Review: NumPy Statistics

Module 3: NumPy

Session 3.6: Statistics

import numpy as np

Exercise

The following code should compute the mean of each row of arr, and print their values as integers. When we run the code, it outputs a single value, 5. Fix it to output [2, 5, 8].

arr = np.array([
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
])

# Compute the mean of each row
mean = int(np.mean(arr))

print(mean)

Exercise

The following code should compute the mean of arr along every axis. When we run the code, it raises AxisError: axis 3 is out of bounds for array of dimension 2. Explain the error(s) and fix this code. We want the output:

{
  "mean_0": [1.0, 4.0],
  "mean_1": [1.5, 2.0, 4.0]
}

arr = np.array([
    [1, 2],
    [1, 3],
    [1, 7]
])

# Get the dimensions of this array
axes = arr.shape  # Expected tuple: (0, 1)

# Initialize an empty dictionary
dict_means = {}

# Loop through the different stats
for axis in axes:
  key = f"mean_{axis}"
  value = np.mean(arr, axis=axis)
  # Use the stat name to call the specific NumPy function
  dict_new = {key: value}
  # Insert the key-value pair into the original dictionary
  dict_stats.append(dict_new)

print(dict_stats)

Exercise

A vector \(\mathbf{x}\) can be normalized to \(\mathbf{\hat{x}}\) by applying the following formula: \[\mathbf{\hat{x}} = \frac{\mathbf{x} - \mu_x}{\sigma_x}\] where \(\mu_x\) is the mean of \(\mathbf{x}\) and \(\sigma_x\) its standard deviation.

A property of any normalized vector is that its mean is always 0. However the output of the code below is \(3.06\) instead of \(0\). Explain the error(s) and fix this code.

arr = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])
mean = np.mean(arr, axis=0)  # Output is 4.5
std = np.std(arr, axis=0)  # Output is 2.58
# Normalize the vector and compute its new mean
arr_norm = arr - mean / std
norm_mean = np.mean(arr_norm, axis=0)
print(norm_mean)  # Expected: 0

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