Mean

The mean is found by dividing the sum of data by the number of elements.

Mean

The arithmetic mean is the sum of the values divided by their count: (x₁ + ... + xₙ) / n. It describes the "centre" of the data.

x = np.array([4, 8, 6, 2])
print(x.mean())        # 5.0
print(np.mean(x))      # the same

The mean is sensitive to outliers: the mean of [4, 8, 6, 2, 100] is 24 and represents no typical value.

Mean along an axis

In a two-dimensional array the axis parameter picks the direction: axis=0 computes per column (along the rows), axis=1 per row.

X = np.array([[1, 10],
              [3, 20],
              [5, 30]])
print(X.mean(axis=0))   # [ 3. 20.]  mean of each feature
print(X.mean(axis=1))   # [ 5.5 11.5 17.5]  mean of each example

In ML, feature means (axis=0) are used in scaling and missing-value filling.

Exercise Feature means

Compute the column means of matrix X with axis=0 and print them.

Show example solution

import numpy as np

X = np.array([[170, 60], [180, 80], [160, 70]])

print(X.mean(axis=0))

Test yourself

What is the mean of <code>[1, 2, 3, 10]</code>?
- 10.0
- 4.0
- 2.5
- 3.0
Show answer

4.0 — (1 + 2 + 3 + 10) / 4 = 16 / 4 = 4.
Compute the mean of each column.
```
m = X.mean(axis=____)
```
Show answer
```
m = X.mean(axis=0)
```
Match the expressions.

x.mean()

Mean of all values
X.mean(axis=0)

Column means
X.mean(axis=1)

Row means
x.sum() / len(x)

Mean by hand

Next lesson: Median

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