NumPy - Statistics

Thomas J. Kennedy

Contents:

1 Overview

NumPy provides a number of operations that are useful for statistics, including min, max, and mean. The NumPy implementations are more performant that the vanilla Python equivalents.

2 An Example Problem

Suppose we need to compute some grade statistics for the following data.

Name	Homework 1	Homework 2	Exam 1	Exam 2
John	100	98	100	90
Tom	100	0	70	90
Bob	100	70	90	80

The first step is to convert the table into…

a list of exercises

exercises = ["Homework 1", "Homework 2", "Exam 1", "Exam 2"]

a list of names
```
students = ["John", "Tom", "Bob"]
```

a NumPy ndarray to store grades by student (row) vs exercise (column)

grades = np.array([[100., 98, 100., 90.],
                   [100.,  0., 70., 90.],
                   [100., 70., 90., 80.]])

3 NumPy Operations and Axis

NumPy provides a number of statistics operations that can be applied by axis. For a two-dimensional ndarray there are two choices:

by row (student)

avg_by_student = grades.mean(axis=1)
min_by_student = grades.min(axis=1)
max_by_student = grades.max(axis=1)

Name	Avg	Min	Max
John	97.0	90.0	100.0
Tom	65.0	0.0	100.0
Bob	85.0	70.0	100.0

by column (exercise)

avg_by_exercise = grades.mean(axis=0)
max_by_exercise = grades.max(axis=0)
std_by_exercise = grades.std(axis=0)

Exercise	Avg	Max	Std Dev
Homework 1	100.0	100.0	0.0
Homework 2	56.0	98.0	41.2
Exam 1	86.7	100.0	12.5
Exam 2	86.7	90.0	4.7

Take note of the axis keyword argument. For a 2-D ndarray a zero (0) indicates analysis by column and a one (1) indicates analysis by row.