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# Variance

In statistics, variance is measured to calculate the total spread of the values in a data set. Under the concept regarding moments about the origin (or the mean), variance represents the second moment about the mean 1. Along with other measures, such as a skewness and central tendency, variance is a useful characteristic to utilize when discussing the distribution of data and whether or not the sample or population follows a normal distribution.

Variance is not the only measure which can be implemented to evaluate the spread of scores, but it is the most frequently used characteristic and is a term related to the standard deviation2. The relationship between variance and the standard deviation can be easily seen when analyzing the formula for variance.

Formula: S2X = ∑(X - Xbar)2/n = SSX/n

Variables:

S2 = Variance

Xbar = mean of the scores

X – Xbar = deviation from the mean

n = sample size

SS = sum of the squared deviations

In statistics, data sets should always possess some degree of variance because during data collection, there will always be some difference between the measures or scores recorded. Therefore, numerically measuring the spread of data and understanding how data deviates from the normal distribution is a critical skill in statistics. Furthermore, through visual inspection, it can also be quite obvious that variance in a data set exists and thus, through the presentation of data, this characteristic can also be measured.

Reference:

1. Probability and Statistics for Engineers, Eighth Edition – Prentice Hall 2011

2. http://knowledge.sagepub.com.proxy.queensu.ca/view/researchdesign/n491.xml?rskey=bApIWo&row=1

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