# Scatter Plot Calculator

URL: https://speedycalculator.com/calculators/math/scatter-plot/
Last updated: 2026-10-30

> The scatter plot calculator summarises paired data (x, y): the number of points, means, ranges, the correlation coefficient and the regression line you would draw through the scatter plot.

## Inputs

- x values
- y values (same order)

## Results

- Correlation coefficient r
- Number of points
- Mean of x
- Mean of y
- Range of x
- Range of y
- Trend line slope
- Trend line intercept
- Strength of the linear relationship

## Formula

```
r = Σ(x − x̄)(y − ȳ) ÷ √[Σ(x − x̄)² Σ(y − ȳ)²],  ŷ = a·x + b
```

## Explanation

A scatter plot shows whether two variables move together. Before drawing one, it helps to know its ranges (for the axes), the strength of the relationship (r) and the trend line.

### How to use the Scatter Plot Calculator

- Enter the x values.
- Enter the matching y values in the same order.
- Read the summary and trend line.

Results update as you type, and everything is calculated in your browser.

### How it works

Means and ranges set up the axes; the correlation coefficient measures the linear relationship; the least squares line gives the trend.

### Tips

- Sketch the points first – a quick drawing shows whether a slope should be positive or negative.
- Keep the order of the points consistent in every formula.
- Vertical lines have an undefined slope; horizontal lines have slope zero.
- Use the same units on both axes when you measure distances or angles.

### Common mistakes to avoid

- Swapping x and y coordinates.
- Subtracting the coordinates in a different order in the numerator and denominator of the slope.
- Forgetting that the distance is always positive.

### Inputs explained

FieldWhat to enterx valuesA list of numbers separated by commas, spaces or new linesy values (same order)A list of numbers separated by commas, spaces or new lines

### What each result means

- **Correlation coefficient r** = corr([x values], [y values (same order)])
- **Number of points** = min(count([x values]), count([y values (same order)]))
- **Mean of x** = mean([x values])
- **Mean of y** = mean([y values (same order)])
- **Range of x** = max([x values]) - min([x values])
- **Range of y** = max([y values (same order)]) - min([y values (same order)])
- **Trend line slope** = slope([x values], [y values (same order)])
- **Trend line intercept** = intercept([x values], [y values (same order)])

## Worked example

Inputs — x values: 160, 165, 170, 175, 180, 185; y values (same order): 55, 60, 64, 70, 74, 80.

Results — **Correlation coefficient r = 0.998511**; Number of points = 6; Mean of x = 172.5; Mean of y = 67.166667; Range of x = 25; Range of y = 25; Trend line slope = 0.988571; Trend line intercept = -103.361905; Strength of the linear relationship = Strong.

## Key terms

- **Correlation**: The strength and direction of a linear relationship.

## FAQ

**What does a scatter plot show?**
The relationship between two quantitative variables, one point per observation.

**What does r close to 0 mean?**
No linear relationship – though there may be a curved one.

**What is an outlier?**
A point far from the overall pattern; it can change r a lot.

**Should I always add a trend line?**
Only when the relationship looks roughly linear.

**What formula does the Scatter Plot Calculator use?**
r = Σ(x − x̄)(y − ȳ) ÷ √[Σ(x − x̄)² Σ(y − ȳ)²],  ŷ = a·x + b.


## Sources

- [OpenStax – Introductory Statistics 2e: Scatter plots](https://openstax.org/details/books/introductory-statistics-2e)