample vesus Sub-Samples***From:*Jeph Herrin <junk@spandrel.net>

**Re: st: Average of Sample vesus Sub-Samples***From:*Tim Scharks <tim.scharks@gmail.com>

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