Variance | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-05-07

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Variance


00:01:21 1 Definition
00:06:11 1.1 Discrete random variable
00:12:39 1.2 Continuous random variable
00:17:02 2 Examples
00:17:11 2.1 Normal distribution
00:20:35 2.2 Exponential distribution
00:23:11 2.3 Poisson distribution
00:25:46 2.4 Binomial distribution
00:29:29 2.5 Fair die
00:34:16 3 Properties
00:34:25 3.1 Basic properties
00:45:15 3.2 Sum of uncorrelated variables (Bienaymé formula)
00:52:35 3.3 Sum of correlated variables
00:57:29 3.4 Matrix notation for the variance of a linear combination
01:00:06 3.5 Weighted sum of variables
01:02:32 3.6 Product of independent variables
01:04:14 3.7 Product of statistically dependent variables
01:06:45 3.8 Decomposition
01:18:15 3.9 Formulae for the variance
01:19:40 3.10 Calculation from the CDF
01:21:05 3.11 Characteristic property
01:23:25 3.12 Units of measurement
01:24:58 4 Approximating the variance of a function
01:26:15 5 Population variance and sample variance
01:30:47 5.1 Population variance
01:32:18 5.2 Sample variance
01:45:52 5.3 Distribution of the sample variance
01:46:06 5.4 Samuelson's inequality
01:48:59 5.5 Relations with the harmonic and arithmetic means
01:49:53 6 Tests of equality of variances
01:52:32 7 History
01:54:06 8 Moment of inertia
01:56:06 9 Semivariance
01:58:18 10 Generalizations
01:59:02 10.1 For complex variables
01:59:12 10.2 For vector-valued random variables
02:00:21 10.2.1 As a matrix
02:00:32 10.2.2 As a scalar
02:03:20 11 See also
02:04:30 12 Notes
02:04:39 Notes



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SUMMARY
=======
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.  Informally, it measures how far a set of (random) numbers are spread out from their average value. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by 
  
    
      
        
          σ
          
            2
          
        
      
    
    {\displaystyle \sigma ^{2}}
  , 
  
    
      
        
          s
          
            2
          
        
      
    
    {\displaystyle s^{2}}
  , or 
  
    
      
        Var
        ⁡
        (
        X
        )
      
    
    {\displaystyle \operatorname {Var} (X)}
  .