【standard（deviation）】Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of values. It indicates how far the data points are from the mean (average) value. A low standard deviation means that the data points are close to the mean, while a high standard deviation suggests that the data points are spread out over a wider range.
Understanding standard deviation is essential for analyzing data in various fields such as finance, science, and engineering. It helps in making informed decisions based on the variability of data.
Below is a summary of key concepts related to standard deviation:
| Concept | Description |
| Definition | A measure of how spread out the numbers in a data set are. |
| Formula | σ = √[Σ(x - μ)² / N] (for population), s = √[Σ(x - x̄)² / (n - 1)] (for sample) |
| Mean (μ or x̄) | The average of all data points. |
| Variance | The square of the standard deviation. |
| Population vs. Sample | Standard deviation can be calculated for an entire population or a sample of it. |
| Use Cases | Used in risk assessment, quality control, and performance evaluation. |
In conclusion, standard deviation is a fundamental concept in statistics that provides valuable insights into the distribution of data. By understanding this measure, individuals can better interpret data and make more accurate predictions.
