Variance and Standard Deviation are both essential concepts in statistics and finance. Let’s explore the differences between them:
Variance:
Definition: Variance is a numerical value that describes the variability of observations from their arithmetic mean.
Calculation: To find the variance, calculate the squared differences between each data point and the mean, then average these squared differences.
Formula:
For a population (N data points): Variance = Sum of squared differences / N.
For a sample (N-1 data points): Variance = Sum of squared differences / (N-1).
Interpretation: Variance represents the average degree of deviation of each data point from the mean.
Use: It is useful for measuring volatility and understanding the distribution of returns in financial data.
Standard Deviation:
Definition: Standard deviation measures how far a group of numbers is from the mean. It is the spread of a data set.
Calculation: Standard deviation is the square root of the variance.
Formula: Standard deviation = √(Variance).
Interpretation: A higher standard deviation indicates greater deviation within the data.
In summary, while standard deviation is the square root of the variance, variance is the average of the squared differences of each data point from the mean. Both concepts play a crucial role in understanding data variability and risk .
Watch the video for example and more detail .
References
1
investopedia.com
2
diffen.com
3
keydifferences.com
4
byjus.com