# Fitting Bell Curves to Data Distributions using Visualization

arXiv: https://arxiv.org/abs/2301.04717 · HTML: https://mlsanity.com/paper/2301.04717/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jan 2023.

## 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)

Idealized probability distributions, such as normal or other curves, lie at the root of confirmatory statistical tests. But how well do people understand these idealized curves? In practical terms, does the human visual system allow us to match sample data distributions with hypothesized population distributions from which those samples might have been drawn? And how do different visualization techniques impact this capability? This paper shares the results of a crowdsourced experiment that tested the ability of respondents to fit normal curves to four different data distribution visualizations: bar histograms, dotplot histograms, strip plots, and boxplots. We find that the crowd can estimate the center (mean) of a distribution with some success and little bias. We also find that people generally overestimate the standard deviation, which we dub the "umbrella effect" because people tend to want to cover the whole distribution using the curve, as if sheltering it from the heavens above, and that strip plots yield the best accuracy.