Tip: Press Tab then Enter to calculate quickly.
| Value (xi) | Frequency (fi) | Remove |
|---|---|---|
| Lower (L) | Upper (U) | Frequency (f) | Remove |
|---|---|---|---|
Results
Enter data and click Calculate Mean.
Example Data
These examples illustrate formats supported by the calculator.
| Type | Data | Mean |
|---|---|---|
| Raw | 8, 10, 12, 14, 16, 18 | 13 |
| Value‑Frequency | (10,2), (12,3), (15,5), (18,2) | 14 |
| Grouped Intervals | [0–10):4, [10–20):6, [20–30):5 | ≈ 16.8 |
Formulas Used
- Raw (ungrouped) data:
μ = (Σ xi) / n - Discrete distribution:
μ = (Σ xi fi) / Σ fi - Grouped intervals (approximate):
μ ≈ (Σ mi fi) / Σ fi, wheremi = (Li + Ui) / 2
How to Use This Calculator
- Choose an input mode: Raw Data, Value‑Frequency, or Grouped Intervals.
- Enter numbers, pairs, or intervals with frequencies. Use the examples as templates.
- Click Calculate Mean to compute the arithmetic mean and see detailed steps.
- Export the results and inputs using Download CSV or Download PDF.
- Fix any highlighted validation errors and recalculate as needed.
FAQs
It is the arithmetic average of a dataset or a probability distribution, computed as the sum of values (or midpoints) times frequencies divided by total frequency.
Yes. The calculator accepts negative and decimal values across all modes. Ensure intervals are ordered and non‑overlapping in the grouped mode.
The grouped mean is an approximation using each interval’s midpoint. Accuracy improves with narrower intervals and uniform distributions within classes.
No. For mean, the order of values does not affect the result; duplicates are handled through frequencies or repeated entries.
Practically, browser memory limits apply. For very large datasets, prefer the value‑frequency or grouped input to avoid pasting extremely long raw lists.
Dataset A — Discrete Distribution Example (Value–Frequency)
Small sales basket counts observed over 12 customers.
| xi (items) | fi (customers) | xi·fi |
|---|---|---|
| 1 | 2 | 2 |
| 2 | 4 | 8 |
| 3 | 3 | 9 |
| 5 | 3 | 15 |
| — | Σf = 12 | Σ(x·f) = 34 |
Mean: μ = Σ(x·f)/Σf = 34/12 ≈ 2.833333
Dataset B — Grouped Distribution Example (Intervals)
Response times (ms) grouped into equal-width classes.
| Class [L, U) | Midpoint m | f | m·f |
|---|---|---|---|
| [0, 50) | 25 | 8 | 200 |
| [50, 100) | 75 | 14 | 1050 |
| [100, 150) | 125 | 6 | 750 |
| [150, 200) | 175 | 2 | 350 |
| — | — | Σf = 30 | Σ(m·f) = 2350 |
Approx. Mean: μ ≈ Σ(m·f)/Σf = 2350/30 ≈ 78.333333
Dataset C — Raw Data Example
Daily temperatures (°C) over a week.
| Day | xi (°C) |
|---|---|
| Mon | 28.4 |
| Tue | 31.0 |
| Wed | 29.5 |
| Thu | 30.2 |
| Fri | 27.9 |
| Sat | 26.8 |
| Sun | 29.1 |
| Σx | 202.9 |
| n | 7 |
Mean: μ = Σx/n = 202.9/7 ≈ 28.985714