# The Weighted Average Illusion: Biases in Perceived Mean Position in Scatterplots

arXiv: https://arxiv.org/abs/2108.03766 · HTML: https://mlsanity.com/paper/2108.03766/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2021.

## Built on by (most cited first, 2 of 2)

- [Visual Validation versus Visual Estimation: A Study on the Average Value in Scatterplots](https://mlsanity.com/paper/2307.09330/) (2023)
- [Beware of Validation by Eye: Visual Validation of Linear Trends in Scatterplots](https://mlsanity.com/paper/2407.11625/) (2024)

## Abstract (arXiv)

Scatterplots can encode a third dimension by using additional channels like size or color (e.g. bubble charts). We explore a potential misinterpretation of trivariate scatterplots, which we call the weighted average illusion, where locations of larger and darker points are given more weight toward x- and y-mean estimates. This systematic bias is sensitive to a designer's choice of size or lightness ranges mapped onto the data. In this paper, we quantify this bias against varying size/lightness ranges and data correlations. We discuss possible explanations for its cause by measuring attention given to individual data points using a vision science technique called the centroid method. Our work illustrates how ensemble processing mechanisms and mental shortcuts can significantly distort visual summaries of data, and can lead to misconceptions like the demonstrated weighted average illusion.