standard deviation

standard deviation (tsz. standard deviations)

1. (matematika) standard deviáció, szórás

Standard deviation is a measure of the amount of variation or dispersion in a set of values. It quantifies how much the values in a dataset differ from the mean (average) of the dataset.

Here’s the formula for standard deviation for a dataset ${\textstyle x_{1},x_{2},\dots ,x_{n}}$:

Population Standard Deviation (for an entire population)

$${\displaystyle \sigma ={\sqrt {{\frac {1}{n}}\sum _{i=1}^{n}(x_{i}-\mu )^{2}}}}$$ Where: - ${\textstyle \sigma }$ is the population standard deviation, - ${\textstyle n}$ is the number of data points, - ${\textstyle x_{i}}$ is each individual data point, - ${\textstyle \mu }$ is the mean of the population.

Sample Standard Deviation (for a sample of the population)

$${\displaystyle s={\sqrt {{\frac {1}{n-1}}\sum _{i=1}^{n}(x_{i}-{\bar {x}})^{2}}}}$$ Where: - ${\textstyle s}$ is the sample standard deviation, - ${\textstyle n}$ is the sample size, - ${\textstyle x_{i}}$ is each individual data point, - ${\textstyle {\bar {x}}}$ is the sample mean.

The main difference between the two formulas is that the sample standard deviation divides by ${\textstyle n-1}$ (Bessel’s correction) to account for the bias in estimating the population standard deviation from a sample.

• standard deviation - Szótár.net (en-hu)
• standard deviation - Sztaki (en-hu)
• standard deviation - Merriam–Webster
• standard deviation - Cambridge
• standard deviation - WordNet
• standard deviation - Яндекс (en-ru)
• standard deviation - Google (en-hu)
• standard deviation - Wikidata
• standard deviation - Wikipédia (angol)