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Related Concept Videos

Calculating Standard Deviation01:08

Calculating Standard Deviation

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The standard deviation is the most common measure of variation. It is a value that tells us how far a data value is from the mean value in a dataset. Further, the standard deviation is always a positive value or zero.
The standard deviation value is small when all the data is concentrated close to the mean. Here the data exhibits low variation. The standard deviation value is larger when the data values are more spread out from the mean. Here, the data displays high...
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Range Rule of Thumb to Interpret Standard Deviation01:13

Range Rule of Thumb to Interpret Standard Deviation

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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.
For instance, the range rule of thumb can be used to find the tallest and the shortest student in a class, given the mean student height and standard deviation. If the mean student height is 1.6 m and the standard deviation, s is 0.05 m, the height...
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Empirical Method to Interpret Standard Deviation01:09

Empirical Method to Interpret Standard Deviation

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The empirical rule, also known as the three-sigma rule, allows a statistician to interpret the standard deviation in a normally distributed dataset. The rule states that 68% of the data lies within one standard deviation from the mean, 95% lies within two standard deviations from the mean, and 99.7% lies within three standard deviations from the mean. Additionally, this rule is also called the 68-95-99.7 rule.
This rule is used widely in statistics to calculate the proportion of data values...
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Testing a Claim about Standard Deviation01:19

Testing a Claim about Standard Deviation

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A complete procedure to test a claim about population standard deviation or population variance is explained here.
The hypothesis testing for the claim of population standard deviation (or variance) requires the data and samples to be random and unbiased. The population distribution also must be normal. There is no specific requirement on the sample size as the estimation is based on the chi-square distribution.
As a first step, the hypothesis (null and alternative) concerning the claim about...
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Introduction to Normal Distributions01:29

Introduction to Normal Distributions

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Standardized test scores often follow a symmetric distribution that can be modeled with the normal distribution, a fundamental concept in statistics. This distribution is particularly useful for interpreting test performance fairly across populations, as it provides a mathematical framework for understanding variability and central tendency in large datasets.From Histogram to Frequency DistributionRaw test data are often displayed using histograms, where the height of each bar represents the...
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Variation: Normal Distribution, Range, and Standard Deviation02:32

Variation: Normal Distribution, Range, and Standard Deviation

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In the field of psychology, there are several ways to organize measurements of a trait, feature, or characteristic (i.e., variables). Qualitative data, such as ethnicity, can be tabulated into a frequency count to provide information about the proportion, as well as the variety of groups in a sample or population. On the other hand, researchers can perform a wider set of calculations on quantitative data. The mean, mode, and median, for instance, are central tendency measures to identify a...
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Related Experiment Video

Updated: Apr 22, 2026

Author Spotlight: Validation of SICOLE-R for Assessing Cognitive and Reading Skills in Spanish-Speaking Children and Its Role in Personalized Education
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A better norm-referenced grading using the standard deviation criterion.

Wing-shing Chan1

  • 1a Office of Educational Services, Faculty of Medicine , The Chinese University of Hong Kong , Shatin , Hong Kong.

Teaching and Learning in Medicine
|October 16, 2014
PubMed
Summary

Standard deviation grading offers a more accurate and flexible approach to norm-referenced grading compared to fixed percentiles. This method better reflects students' differential achievements in educational assessments.

Keywords:
gradingnorm-referencedstandard deviation

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Area of Science:

  • Educational Assessment
  • Medical Education Statistics

Background:

  • Traditional norm-referenced grading uses fixed percentiles, which can obscure score distributions.
  • This method fails to account for the actual score differences between students.

Purpose of the Study:

  • To propose a simple norm-referenced grading method using standard deviation for routine educational assessment.
  • To offer an alternative to fixed percentile grading systems.

Main Methods:

  • Utilized the standard deviation of a student's score from the class mean as a measure of achievement.
  • Employed the cumulative probability of a normal distribution to determine grade allocations.
  • Illustrated the method using results from the top 12 students in a medical examination.

Main Results:

  • Grading by standard deviation demonstrated superior cutoffs for allocating grades based on differential student achievement.
  • This approach reduced the likelihood of arbitrary cutoffs between closely scored students compared to fixed percentiles.
  • The method proved more effective in reflecting individual academic performance.

Conclusions:

  • Grading by standard deviation is more advantageous and flexible than fixed percentile grading for norm-referenced assessments.
  • This statistical approach enhances the precision of educational grading systems.
  • The method provides a more nuanced evaluation of student performance.