Question
The mean of 10 numbers is 12.5; the mean of the first six is 15 and the last five is 10. The sixth number is
Answer: Option A
:
A
LetthemeanofthelastfourbeA2.Thenbytheformulaforcombinedmean,12.5=6×15+4×A26+4;or125=90+4A2;∴A2=354Letthesixthnumber=x;thentakingthesixthnumberasacollection,thecombinedmeanofthiscollectionandthecollectionofthelastfiveis10,byquestion.∴Bydefinitionofcombinedmean10=1×x+4×3541+4;50=x+35;∴x=15∴sixthnumber=15
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:
A
LetthemeanofthelastfourbeA2.Thenbytheformulaforcombinedmean,12.5=6×15+4×A26+4;or125=90+4A2;∴A2=354Letthesixthnumber=x;thentakingthesixthnumberasacollection,thecombinedmeanofthiscollectionandthecollectionofthelastfiveis10,byquestion.∴Bydefinitionofcombinedmean10=1×x+4×3541+4;50=x+35;∴x=15∴sixthnumber=15
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