Maths📅 24 March 2025⏱ 4 min read
How to Calculate a Weighted Average
A regular average treats all values equally. A weighted average accounts for the fact that some values matter more than others. Here is the formula and when to use each.
JW
James WhitfieldPersonal Finance & Maths WriterJames has written about personal finance, health metrics, and everyday mathematics for over six years. He holds a BSc in Mathematics from the University of Leeds.
Weighted averages appear in grade calculations, portfolio returns, price indices, and survey analysis. The idea is simple -- values with more importance get more weight in the final average.
Simple vs Weighted Average
Simple average: sum all values, divide by count
Values: 60, 70, 80
Simple average = (60 + 70 + 80) / 3 = 70
Weighted average: multiply each value by its weight, sum, divide by total weight
Same values, different weights:
60 (weight 1), 70 (weight 2), 80 (weight 3)
Weighted average = (60x1 + 70x2 + 80x3) / (1+2+3)
= (60 + 140 + 240) / 6
= 440 / 6 = 73.33
The value of 80 carries more influence, pulling the average up.
Exam Grade Calculation
A-level grade breakdown:
Component A (coursework): 40% weighting, score 72%
Component B (exam 1): 30% weighting, score 58%
Component C (exam 2): 30% weighting, score 81%
Weighted average = (72x0.40) + (58x0.30) + (81x0.30)
= 28.8 + 17.4 + 24.3
= 70.5%
Simple average: (72+58+81)/3 = 70.33%
Close here but can differ significantly when weights and scores vary more.
Investment Portfolio Return
Portfolio:
Fund A: £20,000 value, returned +12%
Fund B: £50,000 value, returned +5%
Fund C: £30,000 value, returned -3%
Total portfolio: £100,000
Weighted return = (20,000x12 + 50,000x5 + 30,000x-3) / 100,000
= (240,000 + 250,000 - 90,000) / 100,000
= 400,000 / 100,000
= +4.0%
Simple average return: (12+5-3)/3 = 4.67%
The simple average overstates performance because the best-performing
fund was the smallest, and the worst-performing is mid-sized.
Weighted Average in Cost Accounting (AVCO)
Average Cost method (AVCO) for stock valuation:
Opening stock: 100 units at £5.00 = £500
Purchase 1: 200 units at £5.50 = £1,100
Purchase 2: 150 units at £6.00 = £900
Total: 450 units, £2,500
Weighted average cost = £2,500 / 450 = £5.56 per unit
Sell 200 units: 200 x £5.56 = £1,111.11 cost of sales
Remaining stock: 250 units x £5.56 = £1,388.89
AVCO smooths out price fluctuations in cost of goods sold,
making profit figures more stable than FIFO (first-in, first-out).