Calculator Inputs
Enter raw values, optional frequencies, optional weights, a trim percentage, and preferred decimal precision. Results update after submission.
Example Data Table
This sample dataset shows how the calculator handles repeated values and summarizes the main central tendency measures.
| Observation | Value | Frequency | Weighted Example |
|---|---|---|---|
| 1 | 12 | 1 | 0.7 |
| 2 | 15 | 1 | 0.9 |
| 3 | 15 | 1 | 1.0 |
| 4 | 18 | 1 | 1.1 |
| 5 | 18 | 1 | 1.3 |
| 6 | 18 | 1 | 1.4 |
| 7 | 20 | 1 | 1.0 |
| 8 | 22 | 1 | 0.8 |
| 9 | 24 | 1 | 0.7 |
| 10 | 30 | 1 | 0.6 |
Formula Used
- Arithmetic Mean: Mean = Σx / n
- Median: Middle value after sorting. For even counts, median = (xn/2 + xn/2+1) / 2
- Mode: The value or values with the highest frequency.
- Weighted Mean: Weighted Mean = Σ(wx) / Σw
- Weighted Median: The smallest value where cumulative weight reaches half of total weight.
- Geometric Mean: Geometric Mean = (x1 × x2 × ... × xn)1/n
- Harmonic Mean: Harmonic Mean = n / Σ(1 / x)
- Trimmed Mean: Remove the chosen percentage from both tails, then compute the average of remaining values.
- Midrange: Midrange = (Minimum + Maximum) / 2
- Range: Range = Maximum − Minimum
How to Use This Calculator
- Enter your numeric dataset in the values box.
- Add frequencies only when each value represents repeated observations.
- Add weights when you need weighted mean and weighted median.
- Choose a trim percent and decimal precision.
- Press the calculate button to view results, chart output, and export options.
Frequently Asked Questions
1) What does this calculator measure?
It measures the central location of a dataset using arithmetic mean, median, mode, weighted metrics, trimmed mean, geometric mean, harmonic mean, range, and midrange.
2) When should I use the median instead of the mean?
Use the median when your data has strong outliers or skew. It is more resistant to extreme values than the arithmetic mean.
3) What happens when more than one mode exists?
The calculator returns every value tied for the highest frequency. That means your dataset is multimodal rather than having a single mode.
4) Why would I enter frequencies?
Frequencies help when your data is summarized as value-count pairs. They rebuild the effective dataset without manually repeating the same values.
5) Why might geometric mean be unavailable?
Geometric mean requires all values to be positive. Zero or negative entries break the logarithmic calculation used to compute it safely.
6) Why might harmonic mean be unavailable?
Harmonic mean cannot be calculated when any value is zero, because it relies on reciprocals and division by zero is undefined.
7) What does the trimmed mean help with?
Trimmed mean reduces the effect of unusually small or large observations. It is useful when you want a more stable average without full outlier removal rules.
8) What does the graph show after calculation?
The graph displays the data distribution by value and frequency. It also marks major statistics like mean, median, mode, midrange, and other available lines.