Math and Statistics Functions
In this lesson, you’ll learn about new and improved
statistics functions in Python 3.8. Python 3.8 brings many improvements to existing standard library packages and modules.
math in the standard library has a few new
math.prod() works similarly to the built-in
sum(), but for multiplicative products:
>>> import math >>> math.prod((2, 8, 7, 7)) 784 >>> 2 * 8 * 7 * 7 784
The two statements are equivalent.
prod() will be easier to use when you already have the factors stored in an iterable.
Another new function is
math.isqrt(). You can use
isqrt() to find the integer part of square roots:
>>> import math >>> math.isqrt(9) 3 >>> math.sqrt(9) 3.0 >>> math.isqrt(15) 3 >>> math.sqrt(15) 3.872983346207417
The square root of 9 is 3. You can see that
isqrt() returns an
integer result, while
math.sqrt() always returns a
float. The square root of 15 is almost 3.9. Note that
isqrt() truncates the answer down to the next integer, in this case
Finally, you can now more easily work with n-dimensional points and vectors in the standard library. You can find the distance between two points with
math.dist(), and the length of a vector with
>>> import math >>> point_1 = (16, 25, 20) >>> point_2 = (8, 15, 14) >>> math.dist(point_1, point_2) 14.142135623730951 >>> math.hypot(*point_1) 35.79106033634656 >>> math.hypot(*point_2) 22.02271554554524
This makes it easier to work with points and vectors using the standard library. However, if you will be doing many calculations on points or vectors, you should check out NumPy.
statistics module also has several new functions:
statistics.fmean()calculates the mean of float numbers.
statistics.geometric_mean()calculates the geometric mean of float numbers.
statistics.multimode()finds the most frequently occurring values in a sequence.
statistics.quantiles()calculates cut points for dividing data into n continuous intervals with equal probability.
The following example shows the functions in use:
>>> import statistics >>> data = [9, 3, 2, 1, 1, 2, 7, 9] >>> statistics.fmean(data) 4.25 >>> statistics.geometric_mean(data) 3.013668912157617 >>> statistics.multimode(data) [9, 2, 1] >>> statistics.quantiles(data, n=4) [1.25, 2.5, 8.5]
In Python 3.8, there is a new
statistics.NormalDist class that makes it more convenient to work with the Gaussian normal distribution. To see an example of using
NormalDist, you can try to compare the speed of the new
statistics.fmean() and the traditional
>>> import random >>> import statistics >>> from timeit import timeit >>> # Create 10,000 random numbers >>> data = [random.random() for _ in range(10_000)] >>> # Measure the time it takes to run mean() and fmean() >>> t_mean = [timeit("statistics.mean(data)", number=100, globals=globals()) ... for _ in range(30)] >>> t_fmean = [timeit("statistics.fmean(data)", number=100, globals=globals()) ... for _ in range(30)] >>> # Create NormalDist objects based on the sampled timings >>> n_mean = statistics.NormalDist.from_samples(t_mean) >>> n_fmean = statistics.NormalDist.from_samples(t_fmean) >>> # Look at sample mean and standard deviation >>> n_mean.mean, n_mean.stdev (0.825690647733245, 0.07788573997674526) >>> n_fmean.mean, n_fmean.stdev (0.010488564966666065, 0.0008572332785645231) >>> # Calculate the lower 1 percentile of mean >>> n_mean.quantiles(n=100) 0.6445013221202459
In this example, you use
timeit to measure the execution time of
fmean(). To get reliable results, you let
timeit execute each function 100 times, and collect 30 such time samples for each function. Based on these samples, you create two
NormalDist objects. Note that if you run the code yourself, it might take up to a minute to collect the different time samples.
NormalDist has many convenient attributes and methods. See the documentation for a complete list. Inspecting
.stdev, you see that the old
statistics.mean() runs in 0.826 ± 0.078 seconds, while the new
statistics.fmean() spends 0.0105 ± 0.0009 seconds. In other words,
fmean() is about 80 times faster for these data.
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