Variance is a descriptive statistical measurement used in many psychological research studies to identify the distribution of a variable in a data set relative to the mean. A large variance indicates highly scattered data that are distributed far from the mean; whereas a small variance identifies a data set with values distributed very close to the mean. It is calculated as the squared deviation of each value from the mean; thus, it is reported in squared units of the variable. The standard deviation identifies how much variation there is from the mean and is calculated as the square root of the variance. It is more commonly reported in scientific studies due to the fact that it is expressed in the same units of the data making it more easily interpreted than variance. For scientific studies, a statistical program should be used in variance calculations to ensure accurate values for large data sets and to perform additional analysis of variance, or ANOVA, tests. However, the calculation of variation is a straightforward process that can be done without the use of these programs.
Instructions
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1
Obtain a data set with N variables and calculate the mean. The mean, or average, is calculated as the sum of the variables divided by the count of the variables denoted as N.
Mean = (x1 + x2 + x3...)/ N
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2
Square the difference of each variable from the mean.
(x1-- mean)^2, (x2 -- mean)^2, (x3 -- mean)^2 , etc.
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3
Find the variance. The square of the difference of each variable from the mean, as calculated in step 2, is added together for the entire data set. This resulting value is then divided by the total number of variables within the data set minus 1, or N-1, to give the variance. A guide for reporting the variance in APA format is provided in the resources section.