Measures of Variation: What is Range?

Definition of Measures of Variation

Let’s first understand what we mean by the phrase ‘measures of variation’. Measures of variation can be explained as a mathematical value that can represent variation among the data points in a given data set.

What is Variation?

In this post, we will only briefly explain what variation is. We intend to write a series of 3 articles on measures of variation which will cover Range, Variance, and Standard Deviation. By the end of these 3 articles, you will be able to explain what variation means.

For now, understand that variation simply is the difference between various data points in a data set. In other words, variation is termed as dispersion or spread in data. That is, how much spread / dispersion exists within the data points in a given data set. The simplest ways to measure variation is range.

What is Range?

Mathematically, range is the difference between the lowest value in a data set and the highest value in the data set. The formula to calculate range is:

Range = Max Value – Min Value

For example, you decide to find out the variation in the amount of time it takes you to reach your office and you decide to collect the data for 20 days. You get the following data:

Date Time Taken to Reach Office [In Mins]
05/07/2017 46
05/08/2017 52
05/09/2017 57
05/10/2017 57
05/11/2017 53
05/12/2017 35
05/13/2017 40
05/14/2017 35
05/15/2017 56
05/16/2017 56
05/17/2017 33
05/18/2017 58
05/19/2017 42
05/20/2017 45
05/21/2017 35
05/22/2017 34
05/23/2017 43
05/24/2017 42
05/25/2017 57
05/26/2017 55

 

Can you calculate the range for the data above? Follow the steps below:

Step 1: Find out the max value in the data set. In the example, the max value is 58 mins.

Step 2: Find out the min value. In our example, the min value is 33 mins.

Step 3: Apply the range formula (Range = Max Value – Min Value). For our example, the range is 25 mins (58 mins – 33 mins).

How to Interpret Range?

In our example, we learnt that the range of data is 25 mins. That means, that there is a simple variation of 25 mins in the sample you collected. In other words, there is a spread of 25 mins between the minimum time it takes you to reach office and the maximum time.

How to Calculate Range in Microsoft Excel?

There is no direct formula to calculate range in MS Excel. To find range in MS Excel, follow the steps below:

Step 1: Find the Max Value in the data set.

You do so by applying the formula “=MAX(ARRAY)” to find out the max value in the data set. Refer to picture below:

Step 2: Find the Min Value in the data set.

Apply the formula “=MIN(ARRAY)” to find out the min value. Refer to picture below:

Step 3: Subtract the Min Value from the Max Value to find out the Range.

Hope you enjoyed learning! Please leave your comments in the comments section below to give us feedback!

 

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