Solutions

After completing the tutorial attempt the following exercises.

If you are not sure how to do something, have a look at the “How To” section.

Write tests for the statistics.py file written in the exercises of Modularisation Exercises.

We start by writing the tests for the code. The following is in a test_stats.py file:

import stats


def test_get_mean():
    """
    This tests the `get_mean` function for a small iterable
    """
    iterable = (1, 2, 3)
    assert stats.get_mean(iterable) == 2


def test_get_population_variance():
    """
    This tests the `get_population_variance` function for a small iterable
    """
    iterable = (1, 2, 3)
    assert round(stats.get_population_variance(iterable), 3) == 0.667


test_get_mean()
test_get_population_variance()

Next to test the documentation we modify the code snippets in the documentation written in Documentation Exercises so that it becomes the following which we put in a file called README.md:

# Stats

Functionality for basic statistical operations.

## Tutorial

In this tutorial we will see how to use `stats.py` to compute the mean and
population variance of the following set of data:

```
x = (1, 2, 3, 1, 1, 1, 2, 3, 54, 5, 6, 70, 10, 12, 10)
```

First we import the library:


```python
>>> import stats

```

Next let us define the data:

```python
>>> x = (1, 2, 3, 1, 1, 1, 2, 3, 54, 5, 6, 70, 10, 12, 10)

```

To view the mean we use `stats.get_mean`:

```python
>>> round(stats.get_mean(x), 5)
12.06667

```

To view the population variance we use `stats.get_population_variance`:

```python
>>> round(stats.get_population_variance(x), 5)
404.46222

```

## How to guide

### How to compute a mean

To compute a mean we use `stats.get_mean`:

```python
>>> import stats
>>> stats.get_mean((1, 2, 3, 4))
2.5

```

### How to compute population variance

To compute a mean we use `stats.get_population_variance`:

```python
>>> import stats
>>> stats.get_population_variance((1, 2, 3, 4))
1.25

```

## Explanation

The mean is calculated using the following formula:

$$
 \bar x \frac{\sum_{i=1}^{N} x_i}{N}
$$


The population variance is defined by:

$$
 \sigma ^ 2 = \frac{\sum_{i=1}^{N} (x_i - \bar x) ^ 2}{N}
$$

Note that the population variance differs from the sample variance.

## Reference

### List of functionality

The following functions are written in `absorption`:

- `get_mean`
- `get_population_variance`

### Bibliography

The wikipedia page on the mean and population variance gives a good overview of the
topic:

- Mean: <https://en.wikipedia.org/wiki/Mean#Arithmetic_Mean_(AM)>
- Population variance: <https://en.wikipedia.org/wiki/Variance#Population_variance>

This introductory statistics text book is recommended reading:

> Ross, Sheldon M. Introductory statistics. Academic Press, 2017.

Run the tests.

To run the tests:

$ python test_stats.py

To run the doctests:

$ python -m doctest README.md