Calculator Form
Example Data Table
| id | x | y | z | cluster | weight |
|---|---|---|---|---|---|
| 1 | 2.4 | 5.1 | 8.0 | A | 1.0 |
| 2 | 2.8 | 5.4 | 7.6 | A | 1.5 |
| 3 | 9.2 | 1.3 | 3.5 | B | 1.0 |
| 4 | 3.1 | 5.9 | 8.4 | A | 2.0 |
| 5 | 8.9 | 1.7 | 3.1 | B | 1.2 |
| 6 | 2.6 | 5.3 | 8.1 | A | 1.1 |
Formula Used
For cluster c, first select every row where the cluster label equals c. Then choose numeric columns as feature dimensions. The mean center for feature j is:
centerj = sum(xij) / n
The weighted center is:
centerj = sum(wixij) / sum(wi)
The median center uses the middle value of each feature. The trimmed mean removes extreme values from both ends. Euclidean distance is the square root of squared differences. Manhattan distance sums absolute differences.
How to Use This Calculator
- Paste a dataframe style table into the data box.
- Select the delimiter, or leave auto detection enabled.
- Enter the cluster column name, such as cluster.
- Enter the cluster value c, such as A.
- Enter feature columns, or leave blank for numeric detection.
- Choose mean, median, weighted mean, or trimmed mean.
- Pick a missing value rule and distance metric.
- Press the calculate button and export the result.
Understanding a Cluster Center
What the Tool Measures
A cluster center is a compact summary of grouped data. It shows the typical position of one cluster. The calculator reads rows from a dataframe style input. Each row must contain feature values. It must also contain a cluster label. The selected label is called c. Only rows matching c are used. Other rows stay in the dataset. They do not affect the chosen center.
Why Centers Matter
Centers help explain grouped observations. They are useful in segmentation work. They also support quality checks. A center can describe a customer group. It can describe sensor behavior. It can describe location based patterns. Analysts often compare centers between clusters. Large differences show separation. Small differences may show overlap.
Choosing the Right Method
The mean is common and simple. It works well with balanced numeric data. The median is safer with outliers. It resists very large or small values. A weighted mean adds importance to selected rows. Use it when some records matter more. The trimmed mean removes edge values. It gives a stable middle estimate. This is useful for noisy data.
Reading the Output
The result table lists every feature. Each row gives its center value. It also shows count, mean, median, spread, and range. These details help verify data quality. The distance summary measures row closeness. A low average distance means tight grouping. A high value suggests a wide cluster. The nearest row can represent the cluster. Export files help save the analysis.
FAQs
What is cluster c?
Cluster c is the label you want to analyze. The calculator filters rows where the cluster column equals that value.
Can I use column numbers?
Yes. You can enter 1-based column numbers. You can also use header names when the first row contains headers.
Which center method should I choose?
Use mean for normal data. Use median for outliers. Use weighted mean when rows have importance scores. Use trimmed mean for noisy samples.
What does weighted mean require?
It needs a weight column with numeric values. Rows with higher weights pull the center more strongly toward their feature values.
What happens to missing values?
You can skip missing cells, drop incomplete rows, or replace missing values with zero. Choose the rule that matches your analysis.
What is average distance?
It is the average distance from cluster rows to the computed center. Lower values usually mean a more compact cluster.
Can I paste spreadsheet data?
Yes. Copy rows from a spreadsheet and paste them into the data box. Select tab delimiter when needed.
Can I export the result?
Yes. Use the CSV button for table data. Use the PDF button for a printable summary of the calculated center.