It means that the variance remains the same across the range of values of the variable.
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Homogeneity means that the statistical properties of the variable which is being studied remain the same across the population. Heterogeneity means that they do not: it could be that the mean changes between different subsets of the population or the variance does.
Mean = 2. Variance = 1.
Variance is the squared deviation from the mean. (X bar - X data)^2
The mean, by itself, does not provide sufficient information to make any assessment of the sample variance.
Formally, the standard deviation is the square root of the variance. The variance is the mean of the squares of the difference between each observation and their mean value. An easier to remember form for variance is: the mean of the squares minus the square of the mean.