Variance: Variance is nothing but the average of the squares of the deviations.
Standard Deviation: Standard Deviation is the square root of the numerical value obtained while calculating variance.
Definition of Variance
In statistics, variance is defined as the measure of variability that represents how far members of a group are spread out. It finds out the average degree to which each observation varies from the mean. When the variance of a data set is small, it shows the closeness of the data points to the mean whereas a greater value of variance represents that the observations are very dispersed around the arithmetic mean and from each other.
Definition of Standard Deviation
Standard deviation is a measure that quantifies the amount of dispersion of the observations in a dataset. The low standard deviation is an indicator of the closeness of the scores to the arithmetic mean and a high standard deviation represents; the scores are dispersed over a higher range of values.
Key Differences Between Variance and Standard Deviation
The difference between standard deviation and variance can be drawn clearly on the following grounds:
- Variance is a numerical value that describes the variability of observations from its arithmetic mean. Standard deviation is a measure of dispersion of observations within a data set.
- Variance is nothing but an average of squared deviations. On the other hand, the standard deviation is the root mean square deviation.
- Variance is denoted by sigma-squared (σ2) whereas standard deviation is labelled as sigma (σ).
- Variance is expressed in square units which are usually larger than the values in the given dataset. As opposed to standard deviation which is expressed in the same units as the values in the set of data.
- Variance measures how far individuals in a group are spread out. Conversely, Standard Deviation measures how much observations of a data set differs from its mean.
Illustration
Mean
Variance
Standard Deviation
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