Description
The Standard Deviation is a measure of how much values in a group deviate from the average of the group. For example, if a collection of values is 2, 20, -50, and 8, then the standard deviation is high (as the values are all far away from the average of -5). If the values are 2, 3, 1, and 2, then the standard deviation is low (as the values stay close to the average of 2). A related concept to the standard deviation is the variance, which is defined as the square of the standard deviation. The standard deviation is the square root of the variance.
Example
For example, let’s say we have the past 5 days of ETH/USD close price data: {100, 110, 90, 105, 120}
To get the variance, we must first get the mean of these data-points. Then, we must take the difference of each data point from the mean, square it, and sum this up for all data points and divide by the number of data points.
- Mean = (100+110+90+105+120) / 5 = 105
- Difference from the mean for each data point
- 100-105 = -5
- 110-105 = 5
- 90-105 = -15
- 105-105 = 0
- 120-105 = 15
- Then we must square each difference
- (-5)^2 = 25
- (5)^2 = 25
- (-15)^2 = 225
- (0)^2 = 0
- (15)^2 = 225
- Then take the average of the differences above to get the Variance
- Variance = (25+25+225+0+225) / 5 = 100
- Finally, to get the Standard Deviation, take the square root of the Variance
- Standard Deviation = sqrt(100) = 10
Formula
