Average Calculator
Calculate mean (average), weighted average, or average rate of change in seconds. Paste numbers (comma/space/newline-separated), choose options, and get clear results with optional step-by-step.
Background
An average is a single value that summarizes a set of numbers. The most common is the mean (sum ÷ count). A weighted average gives more importance to some values via weights (Σ(w·x) ÷ Σ(w)). Average rate of change describes how fast a value changes between two points (Δy ÷ Δx).
How to use this calculator
- Choose Mean, Weighted Average, or Average Rate of Change.
- Enter the values (or pairs) shown for that mode.
- Click Calculate to get the answer + optional steps.
How this calculator works
- Mean: mean = Σx / n
- Weighted: weighted mean = Σ(w·x) / Σw
- Rate of change: average rate = (y₂ − y₁) / (x₂ − x₁)
Formula & Equation Used
Mean: x̄ = (x₁ + x₂ + … + xₙ) / n
Weighted average: x̄_w = Σ(wᵢxᵢ) / Σ(wᵢ)
Average rate of change: (y₂ − y₁) / (x₂ − x₁)
Example Problems & Step-by-Step Solutions
Example 1 — Mean
Find the average of 78, 82, 90, 86.
- Sum: 78 + 82 + 90 + 86 = 336
- Count: n = 4
- Mean: 336 ÷ 4 = 84
Example 2 — Weighted average
Final grade: Exam 90 (30%), Homework 80 (70%).
- Compute: (90×0.30) + (80×0.70) = 27 + 56 = 83
- Answer: 83
Example 3 — Average rate of change
From (0, 10) to (5, 25):
- Δy = 25 − 10 = 15
- Δx = 5 − 0 = 5
- Rate = 15 ÷ 5 = 3 units per x
Frequently Asked Questions
Q: What’s the difference between mean and weighted average?
Mean treats all values equally. Weighted average lets some values count more using weights.
Q: Do weights need to sum to 1?
Not necessarily. This calculator can auto-normalize weights, or you can require a strict sum-to-1 check.
Q: What if my list includes invalid entries?
Invalid tokens are ignored and listed so you can fix them.
Q: Is average rate of change the same as slope?
Between two points, yes: it’s the slope of the secant line between those points.
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