Measures of Variance

The Range

Learning Objectives

Calculate the range by first calculating the maximum and minimum value in a data set.

The Range, by definition, is the difference between the greatest and smallest values within a data set.

  • It is easy to find and easy to understand,
  • but only takes into account two of the numbers, the smallest and the largest
  • and ignores all the rest.

Example 5.1.1

Let’s look at these 3 sets of numbers:

Data Set Value 1 Value 2 Value 3 Value 4 Value 5 Value 6 Value 7
#1 20 25 30 35 40 45 50
#2 20 21 22 23 24 25 50
#3 20 45 46 47 48 49 50

Let’s examine their ranges:

Data Set Max Value Min Value Range
#1 50 20 50−20 = 30
#2 50 20 50−20 = 30
#3 50 40 50−20 = 30

For these 3 sets of numbers, they have the same range of 30, but they are spread out differently.

  • In the first set, the numbers are equally spaced.
  • In the second set, all the numbers except one are located at the lower end.
  • In the third set, all the numbers except one are concentrated at the upper end.
  • All the numbers in the middle, between 20 and 50, are ignored.
  • For this reason, the range is NOT a very good measure of dispersion, or how the numbers are spread apart.

Example 5.1.2 (Excel)

Let us try this example in Excel:

using the =max() and =min() formulas gives us the ranges shown below:

Click here to download the spreadsheet shown above.

Key Takeaways

Key Takeaways: The Range

  • It is easy to find and easy to understand
  • It only takes into account two of the numbers, the smallest and the largest
  • It is simple but not often the best measure of average dispersion/spread of the data

Your Own Notes

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An Introduction to Business Statistics for Analytics (1st Edition) Copyright © 2024 by Amy Goldlist; Charles Chan; Leslie Major; Michael Johnson is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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