Table of Contents
Explain in Detail :Variance Formula
The variance formula is used to calculate the variance of a population or a sample. The variance is a measure of the variability of a set of data. It is calculated by taking the square of the standard deviation. Difference Between Variance and Standard Deviation.
The variance formula is:
Var = (x – µ)² / n
Standard Deviation Definition
Standard deviation is a measure of the dispersion of a set of data from its mean. It is calculated as the square root of the variance.
Standard Deviation Formula
Standard deviation is a measure of how much a set of data varies from the average of that set. The standard deviation formula is:
\(\sigma = \sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})^2}\)
Where:
\(\sigma\) = Standard Deviation
\(\bar{x}\) = Average of the set of data
\(x_i\) = Value of the data point
Key Differences Between Variance And Standard Deviation
- The variance is a measure of the spread of a set of data, while the other is a measure of the variability of a set of data.
- The variance is always positive, while the other can be positive or negative.
- The variance is always calculated using the squared deviations from the mean, while the other is always calculated using the deviations from the mean
- In statistics, the variance and the standard deviation are two measures of dispersion. The variance is a measure of the variability of a set of data and the standard deviation is a measure of the average distance of the data points from the mean.
- The variance is calculated by taking the sum of the squared differences between each data point and the mean, divided by the number of data points. The standard deviation is the square root of the variance.
- The variance is a measure of the variability of a set of data. The standard deviation is a measure of the average distance of the data points from the mean.
- The variance is a more sensitive measure than the standard deviation. The standard deviation is more efficient to calculate than the variance.
