• Skip to secondary menu
  • Skip to main content
  • Skip to primary sidebar
  • My Store
  • Glossary
  • Home
  • About Me
  • Contact Me

Statistics By Jim

Making statistics intuitive

  • Graphs
  • Basics
  • Hypothesis Testing
  • Regression
  • ANOVA
  • Probability
  • Time Series
  • Fun

Range Rule of Thumb: Overview and Formula

By Jim Frost 2 Comments

What is the Range Rule of Thumb?

The range rule of thumb allows you to estimate the standard deviation of a dataset quickly. This process is not as accurate as the actual calculation for the standard deviation, but it’s so simple you can do it in your head.

Photo of a thumb with a smiley face.Use this method when you need a rough estimate quickly or have a dataset summary that doesn’t provide enough information to calculate the actual standard deviation.

The range of a dataset is simply the maximum value minus the minimum value. So, you can estimate the StDev knowing only those two values.

The range and standard deviation are both measures of variability, but there is no precise mathematical relationship between the two. However, you can use the range to estimate the standard deviation.

Range Rule of Thumb Formula

The range rule of thumb formula is the following:

Range rule of thumb formula.

Subtract the smallest value in a dataset from the largest and divide the result by four to estimate the standard deviation.

In other words, the StDev is roughly ¼ the range of the data.

Example Calculations

Let’s apply the range rule of thumb formula to actual data. From a research study I helped run, I have a dataset containing 88 heights. Download the Excel data file: RangeRuleofThumb.

Excel’s descriptive statistics say the height data have the following properties:

  • Mean: 1.51m
  • Standard Deviation: 0.07m
  • Maximum: 1.66m
  • Minimum: 1.33m

Now suppose you’re reading a summary of the height dataset. While the summary includes the maximum and minimum value, pretend it doesn’t list the StDev. Let’s try it out!

Example calculations for the range rule of thumb.

Voila, you have estimated the StDev using two numbers from the dataset!

The range rule of thumb’s estimate (0.08) is close to the correct standard deviation of 0.07.

How Does the Range Rule of Thumb Work?

It might seem odd that you can just divide the range by four to estimate the standard deviation. However, the range rule of thumb uses the properties of the normal distribution and the empirical rule.

When data follow the normal distribution, the empirical rule states that 95% of the values fall between the mean ± 2 StDevs.

Graph of the standard normal distribution that displays the empirical rule percentages.

Given these properties, virtually all values in a sample fall within a four standard deviation spread that centers on the mean.

Therefore, the range of a dataset approximates the four StDev spread. Hence, dividing the range by four approximates one StDev.

Limitations

By understanding how it works, you can work out its limitations. The range rule of thumb:

  • Works best with data that at least roughly follow a normal distribution.
  • Is sensitive to outliers. One unusually high or low value can affect the estimate.
  • Depends on the sample size. Very small samples tend to underestimate, while very large samples overestimate.
  • Does not produce more precise estimates with larger sample sizes, unlike most estimates.

Share this:

  • Tweet

Related

Filed Under: Basics Tagged With: analysis example, distributions

Reader Interactions

Comments

  1. Riccardo says

    May 18, 2023 at 5:53 am

    Which is the optimal dimension of the datased to make this rule of thumb work best? Is it in the order of 100 sample points as in the example?

    Reply
    • Jim Frost says

      May 18, 2023 at 5:28 pm

      Hi Riccardo,

      I was curious about this myself, so I ran a simulation study. I drew random samples from a standard normal distribution that ranged in size from 5 to 200. I calculated the actual standard deviation and the range rule of thumb estimate for each sample. Then found the difference: Range Rule of Thumb – Actual StDev.

      The Y-units are standard deviations. So, a difference of 1 indicates that the rule of thumb was higher than the actual standard deviation by 1 SD (or 100%). -1 indicates it’s lower by 1 SD (-100%). Of course, no difference was a large as a full SD in either direction.

      Below are the results.
      Scatter plot that illustrates the range rule of thumb's accuracy by different sample sizes.

      There seems to be a sweet spot for samples between 15 – 35. In this range, the rule of thumb is off by an overall average of 0.6%. The lower end of that range tends to underestimate by about 3% while the upper end overestimates by 4%. As your sample size goes further outside that range, smaller samples tend to underestimate by more and larger samples will tend to overestimate by more.

      Samples sizes around 100 (between 95 and 105), tend to overestimate by 23%. The largest samples in my study overestimated by an average of about 40%.

      Also notice how larger sample sizes do not produce more precise estimates. They’re not only biased high (see above), but the vertical spread of estimates also increases as sample size increases. Usually with estimates, larger sample sizes will reduce the spread (greater precision).

      The range rule of thumbs only gives you a rough idea of the standard deviation. However, knowing the sample size can help you adjust its estimate. Also note that these results apply to data the follow a normal distribution. It’s likely to differ with other distributions.

      My dataset has n=88. Based on the above, you’d expect the range rule of thumb estimate to be about 23% too high. In reality it was 14.3% too high, but it’s well within the spread of values on the graph for a sample of that size.

      Reply

Comments and Questions Cancel reply

Primary Sidebar

Meet Jim

I’ll help you intuitively understand statistics by focusing on concepts and using plain English so you can concentrate on understanding your results.

Read More...

Buy My Introduction to Statistics Book!

Cover of my Introduction to Statistics: An Intuitive Guide ebook.

Buy My Hypothesis Testing Book!

Cover image of my Hypothesis Testing: An Intuitive Guide ebook.

Buy My Regression Book!

Cover for my ebook, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models.

Subscribe by Email

Enter your email address to receive notifications of new posts by email.

    I won't send you spam. Unsubscribe at any time.

    Follow Me

    • FacebookFacebook
    • RSS FeedRSS Feed
    • TwitterTwitter

    Top Posts

    • How to Interpret P-values and Coefficients in Regression Analysis
    • How To Interpret R-squared in Regression Analysis
    • F-table
    • Multicollinearity in Regression Analysis: Problems, Detection, and Solutions
    • Weighted Average: Formula & Calculation Examples
    • Z-table
    • Mean, Median, and Mode: Measures of Central Tendency
    • How to do t-Tests in Excel
    • One-Tailed and Two-Tailed Hypothesis Tests Explained
    • Interpreting Correlation Coefficients

    Recent Posts

    • Sum of Squares: Definition, Formula & Types
    • Mann Whitney U Test Explained
    • Covariance: Definition, Formula & Example
    • Box Plot Explained with Examples
    • Framing Effect: Definition & Examples
    • Trimmed Mean: Definition, Calculating & Benefits

    Recent Comments

    • Jerry on Sum of Squares: Definition, Formula & Types
    • Karly on Choosing the Correct Type of Regression Analysis
    • Jim Frost on How to Interpret P-values and Coefficients in Regression Analysis
    • Miriam on How to Interpret P-values and Coefficients in Regression Analysis
    • Klaus on Linear Regression Equation Explained

    Copyright © 2023 · Jim Frost · Privacy Policy