Calculate the variance of the numbers from a file

Write a function calculate_variance in Python that receives the name of a file and reads a number of real numbers from this file, storing them in a list. Then it shows the variance of these data on the screen. The variance is calculated as the sum of the squared differences between each element in the list, v[i], and the mean, all divided by the number of elements (N): \(w = \frac{\sum_{i=1}{n} (x[i]-mean)^{2}}{N}\)

For example, imagine we have:

6.64 
136.33 
32.02 
56.16 
97.67 
160.56 

>>> calculate_variance("numbers.txt")
    3035.443822222222

To test your function we are going to use Exercise [generate_files]{reference-type=”ref” reference=”generate_files”} to generate a number of files (eg 5 files numbers1.txt, numbers2.txt, numbers3.txt, numbers4.txt and numbers5.txt).

Then we go to https://www.calculatorsoup.com/calculators/statistics/variance-calculator.php to calculate the variance of the data in these 5 files. In this way we have the expected results of our function.

Then finish the following pytest code to run your tests automatically:

import pytest

@pytest.mark.parametrize("testcase, f_input, expected_output",[
(1, "numbers1.txt", 3713.1622346939), (2, "numbers2.txt", ...
(3, (4, (5, ])

def test_calculate_variance(testcase, f_input, expected_output):
    assert abs(calculate_variance(f_input) - expected_output) < 10**-7 , "case 0".format(testcase)

Remember to keep in mind that comparing floats for equality has rounding and precision problems. That is why we must compare that the difference between what comes out of our function and what we expect is less than, for example, \(10^{-7}\).