Mid Range

TL;DR

• A simple central-value summary found by averaging the minimum and maximum of a dataset.
• Quick to compute and gives a rough sense of the dataset’s center.
• Not robust: sensitive to outliers and extreme values.

Definition

Mid-range, also known as the mid-maximum range, is a measure of central tendency calculated by taking the average of the highest and lowest values in a dataset.

Explanation

The mid-range identifies the “middle” of a dataset by averaging its smallest and largest observations. It provides a quick summary of where values are centered when considering the dataset’s extremes. Because it depends only on the minimum and maximum, the mid-range can be strongly affected by extreme values (outliers) and so is not considered a particularly robust measure of central tendency. It is most useful for small or moderately-sized datasets or when a rapid, simple summary of the data’s center is needed.

Examples

Exam scores

Suppose we have a dataset of exam scores for a class of students. The scores range from 60 to 95, with a mid-range of 77.5. This tells us that the majority of students scored between 60 and 95 on the exam, with the average score being 77.5.

Home prices

A dataset of home prices in a particular neighborhood ranges from $200,000 to$400,000, with a mid-range of $300,000. This indicates that the majority of homes in the neighborhood are priced between$200,000 and $400,000, with the average price being$300,000.

Use cases

• Useful when working with small or moderately-sized datasets where the influence of extreme values is less significant.
• Serves as a quick and easy way to identify the dataset’s middle for a rapid summary.

Notes or pitfalls

• The mid-range is not a particularly robust statistic because it is sensitive to outliers and can be affected by extreme values in the dataset.

Related terms

• Mid-maximum range
• Measure of central tendency
• Outlier