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Range in Statistics

 The Range is the difference between the highest and lowest values in a set of data.

In this post:

  The Range
  The Interquartile Range
  Semi Interquartile Range 
  Max and Min Values

Cite this post

Sutton, G. W. (2026, August 6). Range in statistics. Assessment, Statistics, and Research. https://statistics.suttong.com/2026/08/range-in-statistics.html


In statistics, the Range is represented by the letter "R", the highest value is the Maximum abbreviated as Max and the smallest value is the Minimum abbreviated as Min. To calculate the range, subtract Min from Max.

R = Max - Min

Example:

Rating Scale Data Set: 2,3,4,5,7

R = 7 - 2. R = 5

Using the Range

The range is used in conjunction with the median (Mdn), Max and Min to describe basic characteristics of a set of values. The range is a rough index of the spread of values in a data set. Statisticians refer to the spread as dispersion thus, the range is a measure of dispersion. The Median and the Range may better represent a data set when extreme values distort the mean and standard deviation.

Another example:

Data set of IQ scores: 71, 84, 100, 122, 131.

R = 131 - 71. R = 60.

Interquartile Range (IQR)

The Interquartile Range (IQR) describes the spread of the middle half of a data set. The quartiles are the four sections of a data set. The median, is the middle of a data set so, half of the values are above the median and half are below the median. The first quartile (Q1) is the median of the lower half of values. The third quartile (Q3) is the median of the upper half of values. The Interquartile Range is the difference between Q3 and Q1, which tells you the spread of the middle half of the data in the data set.

IQR and Percentages

Another way to understand IQR is to think of what percentage of scores can be found in each part of a data set.

The Median is the middle score so 50% of the scores are above the Mdn and 50% are below it.

Each quartile contains 25% of the scores.

  

Quartiles

How to Calculate the Interquartile Range

1. Arrange the data from the lowest to the highest value.

2. Find the median (the middle value) which is Q2.

3. Use the median to separate your data set into two halves (half above and half below the median).

4. Find the median of each half:

  Q1 is the median of the lower half.

  Q3 is the median of the upper half.

5. Calculate IQR. IQR = Q3-Q1.

In words, find the Interquartile Range by subtracting Q1 from Q3.

Example

Dataset: 85 98 99 103 106 113 116

Mdn = 103

Lower half = 85 98 99. Median of lower half = 98 (Q1)

Upper half = 106 113 116. Median of the upper half = 113 (Q3)

IQR = 113 - 98. IQR = 15

Using the IQR

The Interquartile Range is useful for detecting extreme values in a data set. Extreme values are called outliers in statistics. Sometimes an extreme value or score is a true data point, but sometimes they represent mistakes or errors. Whatever the reason, outliers can interfere with understanding what is typical of the values or scores that represent some measured characteristic of a sample or an entire population of values.

Semi Interquartile Range (SIQR)

The semi interquartile range is half of the interquartile range. Divide the IQR by 2 to find the SIQR. In the example, the IQR was 15. Half of 15 is 7.5. The semi interquartile range is 7.5, which reveals the set of scores closer to the middle of the dataset than those in the IQR.

Reference for using scales in research:

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Post Author

Geoffrey W. Sutton, Professor Emeritus of Psychology at Evangel University, holds a master’s degree in counseling and a PhD in psychology from the University of Missouri-Columbia. His postdoctoral work encompassed education and supervision in forensic and neuropsychology. As a licensed psychologist, he conducted clinical and neuropsychological evaluations and provided psychotherapy for patients in various settings, including schools, hospitals, and private offices. During his tenure as a professor, Dr. Sutton taught courses on psychotherapy, assessment, and research. He has authored over one hundred publications, including books, book chapters, and articles in peer-reviewed psychology journals. His website is https://suttong.com You can find Dr. Sutton's books on   AMAZON    and  GOOGLE. Many publications are free to download at ResearchGate   and Academia  

 

Note

Most clinicians and researchers calculate and report the mean and standard deviation for their data; however, when the data are skewed the median, range and interquartile range may be a better choice of statistics to describe a data set. A common example, can be found in the tendency to report age means and standard deviations for traditional college student samples in psychology classes whose ages may mostly fall between 18 and 21 with a few above age 30. Likely, the median and range would be more informative.




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