Difference between revisions of "Página de pruebas"

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====Standard Deviation====
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====Skewness====
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https://statistics.laerd.com/statistical-guides/measures-of-spread-standard-deviation.php
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https://en.wikipedia.org/wiki/Skewness
  
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The Standard Deviation is the square root of the variance. This measure is the most widely used to express deviation from the mean in a variable.
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https://www.investopedia.com/terms/s/skewness.asp
  
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https://towardsdatascience.com/histograms-and-density-plots-in-python-f6bda88f5ac0
  
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<br />
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https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.skew.html
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: '''Population standard deviation''' (<math>\sigma</math>)
 
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<blockquote>
 
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<math>\sigma = \sqrt{\frac{\sum_{i=1}^{N}(x_{i} - \mu)^2}{N}}</math>
 
  
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<math>\mu: \text{population mean};\ \ \ N: \text{Number of scores in the population}</math>
 
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</blockquote>
 
  
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Skewness is a method for quantifying the lack of symmetry in the probability distribution of a variable.
  
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<br />
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* <spam style="background:#E6E6FA">'''Skewness = 0</spam> : Normally distributed'''.
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: '''Sample standard deviation formula''' (<math>s</math>)
 
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<blockquote>
 
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Sometimes our data is only a sample of the whole population. In this case, we can still estimate the Standard deviation; but when we use a sample as an estimate of the whole population, the Standard deviation formula changes to this:
 
  
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<math>s = \sqrt{\frac{\sum_{i=1}^{n}(x_{i} - \bar{x})^2}{n -1}}</math>
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* <spam style="background:#E6E6FA">'''Skewness < 0</spam> : Negative skew: The left tail is longer.''' The mass of the distribution is concentrated on the right of the figure. The distribution is said to be left-skewed, left-tailed, or skewed to the left, despite the fact that the curve itself appears to be skewed or leaning to the right; left instead refers to the left tail being drawn out and, often, the mean being skewed to the left of a typical center of the data. A left-skewed distribution usually appears as a right-leaning curve. https://en.wikipedia.org/wiki/Skewness
  
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* <spam style="background:#E6E6FA">'''Skewness > 0 : Positive skew</spam> : The right tail is longer.''' the mass of the distribution is concentrated on the left of the figure. The distribution is said to be right-skewed, right-tailed, or skewed to the right, despite the fact that the curve itself appears to be skewed or leaning to the left; right instead refers to the right tail being drawn out and, often, the mean being skewed to the right of a typical center of the data. A right-skewed distribution usually appears as a left-leaning curve.
  
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<math>\bar{x}: \text{Sample mean};\ \ \ n: \text{Number of scores in the sample}</math>
 
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</blockquote>
 
  
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[[File:Skewness.png|400px|thumb|center|]]
  
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<br />
 
  
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* The higher the value the more widely distributed are the variable data values around the mean.
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[[File:Relationship_between_mean_and_median_under_different_skewness.png|600px|thumb|center|Taken from https://en.wikipedia.org/wiki/Skewness]]
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* Assuming the frequency distributions approximately normal, about <math>68%</math> of all observations are within <math> +/-\ 1 </math> standard deviation.
 
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* Approximately <math>95%</math> of all observations fall within two standard deviations of the mean (if data is normally distributed).
 
  
  
 
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Revision as of 19:59, 14 December 2020

Skewness

https://en.wikipedia.org/wiki/Skewness

https://www.investopedia.com/terms/s/skewness.asp

https://towardsdatascience.com/histograms-and-density-plots-in-python-f6bda88f5ac0

https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.skew.html


Skewness is a method for quantifying the lack of symmetry in the probability distribution of a variable.

  • <spam style="background:#E6E6FA">Skewness = 0</spam> : Normally distributed.
  • <spam style="background:#E6E6FA">Skewness < 0</spam> : Negative skew: The left tail is longer. The mass of the distribution is concentrated on the right of the figure. The distribution is said to be left-skewed, left-tailed, or skewed to the left, despite the fact that the curve itself appears to be skewed or leaning to the right; left instead refers to the left tail being drawn out and, often, the mean being skewed to the left of a typical center of the data. A left-skewed distribution usually appears as a right-leaning curve. https://en.wikipedia.org/wiki/Skewness
  • <spam style="background:#E6E6FA">Skewness > 0 : Positive skew</spam> : The right tail is longer. the mass of the distribution is concentrated on the left of the figure. The distribution is said to be right-skewed, right-tailed, or skewed to the right, despite the fact that the curve itself appears to be skewed or leaning to the left; right instead refers to the right tail being drawn out and, often, the mean being skewed to the right of a typical center of the data. A right-skewed distribution usually appears as a left-leaning curve.


Skewness.png


Taken from https://en.wikipedia.org/wiki/Skewness



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