Weighted average
A weighted average gives each value a weight for how much it counts, instead of treating them all the same: multiply each value by its weight, add them up and divide by the sum of the weights.
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Three branches delivered 95%, 80% and 60% of their orders on time. What share of all orders do you think arrived on time?
How to calculate it: multiply each value by its weight, add it all up and divide by the sum of the weights. With an exam score of 82 worth 50%, homework at 90 worth 30% and participation at 100 worth 20%: (82 × 50 + 90 × 30 + 100 × 20) ÷ 100 = 88.
When to use it: whenever the values don't count the same. That happens with a class grade, with prices from purchases of different sizes and, above all, when you combine percentages from groups of different sizes, as in the figure. Averaging three branches' percentages treats the one with 50 orders the same as the one with 1,000.
In Excel: =SUMPRODUCT(B2:B4, C2:C4)/SUM(C2:C4), with the values in B and the weights in C. If what you have is each group's part and total, there's a shortcut: add up all the parts and divide by the sum of all the totals.
Practice it in Can you average percentages?.
How it's used
Average cost of your stock
Three purchases of the same part
- 100 units at $20 · 300 units at $25 · 600 units at $30
- marked: (100 × 20 + 300 × 25 + 600 × 30) ÷ 1,000 = $27.50The simple average would say $25: it would count the 100-unit order the same as the 600-unit one.
- =SUMPRODUCT(B2:B4, C2:C4)/SUM(C2:C4)B: price per unit. C: units. Multiply each pair, add them up, divide by the total units.
When to look closer
What if the weights don't add to 100?
A supplier scorecard, out of 10
- Quality 8 (50%) · Price 9 (30%) · Delivery 10 (40%): 120% in all
- marked: =SUMPRODUCT(B2:B4, C2:C4)
The weights add to 120%. If you just multiply and add, what do you think happens to the supplier's score?
Ask your Maestro about Weighted average
It answers from the free course page closest to this word, the way it answers while you study.
You: What does "Weighted average" mean, in plain words?
Your Maestro: I'll explain it with a case of yours: it sticks better than a definition. Which average at work combines groups of different sizes?
Asking about: Answers from the page "How do I count the missing values in each column with pandas?"
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Related terms
- Percentage
A percentage says how many parts out of every 100 something is. You get it by dividing the part by the total and multiplying by 100: 45 out of 180 customers is 45 ÷ 180 × 100 = 25%.
- Median
The median is the middle value when you sort the data from lowest to highest: half sit below it and half above. In Excel you get it with =MEDIAN(B2:B11).
- KPI (key performance indicator)
A KPI is a number a team tracks to know whether it's doing well at what matters most, like monthly sales or orders delivered on time. It only works if it's well defined, so two people who calculate it get the same answer.