Definition

1. Noun:
   • A statistical measure of dispersion: "Standard deviation" is a number that quantifies the amount of variation or dispersion of a set of data values from their mean (average) value. A low standard deviation indicates that the data points tend to be close to the mean, while a high standard deviation indicates that the data points are spread out over a wider range.

Usage

• The term is used primarily in statistics, mathematics, data science, finance, and any field involving quantitative data analysis.
• It describes how spread out the numbers in a dataset are.
• It is calculated as the positive square root of the variance.

Examples

• Noun:
  • The researcher reported a mean score of 100 with a standard deviation of 15.
  • A small standard deviation in manufacturing indicates consistent product quality.
  • To understand the volatility of the investment, look at the standard deviation of its annual returns.

Advanced Usage

• "within one standard deviation": Refers to data points that fall within a range of one standard deviation above and below the mean. In a normal distribution, this encompasses approximately 68% of the data.
  • Most of the students' test scores fell within one standard deviation of the class average.
• "standard deviation from the mean": A common phrase specifying the distance of a particular data point from the average, measured in units of standard deviation.
  • That result is two standard deviations from the mean, which is quite unusual.

Variants and Related Words

• Variance (n): The average of the squared differences from the Mean. The standard deviation is the square root of the variance.
• Population standard deviation (n): Denoted by σ (sigma), it is calculated using data from every member of a population.
• Sample standard deviation (n): Denoted by , it is calculated using data from a sample of a population and includes a correction (Bessel's correction) for bias.

Synonyms

• Spread: (informal) A general term for the extent of variation in data.
• Dispersion: A more formal statistical synonym for the concept of how data is spread out.

Related Phrases

• Standard error: A related but distinct concept that measures the precision of a sample mean estimate, calculated as the standard deviation divided by the square root of the sample size.
• Mean absolute deviation: Another measure of dispersion that averages the absolute differences from the mean.

Noun

1. the square root of the variance