Input
Non-numeric tokens are ignored. Decimals allowed. Thousands separators not required.
| Value | Frequency / Weight |
|---|
Leave frequency as 1 for simple lists. Weights allowed.
Removes that percent from both ends after sorting.
0 disables. Larger removes extreme standardized values.
Results
Waiting for input…
Enter data and click Calculate to see results.
Example data table
| Value | Frequency |
|---|---|
| 12 | 1 |
| 15 | 2 |
| 16 | 1 |
| 21 | 1 |
| 24 | 2 |
| 30 | 1 |
This example yields an arithmetic mean of 19.625.
Formula used
Arithmetic mean (list mode): \\( \\bar{x} = \\frac{1}{n}\\sum_{i=1}^n x_i \\) → implemented as sum of values divided by count.
Weighted/Grouped mean (value–frequency): \\( \\bar{x}_w = \\frac{\\sum_i w_i x_i}{\\sum_i w_i} \\) where w_i are frequencies/weights.
Trimmed mean: sort values; drop \\lfloor n p \\rfloor items from both tails for trim rate p; compute mean on the remainder.
Outlier filter (optional): compute mean and sample standard deviation; remove observations with |z_i| > z_{cut} where z_i = (x_i-\\bar{x})/s.
How to use this calculator
- Choose an input mode: list of numbers or value–frequency table.
- Paste numbers or populate the table. Frequencies may be any positive weights.
- Optionally set decimals, trimming percent, and an outlier z-threshold.
- Click Calculate. Review results and the processed-data table.
- Export your results as CSV or PDF using the buttons provided.
Note: Trimming is applied before outlier filtering for stability.
FAQs
Commas, spaces, tabs, semicolons, and newlines are accepted. Non-numeric tokens are ignored automatically.
No. Any positive weights work. The weighted mean divides by the sum of weights.
Values are sorted; the chosen percentage is dropped from both tails. Remaining data are used for the mean.
If enabled, observations with absolute z-scores above the threshold are excluded, using the sample standard deviation.
Yes. CSV and PDF exports include key summary statistics and the final processed data used to compute the mean.
Reference: Mean variants and when to use them
| Type | Supported here? | Formula | Typical use |
|---|---|---|---|
| Arithmetic mean | Yes | (Σx)/n | Continuous data without weights. |
| Weighted mean | Yes | (Σ w·x)/(Σ w) | Frequencies or importance weights. |
| Trimmed mean | Yes | Mean of middle after removing tails | Robust summary with outliers present. |
| Outlier-filtered mean | Yes | Mean after |z| > zcut removal | Extreme spikes handling. |
Benchmark datasets and expected means
| Dataset | Values / Weights | n or Σw | Expected mean |
|---|---|---|---|
| A (symmetric) | [2, 4, 6, 8] | 4 | 5 |
| B (weighted) | 10(w=2), 30(w=1), 50(w=3) | Σw = 6 | 33.3333 |
| C (trimmed 20%) | [5, 5, 6, 7, 7, 100] | 6 → trim 1 each tail | 6.25 |
Use these to quickly verify the calculator’s results match the references.