What is Standard deviation?
[[Image:standard deviation diagram.svg|325px|thumb|A plot of a [[normal distribution]] (or bell curve). Each colored band has a width of one standard deviation.]] [[Image:Standard deviation illustration.gif|frame|right|A data set with a mean of 50 (shown in blue) and a standard deviation (σ) of 20.]] [[File:Comparison standard deviations.svg|thumb|right|Example of two sample populations with the same mean and different standard deviations. Red population has mean 100 and SD 10; blue population has mean 100 and SD 50.]] '''Standard deviation''' is a number used to tell how measurements for a group are spread out from the average ([[mean]] or [[expected value]]).<ref>{{Cite web|date=2023-03-22|title=What is the Standard Deviation? {{!}} Data Basecamp|url=https://databasecamp.de/en/statistics/standard-deviation|access-date=2023-05-29|language=en-US}}</ref> A low standard deviation means that most of the numbers are close to the [[average]], while a high standard deviation means that the numbers are more spread out.<ref>{{cite journal | last = Gauss | first = Carl Friedrich | authorlink = Carl Friedrich Gauss | title = Bestimmung der Genauigkeit der Beobachtungen | journal = Zeitschrift für Astronomie und verwandt Wissenschaften | volume = 1 | issue = | pages = 187–197 | year = 1816 }}</ref><ref>{{cite book | last = Walker | first = Helen | authorlink = | title = Studies in the History of the Statistical Method | publisher = Williams & Wilkins Co | year = 1931 | location = Baltimore, MD | pages = 24–25 | url = | doi = | isbn = }}</ref> The reported [[margin of error]] is usually twice the standard deviation. [[science|Scientists]] commonly report the standard deviation of numbers from the average number in experiments. They often decide that only differences bigger than two or three times the standard deviation are important. Standard deviation is also useful in [[money]], where the standard deviation on interest earned shows how different one person’s interest earned might be from the avera