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Related Concept Videos

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The sampling variability of a statistic is defined as how much the statistic varies from one sample to another. The sampling variability of a statistic is typically measured by measuring its standard error.
The standard error of the mean is an example of a standard error. It is a unique standard deviation known as the standard deviation of the sampling distribution of the mean. The standard error of the mean is a statistic that calculates how correctly a sample distribution represents a...
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Standard Deviation of Calculated Results01:14

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Standard deviation measures the spread of data around the mean value. Many large data sets follow a Gaussian distribution, also known as a normal distribution. This distribution is bell-shaped curved, with the most frequently observed value (mean or central value) in the middle. The farther away from the central value, the greater the deviation from the central value, and the lower the frequency.
A broad Gaussian distribution curve has a wider standard deviation, representing a data set with...
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Calculating Standard Deviation01:08

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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.
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Variation: Normal Distribution, Range, and Standard Deviation02:32

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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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A complete procedure to test a claim about population standard deviation or population variance is explained here.
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Empirical Method to Interpret Standard Deviation01:09

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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.
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On Using Standard Deviation or Standard Error of the Mean.

Farrokh Habibzadeh1,2,3,4

  • 1Independent Research Consultant, Shiraz, Iran.

Iranian Journal of Medical Sciences
|May 28, 2025
PubMed
Summary
This summary is machine-generated.

The standard deviation (SD) measures data dispersion, while the standard error of the mean (SEM) shows mean precision. Confidence intervals, based on SEM, are common in scientific reporting.

Keywords:
Confidence intervalsMedical writingNormal distributionStatistics

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Area of Science:

  • Statistics
  • Scientific Reporting

Background:

  • The mean is a common measure of central tendency.
  • Mean values are often reported with standard deviation (SD) or standard error of the mean (SEM).

Purpose of the Study:

  • To clarify the distinct roles of SD and SEM in data reporting.
  • To highlight the prevalence of confidence intervals in scientific literature.

Main Methods:

  • Literature review on statistical reporting practices.
  • Analysis of common statistical measures in scientific publications.

Main Results:

  • SD quantifies data dispersion in samples and populations.
  • SEM specifically indicates the precision of the calculated mean.
  • While SEM is less frequently reported directly, the 95% confidence interval, derived from SEM, is widely used.

Conclusions:

  • Understanding the difference between SD and SEM is crucial for accurate data interpretation.
  • Confidence intervals provide valuable insights into the precision of the mean and are a standard in scientific communication.