What is a standard deviation?

A standard deviation (SD) is a statistical measure that quantifies the amount of variation or spread of data points around the mean (average) in a dataset. It expresses how much, on average, each data point deviates from the mean, providing a more informative understanding of data dispersion compared to the simple range.

Formula of the standard deviation:

\[ s = \sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2} . \]

where:

  • s represents the standard deviation
  • xi​ is the value of the $i$th data point
  • xˉ is the mean of the dataset
  • N is the total number of data points

Key points:

  • Unit: The standard deviation is measured in the same units as the original data, making it easier to interpret compared to the variance (which is squared).
  • Interpretation: A larger standard deviation indicates greater spread, meaning data points are further away from the mean on average. Conversely, a smaller standard deviation suggests data points are clustered closer to the mean.
  • Applications: Standard deviation is used in various fields to analyze data variability, assess normality of distributions, compare groups, and perform statistical tests.

Advantages over the range:

  • Considers all data points: Unlike the range, which only focuses on the extremes, the standard deviation takes into account every value in the dataset, providing a more comprehensive picture of variability.
  • Less sensitive to outliers: While outliers can still influence the standard deviation, they have less impact compared to the range, making it a more robust measure.

Remember:

  • The standard deviation is just one measure of variability, and it's essential to consider other factors like the shape of the data distribution when interpreting its meaning.
  • Choosing the appropriate measure of variability depends on your specific data and research question.

Image

Tip category: 
Studies & Exams
Supporting content or organization page:
What are observational, physical and self rapportage measurements?

What are observational, physical and self rapportage measurements?

  • Observational measurements: behavior is observed directly.
  • Physical measurements: processes of the human body are observed that often can not be seen by eye. For example, hart rate, sweating, brain activity and hormonal changes.
  • Self reportage measurements: participants answer questions on questionnaires or interviews themselves.
Understanding data: distributions, connections and gatherings
Tip: type
Advice & Instructions
Tip: date of posting
21-01-2019

Image

Image

Help other WorldSupporters with additions, improvements and tips

Add new contribution

CAPTCHA
This question is for testing whether or not you are a human visitor and to prevent automated spam submissions.
Image CAPTCHA
Enter the characters shown in the image.

Image

Related activities, jobs, skills, suggestions or topics
Activity abroad, study field of working area:
Content access
Content access: 
Public
Statistics
2308 1