How this calculator works
A scatter plot places each observed pair at its x and y coordinates. Pairing must be preserved: sorting one list on its own changes the observations. The point table can retain input order or sort complete pairs by x. Repeated locations represent multiple observations and remain in the statistics, even though their marks would overlap in a drawing. Ranges help choose axis limits. Correlation measures linear alignment and is omitted when either axis has no variation. This tool does not fit a regression line or render the chart.
Formula
x range=max(x)-min(x); y range=max(y)-min(y); means=sum(values)/n. Pearson r=sum((x-xMean)(y-yMean))/sqrt(sum((x-xMean)^2) sum((y-yMean)^2)).
Worked example
The pairs (1,4), (2,3), (2,3), (4,1) contain four observations at three distinct locations. Their means are x=2.25 and y=2.75. Each axis spans 3 units, and the perfect decreasing alignment gives correlation -1.
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Frequently asked questions
Why do repeated pairs count more than once?
They are separate observations, even when a scatter plot places their marks at the same location.
Can I use a constant x value?
Yes. Those points form a vertical stack. The x range is zero and linear correlation is undefined, so that output is omitted.
Does correlation describe the whole pattern?
No. A curved relationship can have zero linear correlation. A rendered scatter plot is needed to assess shape, clusters and outliers.
Can this page draw the chart?
The current engine supports numeric and text outputs. Use the returned pairs in a plotting application for a visual scatter plot.