**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**