 # Math and Statistics Functions

In this lesson, you’ll learn about new and improved `math` and `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 `functions`. `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 `3`.

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 `math.hypot()`:

>>>
``````>>> 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.

The `statistics` module also has several new functions:

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 `statistics.mean()`:

>>>
``````>>> 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 `mean()` and `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 `.mean` and `.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.

If you need more advanced statistics in Python than the standard library offers, check out `statsmodels` and `scipy.stats`.

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