This article is a continuation of our main topic on Measures of Dispersion in Business Statistics. In this section, we explore one of the most fundamental and straightforward absolute measures of dispersion Range along with its relative form, the Coefficient of Range.
What is Range?
The Range is the simplest measure of dispersion. It indicates the spread between the smallest and largest values in a dataset.
Definition:
The range is the difference between the maximum and minimum values in a distribution.
Formula:
Range (R) = Largest value − Smallest value
Symbolically, R = L − S
Example:
Suppose we have the following marks of a student in five tests: 45, 52, 50, 48, 60
- Largest value (L) = 60
- Smallest value (S) = 45
- Range = 60 − 45 = 15
Coefficient of Range
The Coefficient of Range is a relative measure of dispersion. It is unit-free and useful for comparing the variability of two or more datasets.
Formula:
Coefficient of Range = (L − S) / (L + S)
Example:
Using the above data (L = 60, S = 45):
Coefficient of Range = (60 − 45) / (60 + 45) = 15 / 105 ≈ 0.143
Application of Range
Range is commonly used in fields where a quick idea of variability is needed. For example:
- Weather forecasting (temperature variation)
- Stock market (price highs and lows)
- Quality control in manufacturing
Merits of Range
- Very easy to calculate and understand
- Quick indication of data spread
- Useful for preliminary analysis and comparisons
Demerits of Range
- Considers only two values (maximum and minimum), ignoring other data points
- Highly sensitive to extreme values or outliers
- Not a reliable measure for skewed or large datasets
When to Use Range?
- When a quick overview of data spread is needed
- For small datasets with no significant outliers
- In exploratory data analysis where precision is not critical
Range in Grouped Data
For grouped frequency distributions, the range is calculated as:
Range = Upper limit of the highest class − Lower limit of the lowest class
Example:
Class intervals: 10–20, 20–30, 30–40, 40–50
Range = 50 − 10 = 40
Range vs. Other Measures
| Measure | Data Used | Outlier Sensitivity | Complexity |
|---|---|---|---|
| Range | Only Maximum & Minimum | High | Very Low |
| Standard Deviation | All Data Points | Moderate | High |
| Quartile Deviation | Middle 50% of Data | Low | Moderate |
Conclusion
The Range and Coefficient of Range are foundational tools in understanding data variability. While simple and easy to compute, they are best used in small or preliminary datasets. For more comprehensive analysis, one should explore more refined measures like Standard Deviation or Quartile Deviation, which consider more data points and offer better accuracy.