Standard deviation is a number that describes how spread out the values are.
A low standard deviation means that most of the numbers are close to the mean (average) value.
A high standard deviation means that the values are spread out over a wider range.
Example: This time we have registered the speed of 7 cars:
speed = [86,87,88,86,87,85,86]
The standard deviation is:
0.9
Meaning that most of the values are within the range of 0.9 from the mean value, which is 86.4.
Let us do the same with a selection of numbers with a wider range:
speed = [32,111,138,28,59,77,97]
The standard deviation is:
37.85
Meaning that most of the values are within the range of 37.85 from the mean value, which is 77.4.
As you can see, a higher standard deviation indicates that the values are spread out over a wider range.
The NumPy module has a method to calculate the standard deviation:
Example
Use the NumPy std() method to find the standard deviation:
import numpy
speed = [86,87,88,86,87,85,86]
x = numpy.std(speed)
print(x)
Example
import numpy
speed = [32,111,138,28,59,77,97]
x = numpy.std(speed)
print(x)
As we have learned, the formula to find the standard deviation is the square root of the variance:
√1432.25 = 37.85
Or, as in the example from before, use the NumPy to calculate the standard deviation:
Example
Use the NumPy std() method to find the standard deviation:
import numpy
speed = [32,111,138,28,59,77,97]
x = numpy.std(speed)
print(x)
Standard Deviation is often represented by the symbol Sigma: σ
Variance is often represented by the symbol Sigma Squared: σ2