Statistics

Statistics functions reduce many values to one. Called on the whole array, they give one number. With axis=0 they give one result per column, and with axis=1 one result per row.

max, min, and their positions

np.max and np.min find the extremes. You may also see them as np.amax and np.amin, which are older names for the same thing. np.argmax and np.argmin give the position instead of the value.

import numpy as np

A = np.array([[1, 2, 3], [4, 2, 1], [3, 4, 2]])
print(np.max(A), np.min(A))
print(np.max(A, axis=0))
print(np.max(A, axis=1))
print(np.min(A, axis=0))
print(np.argmax(np.array([7, 19, 4, 19])))

Output:

4 1
[4 4 3]
[3 4 4]
[1 2 1]
1

mean and median

The mean is the sum divided by the count. The median is the middle value after sorting. With an even count, it is the average of the two middle values. One very large value moves the mean a lot and the median very little.

import numpy as np

A = np.array([[1, 2, 3], [4, 2, 1], [3, 4, 2]])
print(round(np.mean(A), 3))
print(np.round(np.mean(A, axis=0), 3))
print(np.median(A), np.median(A, axis=1))

print(np.median(np.array([2, 3, 4, 1])))
salaries = np.array([30, 32, 35, 38, 400])
print(np.mean(salaries), np.median(salaries))

Output:

2.444
[2.667 2.667 2.   ]
2.0 [2. 2. 3.]
2.5
107.0 35.0

variance and standard deviation

Variance is the mean of the squared distances from the mean. The standard deviation is its square root, back in the original units. The last line checks the formula by hand.

import numpy as np

A = np.array([[1, 2, 3], [4, 2, 1], [3, 4, 2]])
print(round(np.var(A), 4))
print(round(np.std(A), 4))
print(np.round(np.std(A, axis=0), 4))

by_hand = ((A - A.mean()) ** 2).mean()
print(round(by_hand, 4), round(np.sqrt(by_hand), 4))

Output:

1.1358
1.0657
[1.2472 0.9428 0.8165]
1.1358 1.0657

mode

NumPy has no mode function. The statistics module in the standard library has mode, which gives the first most common value, and multimode, which gives every value tied for most common.

import statistics

import numpy as np

visits = np.array([20, 10, 30, 10, 20, 40, 10, 20])
print(statistics.mode(visits.tolist()))
print(statistics.multimode(visits.tolist()))

Output:

20
[20, 10]

Key takeaways

• No axis gives one number. axis=0 gives one per column, axis=1 one per row

• argmax and argmin give positions

• The median resists outliers better than the mean

• std is the square root of var. mode lives in statistics

• Next: Sums, Products, and Rounding

• Previous: Arithmetic and Broadcasting