A post for students in data analytics:
Variance and standard deviation are both measures of dispersion used in data analysis, but they differ in their calculation, interpretation, and application.
Here’s a breakdown of the key differences:
Definition
- Variance measures the squared deviation of a random variable from the mean. It quantifies the average of the squared differences between each data point and the mean of the dataset.
- Standard Deviation is the square root of the variance.
Calculation
- Variance is calculated by finding the mean, subtracting the mean from each data point, squaring the results, summing the squared results, and dividing by the number of data points minus.
- Standard deviation involves the same steps as calculating variance, but with an additional step of taking the square root of the variance.
Units
- Variance is expressed in squared units, which can be difficult to interpret in relation to the original data.
- Standard deviation is expressed in the same units as the original data, making it easier to understand and apply to the distribution.
Interpretation
- Variance provides a measure of the overall spread or dispersion of the data. A higher variance indicates greater variability in the dataset.
- Standard deviation indicates the average distance of each data point from the mean. It provides a more intuitive understanding of how much the data points deviate from the average.
Application to Normal Distribution
- Standard deviation is particularly useful when applied to a normal distribution. In a normal distribution, approximately 68% of the data points fall within one standard deviation of the mean, 95.4% within two standard deviations, and 99.6% within three standard deviations.
- Data analysts commonly use three standard deviations as a cutoff for identifying and removing outliers in a dataset.
In summary, while both variance and standard deviation measure the spread of data, standard deviation is often preferred due to its ease of interpretation and direct applicability to the original data’s units.