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Weighted Means

Carmen is curious about her final mark in her math class based on 12 assessments. Her scores on the assessments are listed in the following table.


Carmen calculates her mean to be 85% by adding up all the scores and dividing by 12.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mover»«mi»x«/mi»«mo»§#175;«/mo»«/mover»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mrow»«mi»sum«/mi»«mo»§#160;«/mo»«mi»of«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi»values«/mi»«mo»§#160;«/mo»«mi»in«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi»data«/mi»«mo»§#160;«/mo»«mi»set«/mi»«/mrow»«mrow»«mi»total«/mi»«mo»§#160;«/mo»«mi»number«/mi»«mo»§#160;«/mo»«mi»of«/mi»«mo»§#160;«/mo»«mi»values«/mi»«mo»§#160;«/mo»«mi»in«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi»data«/mi»«mo»§#160;«/mo»«mi»set«/mi»«/mrow»«/mfrac»«/mtd»«/mtr»«mtr»«mtd/»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mrow»«mn»90«/mn»«mo»+«/mo»«mn»95«/mn»«mo»+«/mo»«mn»100«/mn»«mo»+«/mo»«mn»80«/mn»«mo»+«/mo»«mn»85«/mn»«mo»+«/mo»«mn»80«/mn»«mo»+«/mo»«mn»100«/mn»«mo»+«/mo»«mn»70«/mn»«mo»+«/mo»«mn»75«/mn»«mo»+«/mo»«mn»95«/mn»«mo»+«/mo»«mn»80«/mn»«mo»+«/mo»«mn»70«/mn»«/mrow»«mn»12«/mn»«/mfrac»«/mtd»«/mtr»«mtr»«mtd/»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mrow»«mn»1«/mn»«mo»§#160;«/mo»«mn»020«/mn»«/mrow»«mn»12«/mn»«/mfrac»«/mtd»«/mtr»«mtr»«mtd/»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»85«/mn»«mo».«/mo»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd/»«mtd/»«mtd/»«/mtr»«/mtable»«/math»

Carmen emailed her teacher to inquire why her final mark is listed online as 81% instead of 85%. Carmen's teacher responded that a weighted mean was used to calculate the final mark based on the course breakdown below.

Assessment	Weight
Assignments	40%
Course Reviews	10%
Exams	50%

What exactly is a weighted mean? How is it calculated?

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