On standard deviation:
Standard deviation (SD) and the correlation coefficient (Pearson r) are old friends who rely on each other. According to Vogt (2007), “The standard deviation is used to describe the variation in a distribution of scores. The correlation coefficient is used to describe how two distributions of scores are related to each other (p. 19)”
The standard deviation (SD) is a measure of the unevenness of a data collection. It tells you how much the scores are spread out (high standard deviation) or are clustered together (low standard deviation) (Vogt, 2007). The standard deviation is a measure of how much all the data in the collection differ on average from the mean. Standard deviation is a measure of the divergence or deviation from the mean or average.
SD’s foundation is the mean. Other statistics are built on variations of the mean. The standard deviation and the square of the standard deviation or the variance are essential in statistics. Vogt (2007), describes the importance of standard deviation. “If the collection of statistical techniques is like a bakery shop filled with a wide variety of breads and pastries, the standard deviation is the flour with which most of them are made (p. 20).
Vogt (2007), also nicely describes the road to standard deviation:
First the mean or average is found. Then come the deviation data, which you get by subtracting the mean from each piece of data. You can take the average of the (absolute) deviation data to get the average deviation. Next comes the all-important variance, which is the mean of the squared deviation data. Finally, there is the standard deviation, which is the square root of the variance. It is hard to over-emphasize the importance of the mean, the deviation scores, the variance, and the standard deviation (p. 22).
Vogt, P.W., (2007). Quantitative Research Methods for Professionals. Boston, MA: Allyn and Bacon.