Question

First, define variance and define standard deviation. What is the importance of variance in statistics?

Answer 1

Variance-- it is defined as expectation of squared deviation of a random variable from its mean. Informally it measure how far a set of random numbers has spread out from its avg. Value .

Standard deviation -it is a quantity expressing by how much the members of a group from the mean value for the group

Importance of variance-

It is extremely important as a means to visualise and understand the data being considered. The point of statistics is to represent some situation (quantified, ostensibly, in a data set) in an efficient, concise, and clear manner. What the "typical” member of the set looks like, and how similar the items are. Statistics in a sense were created to represent the data in two or three numbers. The variance is a measure of how dispersed or spread out the set is, something that the “average” (mean or median) is not designed to do. If I tell you a data set has a variance of zero, for example, you know that every member of it is the same. If the variance is high, especially as a ratio to the mean, that tells you that the data have some very large dis-similarities amongst its members.