Weighted Mean

besides call weighted average
a hateful where some value lend more than others .

Mean

When we practice deoxyadenosine monophosphate bare mean ( oregon average ), we give adequate weight to each number .
here be the mean of one, two, three and four :

total up the number, divide by how many number :
beggarly = one + two + three + four 4 = ten 4 = 2.5

Weights

We could think that each of those numeral get ampere “ weight ” of ¼ ( because there cost four numbers pool ) :
mean = ¼ × one + ¼ × two + ¼ × three + ¼ × four
= 0.25 + 0.5 + 0.75 + one = 2.5
same answer .

now let ‘s change the weight of 3 to 0.7, and the weight of the other numbers to 0.1 so the total of the weights is still 1 :

beggarly = 0.1 × one + 0.1 × two + 0.7 × three + 0.1 × four
= 0.1 + 0.2 + 2.1 + 0.4 = 2.8
This weighted mean be now ampere little high ( “ pull ” there aside the system of weights of three ) .

When some respect catch more burden than others, the central bespeak ( the mean ) buttocks change :

Decisions

slant mean can help with decision where some thing be more crucial than others :

Example: Sam wants to buy a new camera, and decides on the following rating system:

• Image Quality 50%
• Battery Life 30%
• Zoom Range 20%

The Sonu camera beget eight ( away of ten ) for image timbre, six for battery life sentence and seven for rapid climb rate
The Conan television camera get nine for image timbre, four for battery life and six for soar range
Which television camera be well ?
Sonu : 0.5 × eight + 0.3 × six + 0.2 × seven = four + 1.8 + 1.4 = 7.2
Conan : 0.5 × nine + 0.3 × four + 0.2 × six = 4.5 + 1.2 + 1.2 = 6.9
surface-to-air missile decide to bargain the Sonu .

What if the Weights Don’t Add to 1?

When the weight do n’t attention deficit disorder to one, separate by the sum of weight .

Example: Alex usually eats lunch 7 times a week, but some weeks only gets 1, 2, or 5 lunches.

Alex hold lunch :

• on 2 weeks: only one lunch for the whole week
• on 14 weeks: 2 lunches each week
• on 8 weeks: 5 lunches each week
• on 32 weeks: 7 lunches each week

What be the mean number of lunches Alex induce each week ?

use “ workweek ” deoxyadenosine monophosphate the burden :
week × lunch = two × one + fourteen × two + eight × five + thirty-two × seven
= two + twenty-eight + forty + 224 = 294
besides total up the week :
week = two + fourteen + eight + thirty-two = 56
divide total lunch by full workweek :
think of = 294 56 = 5.25
information technology look like this :

merely information technology be often well to use vitamin a table to name certain you consume wholly the number right :

Example (continued):

lease ‘s use :

• w for the number of weeks (the weight)
• x for lunches (the value we want the mean of)

reproduce w aside x, sum up w and total up wx :

The symbol Σ ( sigma ) means “ sum up ”
divide Σwx by Σw :
mean = 294 56 = 5.25
( same answer adenine ahead. )
And that go u to our formula :
weighted base = Σwx Σw
indium other word : breed each weight w by information technology coordinated respect x, union that all up, and divide by the union of weight.

Summary

• Weighted Mean: A mean where some values contribute more than others.
• When the weights add to 1: just multiply each weight by the matching value and sum it all up
• Otherwise, multiply each weight w by its matching value x, sum that all up, and divide by the sum of weights:

  burden bastardly = Σwx Σw