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Standard Deviation - Explained and Visualized - YouTube
Channel: unknown
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have we discovered a new particle in
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physics is a manufacturing process out
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of control what percentage of men are
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taller than LeBron James
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how about taller than Yao Ming all these
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questions can be answered using the
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concept of standard deviation for any
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set of data the mean and standard
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deviation can be calculated for example
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five people may have the following
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amounts of money in their wallets twenty
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one fifty sixty to eighty five and
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ninety dollars the mean is sixty one
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dollars and sixty cents and the standard
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deviation is twenty eight dollars and
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one cent how much does the data vary
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from the average standard deviation is a
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measure of spread that is how spread out
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a set of data is a low standard
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deviation tells us that the data is
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closely clustered around the mean or
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average while a high standard deviation
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indicates the data is dispersed over a
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wider range of values standard deviation
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is used when the distribution of data is
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approximately normal resembling a bell
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curve standard deviation is commonly
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used to understand whether a specific
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data point is standard and expected or
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unusual and unexpected standard
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deviation is represented by the
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lowercase Greek letter Sigma a data
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points distance from the mean can be
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measured by the number of standard
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deviations that it is above or below the
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mean a data point that is beyond a
[90]
certain number of standard deviations
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from the mean represents an outcome that
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is significantly above or below the
[95]
average this can be used to determine
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whether a result is statistically
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significant or part of expected
[102]
variation such as whether a bottle with
[104]
an extra ounce of soda is to be expected
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or warrants further investigation into
[108]
the production line the 6895 99.7 rule
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tells us that about 68% of the data fall
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within one standard deviation of the
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mean about 95 percent of data fall
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within to thinner deviations of the mean
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and about ninety-nine point seven
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percent of data fall within three
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standard deviations of the mean the
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average height of an American adult male
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is 510
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with a standard deviation of three
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inches using the 6895 99.7 rule this
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means that 68% of American men are 510
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plus or minus three inches 95 percent of
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American men are 510 plus or minus six
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inches and ninety-nine point seven
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percent of American men are 510 plus or
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minus nine inches so this means only
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about 0.3 percent of American men
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deviate more than nine inches from the
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average with 0.15 percent taller than
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six seven and point one five percent
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shorter than five one this reasoning
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suggests that LeBron James is one in two
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thousand five hundred and Yao Ming is
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one in 450 million in particle physics
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scientists have what are called five
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Sigma results results that are five
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standard deviations above or below the
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mean a result that varies this much can
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signify a discovery as it has only a 1
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in 3.5 million chance that it is due to
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random fluctuation in summary standard
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deviation is a measure of spread along
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with the mean the standard deviation
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allows us to determine whether AZ value
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is statistically significant or part of
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expected variation
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thanks for watching see you next time
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