Maths⏱ 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.
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).