Enter Data
| # | Value | Weight (weighted mean only) | Remove |
|---|
Results
Example Data Table
| # | Value | Weight |
|---|---|---|
| 1 | 10 | 1 |
| 2 | 12 | 1 |
| 3 | 11 | 2 |
| 4 | 9 | 1 |
| 5 | 14 | 3 |
Click “Load example” above to inject these rows into the calculator.
Formula Used
- Arithmetic mean: x̄ = (Σxᵢ) / n
- Weighted mean: x̄_w = (Σwᵢxᵢ) / (Σwᵢ)
- Geometric mean (all values > 0): G = (∏xᵢ)^(1/n)
- Harmonic mean (no zeros): H = n / (Σ(1/xᵢ))
- Trimmed mean: sort values, remove p% lowest and highest, then apply arithmetic mean on the remaining data.
- Outliers (IQR): compute Q1, Q3, IQR=Q3−Q1. Exclude values < Q1−1.5·IQR or > Q3+1.5·IQR when enabled.
How to Use This Calculator
- Select the Average Type you need.
- Add rows manually, paste values, or upload a CSV.
- Set weights only if using the weighted mean.
- Optional: enable Exclude outliers for IQR-based filtering.
- For Trimmed mean, set the trim percent per tail.
- Choose decimal places, then click Compute Average.
- Download results to CSV or PDF as needed.
Data entry accepts integers or decimals. Non-numeric and empty cells are ignored.
how to find the average rate of change calculator?
Definition. The average rate of change between x = a and x = b is (f(b) − f(a)) / (b − a). With tabular data, use (y₂ − y₁) / (x₂ − x₁).
- Collect two points (x₁, y₁) and (x₂, y₂).
- Compute the slope: (y₂ − y₁) / (x₂ − x₁).
- For multiple intervals, compute each interval’s slope.
- To summarize many intervals, use this tool’s weighted mean with weights equal to interval length (x₂ − x₁), or use arithmetic mean for equal lengths.
Example. From (1, 3) to (5, 11): slope = (11 − 3) / (5 − 1) = 8 / 4 = 2. For three equal-length segments with slopes 1.6, 2.0, 2.4, their average is (1.6 + 2.0 + 2.4) / 3 = 2.0.
Which average should I use?
- Arithmetic mean: baseline for general numeric data.
- Weighted mean: when observations carry different importance.
- Geometric mean: multiplicative growth, indexes; all values > 0.
- Harmonic mean: rates with fixed total, e.g., speed per distance.
- Trimmed mean: robust center when outliers may distort.
Tip: If data include zeros or negatives, avoid geometric mean. If any value is zero, harmonic mean becomes undefined.
Averages of averages and rates
Weighted, not naive. To combine subgroup means, weight each mean by its subgroup size. Example: two classes with means 80 (20 students) and 90 (10 students). Overall mean is (80×20 + 90×10)/(20+10) = 83.33, not (80+90)/2.
Rates. For speeds over equal distances, use the harmonic mean. Example: 60 km/h out, 30 km/h back, equal distance: HM = 2 / (1/60 + 1/30) = 40 km/h.
Different interval lengths. When rates apply over different time or distance lengths, use the weighted mean with weights equal to interval length.