What do the terms variance and standard deviation mean? How are these concepts related? How are they calculated?

     Variability refers to how spread out or closely clustered a set of data is. Variability has two measures, which are variance and standard deviation. A group of scores' variability can be described by the variance and the standard deviation (Aron, Aron, & Coups, 2009). The term variance, which is represented by the symbol (σ2), is the average of the squared deviation of each score from the mean or how far numbers lie from the mean (Aron, Aron, & Coups, 2009). The term standard deviation, which is represented by the symbol sigma (σ), is displays how much variation exists from the average or mean. When data points tend to be close to the mean this is referred to as a low standard deviation and when data points are spread out over a large range of values this is referred to as a high standard deviation. Variance and standard deviation are related because standard deviation is the square root of the variance, which is  (Aron, Aron, & Coups, 2009). 

represents variance, which is calculated by finding the variance then by finding the square root.

represents standard deviation, which is calculated by taking the sum of the squares of the terms in the distribution, and divide by the number of terms in the distribution, and then subtract the square of the mean. 

Reference

Aron, A., Aron, E. N., & Coups, E. (2009). Statistics for psychology (5th ed.). Upper Saddle River, NJ: Pearson Prentice Hall.