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Related Concept Videos

Range Rule of Thumb to Interpret Standard Deviation01:13

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The range rule of thumb in statistics helps us calculate a dataset's minimum and maximum values with known standard deviation. This rule is based on the concept that 95% of all values in a dataset lie within two standard deviations from the mean.
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The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.
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Updated: Dec 8, 2025

Decomposing the Variance in Reading Comprehension to Reveal the Unique and Common Effects of Language and Decoding
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Estimating the sample variance from the sample size and range.

Jan Rychtář1, Dewey T Taylor1

  • 1Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, Virginia, USA.

Statistics in Medicine
|September 16, 2020
PubMed
Summary
This summary is machine-generated.

This study improves methods for estimating standard deviation (SD) from limited data in clinical trials. New estimators enhance data pooling for meta-analysis and systematic reviews when only range and sample size are available.

Keywords:
SDexponential distributionmeta-analysisnormal distributionrangerule of thumb

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Area of Science:

  • Biostatistics
  • Clinical Trials Methodology
  • Medical Research Synthesis

Background:

  • Meta-analysis and systematic reviews require pooled data from clinical trials.
  • Standard deviation (SD) is crucial for data pooling but often unavailable.
  • Trial reports frequently provide only median, min/max values, and sample size.

Purpose of the Study:

  • To develop improved estimators for standard deviation (SD) when only range and sample size are reported.
  • To enhance the accuracy of data pooling in meta-analyses and systematic reviews.

Main Methods:

  • Improved estimation of the "divisor" (ratio of range to SD) for small sample sizes (n ≤ 100).
  • Validation of new SD estimators using simulated and real datasets.
  • Development of estimators for the divisor for large sample sizes across various distributions.

Main Results:

  • The proposed estimators provide more accurate estimates of SD compared to existing methods.
  • Numerical values and a simple approximation formula for the improved estimator are provided.
  • Effective estimators for the divisor are presented for large sample sizes under different distributional assumptions.

Conclusions:

  • The developed methods offer a practical solution for estimating SD from limited data in clinical trials.
  • Improved SD estimation facilitates more reliable data pooling for meta-analysis and systematic reviews.
  • The findings contribute to more robust evidence synthesis in medical research.