The Difference Between Standard Deviation and Variance
In statistics, two key measures of variability are standard deviation and variance. While both measures depict the spread or dispersion of data around its mean, there are key differences between them.
Variance
Variance is a numerical measure of how far a set of data points are from their mean. It is mathematically defined as the average of the squared differences of each data point from the mean. In other words, variance tells us how spread out the data is from the mean.
A low variance indicates that the data points are very close to the mean, whereas a high variance means that the data points are widely dispersed from the mean. The formula for variance is:
Variance = (1/N)Σ(xi – X)2
Where xi is each data point, X is the mean of the data set, and N is the total number of data points.
Standard Deviation
Standard deviation is another measure of variability, which is defined as the square root of variance. It is a measure of the degree of variation or dispersion of a set of values from its mean.
Its calculation is simpler than variance, as it involves taking the square root of the variance. A low standard deviation indicates that the data points are tightly clustered around the mean, while a high standard deviation means that the data points are spread out from the mean. The formula for standard deviation is:
Standard Deviation = √Variance
Difference between Standard Deviation and Variance
Perhaps the most significant difference between standard deviation and variance is that standard deviation is based on square roots, while variance is not. This means that standard deviation measures the dispersion of data points in the same unit as the original data, while variance measures the dispersion in squared units.
Also, variance can take negative values, which is not the case with standard deviation. Finally, standard deviation is regarded as an easier measure to interpret and work with than variance.
In conclusion, while standard deviation and variance are both measures of how far a set of data points are from their mean, they differ in terms of the mathematical formula used, the units of measurement, and the ease of interpretation. It is essential to understand both measures to effectively analyze and interpret statistical data.
Table difference between standard deviation and variance
| Standard Deviation | Variance | |
|---|---|---|
| Definition | The square root of the average of the squared deviations from the mean. | The average of the squared deviations from the mean. |
| Symbols | σ (sigma) | σ² (sigma squared) |
| Unit of measurement | Same as the original data set. | Squared units of the original data set. |
| Use | Measures the amount of variation or dispersion of a set of data values. | Measures the spread of a set of data values. |
| Properties | 1. Always non-negative. 2. Increases when the spread of the data set increases. 3. Zero when all data values are equal. |
1. Always non-negative. 2. Increases when the spread of the data set increases. |