Mean Range Plot

TL;DR

Visualizes each sample’s average (mean) against its variability (range).
Helps spot points that deviate substantially from others (potential outliers).
Indicates data reliability: a wide spread in ranges suggests higher variability; a narrow spread suggests greater consistency.

Definition

A mean-range plot is a type of statistical chart that shows the relationship between the mean and range of a set of data. The mean is the average of all the data points, and the range is the difference between the highest and lowest values in the data set.

Explanation

To create a mean-range plot, plot the mean on the y-axis and the range on the x-axis. Then plot each sample as a point on the chart. The plotted points display how the central tendency (mean) relates to the spread (range) within the data.

Interpreting the plot:

Points that lie noticeably above or below the cluster of others may indicate outliers in the underlying data.
A wide distribution along the x-axis (range) suggests greater variability and lower reliability of the data.
A relatively narrow distribution of ranges suggests the data are more consistent and can be used with greater confidence.

Examples

Heights of 10 people

For a data set representing the heights of 10 people in a group:

The mean is the average height of all 10 people.
The range is the difference between the tallest and shortest person in the group.
A mean-range plot would show each observation’s mean (y-axis) versus its range (x-axis) to visualize their relationship.

Use cases

Identifying potential outliers by locating points that deviate substantially from others on the plot.
Evaluating the reliability of a data set by assessing the spread of range values.

Notes or pitfalls

Identified outliers may be removed to improve the accuracy of subsequent analyses, but removal should be considered carefully.
A wide range of values on the x-axis may indicate that the data are not very reliable due to high variability.

Mean
Range
Outlier
Variability