Mathematical and statistical methods

A number of mathematical functions that calculate statistics over an entire array or over the data along an axis are accessible as methods of the array class. So you can use aggregations such as sum, mean and standard deviation by either calling the array instance method or using the top-level NumPy function.

Below I generate some random data and calculate some aggregated statistics:

import numpy as np


data = np.random.randn(7, 3)

data

array([[ 0.52892401, -0.82705139, -0.13426779],
       [-0.43476595,  0.15431376, -0.15927356],
       [ 0.5437757 , -0.27273503, -0.74511308],
       [ 0.41921053,  0.78804831, -1.39898524],
       [-0.08745354,  0.24346498,  0.5995653 ],
       [ 2.18987033,  0.07709088,  0.81486999],
       [ 0.42570339,  1.23702332,  1.12807273]])

data.mean()

0.24239465071821545

np.mean(data)

0.24239465071821545

data.sum()

5.090287665082524

Functions like mean and sum require an optional axis argument that calculates the statistic over the specified axis, resulting in an array with one less dimension:

data.mean(axis=0)

array([0.51218064, 0.20002212, 0.01498119])

data.sum(axis=0)

array([3.58526448, 1.40015484, 0.10486835])

With data.mean(0), which is the same as data.mean(axis=0), the mean is calculated over the rows, while data.sum(0) calculates the sum over the rows.

Other methods like cumsum and cumprod, however, do not aggregate but create a new array with the intermediate results.

In multidimensional arrays, accumulation functions such as cumsum and cumprod return an array of the same size but with the partial aggregates calculated along the specified axis:

data.cumsum()

array([ 0.52892401, -0.29812737, -0.43239516, -0.86716111, -0.71284735,
       -0.87212091, -0.32834522, -0.60108025, -1.34619332, -0.92698279,
       -0.13893449, -1.53791972, -1.62537326, -1.38190829, -0.78234299,
        1.40752735,  1.48461823,  2.29948822,  2.72519162,  3.96221494,
        5.09028767])

data.cumprod()

array([ 5.28924012e-01, -4.37447338e-01,  5.87350864e-02, -2.55360156e-02,
       -3.94055863e-03,  6.27626816e-04,  3.41288209e-04, -9.30812494e-05,
        6.93560562e-05,  2.90747892e-05,  2.29123384e-05, -3.20540232e-05,
        2.80323775e-06,  6.82490215e-07,  4.09197451e-07,  8.96089358e-07,
        6.90803200e-08,  5.62914796e-08,  2.39634740e-08,  2.96433762e-08,
        3.34398842e-08])

Basic statistical methods for arrays are:

Method	Description
sum	Sum of all elements in the array or along an axis.
mean	Arithmetic mean; for arrays with length zero, NaN is returned.
std, var	Standard deviation and variance respectively
min, max	Minimum and maximum
argmin, argmax	Indices of the minimum and maximum elements respectively
cumsum	Cumulative sum of the elements, starting with 0
cumprod	Cumulative product of the elements, starting with 1