What is Variance?
Variance is the expected value of the squared deviation of a random variable from its mean. In short, it is the measurement of the distance of a set of random numbers from their collective average value. Variance is used in statistics as a way of better understanding a data set's distribution.
How does Variance work?
Variance is calculated by finding the square of the standard deviation of a variable, and the covariance of the variable with itself, as represented by the function:
By JRBrown - Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=10777712
Variance is used often in statistics as a way of better understanding a data set's distribution. A disadvantage of variance is that it places emphasis on outlying values (that are far from the mean), and the square of these numbers can skew conclusions about the data. However, due to the non-negative principle of variance, one will always be able to interpret variability, as all deviations from the mean are calculated equally, regardless of direction.
Applications of Variance
Variance is an extremely useful arithmetic tool for statisticians and data scientists alike. As a function for understanding distribution, variance is applicable in disciplines from finance, to machine learning.
Variance and Finance
Variance and Machine Learning
As a statistical tool, data scientists often use variance to better understand the distribution of a data set. Machine learning uses variance calculations to make generalizations about a data set, aiding in a neural network's understanding of data distribution. Variance is often used in conjunction with probability distributions.