Statistics Sum of XY Calculator

Calculator Input

Example Data Table

Formula Used

Sum of XY: Σxy = x₁y₁ + x₂y₂ + x₃y₃ + ... + xₙyₙ

Mean X: x̄ = Σx / n

Mean Y: ȳ = Σy / n

Cross Deviation: SP = Σxy - (Σx × Σy / n)

Sample Covariance: sxy = SP / (n - 1)

Population Covariance: σxy = SP / n

Correlation: r = SP / √(Sxx × Syy)

Regression Slope: b = SP / Sxx

How to Use This Calculator

1. Enter paired x and y values in the text area.
2. Put each pair on a new line.
3. Use optional scale and shift fields when values need adjustment.
4. Select decimal places for rounded output.
5. Press Calculate to view sum of xy and related results.
6. Use CSV or PDF buttons to save the report.

Statistics Sum of XY Calculator Guide

Purpose

The statistics sum of xy calculator helps you study paired numerical data. It multiplies every x value by its matching y value. Then it adds all products into one useful total. This total is written as Σxy. It is important in regression, correlation, covariance, and many data tables.

Why Σxy Matters

Paired values often describe connected measurements. A teacher may compare study hours and scores. A business may compare price and demand. A researcher may compare weight and height. The x column gives one variable. The y column gives another variable. Their product shows how both variables move together. The total of those products supports deeper analysis.

Advanced Output

This calculator does more than basic multiplication. It also finds Σx, Σy, Σx², and Σy². These totals help build regression equations. They also support covariance and correlation calculations. The tool computes cross deviation. It gives sample covariance and population covariance. It also estimates the correlation coefficient. A simple regression slope and intercept are included.

Data Adjustment

Sometimes raw values need conversion before analysis. You may multiply x or y values by a scale. You may also add a shift. This is useful for unit conversion. It also helps when coded data must be restored. The calculator keeps raw and adjusted values visible. That makes checking easier.

Practical Use

Enter one x,y pair on each line. The calculator accepts commas, spaces, semicolons, and pipes. This flexible entry method helps with copied data. After calculation, review the table. Check each xy product. Then review the final totals. Export the result when you need a saved record.

Accuracy Notes

Clean data gives better results. Make sure each x value has one matching y value. Remove blank or incomplete rows. Use the rounding field only for display. The internal calculations still use numeric values. For serious statistical work, check outliers first. A single extreme pair can change Σxy, covariance, and correlation.

FAQs