Definition weighted average: Each array element has an associated weight. The weighted average is the sum of all array elements, properly weighted, divided by the sum of all weights.

Here’s the problem exemplified:

Quick solution: Before we discuss the solution in great detail, here’s the solution that solves this exact problem:

import numpy as np

array = np.array([[1, 0, 2],
                  [1, 1, 1]])
weights = np.array([[2, 1, 1],
                    [1, 1, 2]])

print(np.average(array, weights=weights))
# 1.0

Want to learn how it works—and how you can average along an axis as well? Let’s dive deeper into the problem next!

Weighted Average with NumPy’s np.average() Function

NumPy’s np.average(arr) function computes the average of all numerical values in a NumPy array. When used with only one array argument, it calculates the numerical average of all values in the array, no matter the array’s dimensionality. For example, the expression np.average([[1,2],[2,3]]) results in the average value (1+2+2+3)/4 = 2.0.

However, what if you want to calculate the weighted average of a NumPy array? In other words, you want to overweight some array values and underweight others.

You can easily accomplish this with NumPy’s average function by passing the weights argument to the NumPy average function.

import numpy as np

a = [-1, 1, 2, 2]

print(np.average(a))
# 1.0

print(np.average(a, weights = [1, 1, 1, 5]))
# 1.5

In the first example, we simply averaged over all array values: (-1+1+2+2)/4 = 1.0. However, in the second example, we overweight the last array element 2—it now carries five times the weight of the other elements resulting in the following computation: (-1+1+2+(2+2+2+2+2))/8 = 1.5.

NumPy Weighted Average Video

NumPy Average Syntax

Let’s explore the different parameters we can pass to np.average(...).

• The NumPy array which can be multi-dimensional.
• (Optional) The axis along which you want to average. If you don’t specify the argument, the averaging is done over the whole array.
• (Optional) The weights of each column of the specified axis. If you don’t specify the argument, the weights are assumed to be homogeneous.
• (Optional) The return value of the function. Only if you set this to True, you will get a tuple (average, weights_sum) as a result. This may help you to normalize the output. In most cases, you can skip this argument.

average(a, axis=None, weights=None, returned=False)

NumPy Weighted Average Along an Axis (Puzzle)

Here is an example how to average along the columns of a 2D NumPy array with specified weights for both rows.

import numpy as np

# daily stock prices
# [morning, midday, evening]
solar_x = np.array(
    [[2, 3, 4], # today
     [2, 2, 5]]) # yesterday

# midday - weighted average
print(np.average(solar_x, axis=0, weights=[3/4, 1/4])[1])

What is the output of this puzzle?
*Beginner Level* (solution below)

You can also solve this puzzle in our puzzle-based learning app (100% FREE): Test your skills now!

Puzzle Explanation

Numpy is a popular Python library for data science focusing on arrays, vectors, and matrices.

This puzzle introduces the average function from the NumPy library. When applied to a 1D NumPy array, this function returns the average of the array values. When applied to a 2D NumPy array, it simply flattens the array. The result is the average of the flattened 1D array.

In the puzzle, we have a matrix with two rows and three columns. The matrix gives the stock prices of the solar_x stock. Each row represents the prices for one day. The first column specifies the morning price, the second the midday price, and the third the evening price.

Now suppose, we do not want to know the average of the flattened matrix but the average of the price in the midday. Moreover, we want to overweight the most recent stock price. Today accounts for three-quarters and yesterday for one-quarter of the final average value.

NumPy enables this via the weights parameter in combination with the axis parameter.

• The weights parameter defines the weight for each value participating in the average calculation.
• The axis parameter specifies the direction along which the average should be calculated.

In a 2D matrix, the row is specified as axis=0 and the column as axis=1. We want to know three average values, for the morning, midday, and evening. We calculate the average along the row, i.e., axis=0. This results in three average values. Now we take the second element to get the midday variance.

Recommended: How to Normalize a NumPy Matrix

Where to Go From Here?

Want to thrive in data science? Master NumPy first. You need to know the most important concepts (such as the axis argument) before you dive into machine learning and data science. Only then, you can properly understand the algorithms and build your career on a solid foundation.

To help you accomplish this, we’ve written an easy-to-read, fun introduction into the NumPy library. It’s 100% based on puzzle-based learning: you solve rated NumPy puzzles, test your skills, and improve over time. Check it out—it’s fun!

Solution

2.75

The post How to Calculate the Weighted Average of a Numpy Array in Python? appeared first on Be on the Right Side of Change.

When applied to a 1D array, this function returns the average of the array values. When applied to a 2D array, NumPy simply flattens the array. The result is the average of the flattened 1D array. Only if you use the optional axis argument, you can average along the rows or columns of the 2D array.

Here’s a visual overview first—we’ll discuss details later:

Let’s start with the simple, flat case first.

Average of Flattened 2D Array

To calculate the average of all values in a two-dimensional NumPy array called matrix, use the np.average(matrix) function.

>>> import numpy as np
>>> matrix = np.array([[1, 0, 2],
                       [1, 1, 1]])
>>> np.average(matrix)
1.0

This calculates the average of the flattened out matrix, i.e., it’s the same as calling np.average([1, 0, 2, 1, 1, 1]) without the two-dimensional structuring of the data.

Column Average of 2D Array

To calculate the average separately for each column of the 2D array, use the function call np.average(matrix, axis=0) setting the axis argument to 0.

>>> np.average(matrix, axis=0)
array([1. , 0.5, 1.5])

The resulting array has three average values, one per column of the input matrix.

Row Average of 2D Array

To calculate the average separately for each row of the 2D array, call np.average(matrix, axis=1) setting the axis argument to 1.

>>> np.average(matrix, axis=1)
array([1., 1.])

The resulting array has two average values, one per row of the input matrix.

NumPy Puzzle Average

To test your skills and train your understanding of the np.average() function, here’s a code puzzle you may enjoy:

import numpy as np

# stock prices (3x per day)
# [morning, midday, evening]
solar_x = np.array(
    [[2, 3, 4], # day 1
     [2, 2, 5]]) # day 2

print(np.average(solar_x))

What is the output of this puzzle?
*Beginner Level* (solution below)

You can solve this code puzzle interactively on our Finxter.com puzzle app here:

The puzzle has a matrix with two rows and three columns. The matrix gives the stock prices of the solar_x stock. Each row represents the prices for one day. The first column specifies the morning price, the second the midday price, and the third the evening price.

Note that NumPy calculates the average as the sum of all values divided by the number of values. The result is a float value.

Are you a master coder?
Test your skills now!

Note that the following tutorial may be interesting to you too:

Recommended Tutorial: How to Get the Length of a 2D NumPy Array

Related Video

The post How to Calculate the Average of a NumPy 2D Array? appeared first on Be on the Right Side of Change.

Differentiations: There are many different variants of this problem:

• Calculate the standard deviation of a 1D array
• Calculate the standard deviation of a 2D array
• Calculate the standard deviation of a 3D array

Then you can also calculate the standard deviation along an axis:

• Calculate the standard deviation of a 2D array along the columns
• Calculate the standard deviation of a 2D array along the rows

All of them use the np.std(array, axis) function that can be customized to the problem at hand.

Syntax: np.std(array, axis=0)

Before we dive into the different ways to calculate the standard deviation in NumPy, let me quickly give you a hint that there are additional optional arguments—but most of them are little-used. You can check them out here.

How to calculate the standard deviation of a 1D array

import numpy as np

arr = np.array([0, 10, 0])
dev = np.std(arr)

print(dev)
# 4.714045207910316

How to calculate the standard deviation of a 2D array

import numpy as np

arr = np.array([[1, 2, 3],
                [1, 1, 1]])
dev = np.std(arr)
print(dev)
# 0.7637626158259734

How to calculate the standard deviation of a 3D array

import numpy as np

arr = np.array([[[1, 1], [0, 0]],
                [[0, 0], [0, 0]]])
dev = np.std(arr)
print(dev)
# 0.4330127018922193

You can pass an n-dimensional array and NumPy will just calculate the standard deviation of the flattened array.

How to calculate the standard deviation of a 2D array along the columns

import numpy as np

matrix = [[1, 2, 3],
          [2, 2, 2]]

# calculate standard deviation along columns
y = np.std(matrix, axis=0)
print(y)
# [0.5 0.  0.5]

How to calculate the standard deviation of a 2D array along the rows

import numpy as np

matrix = [[1, 2, 3],
          [2, 2, 2]]

# calculate standard deviation along rows
z = np.std(matrix, axis=1)
print(z)
# [0.81649658 0.]

Data Science NumPy Puzzle

import numpy as np

# daily stock prices
# [open, close]
google = np.array(
    [[1239, 1258], # day 1
     [1262, 1248], # day 2
     [1181, 1205]]) # day 3

# standard deviation
y = np.std(google, axis=1)

print(y[2] == max(y))

What is the output of this puzzle?
*Advanced Level*

You can solve the puzzle in our interactive Finxter app here:

Numpy is a popular Python library for data science focusing on arrays, vectors, and matrices.

This puzzle introduces the standard deviation function of the NumPy library. When applied to a 1D array, this function returns its standard deviation. When applied to a 2D array, NumPy simply flattens the array. The result is the standard deviation of the flattened 1D array.

In the puzzle, we have a matrix with three rows and two columns. The matrix stores the open and close prices of the Google stock for three consecutive days. The first column specifies the opening price, the second the closing price.

We are interested in the standard deviation of the three days. How much does the stock price deviate from the mean between the opening and the closing price?

Numpy provides this functionality via the axis parameter. In a 2D matrix, the row is specified as axis=0 and the column as axis=1. We want to compute the standard deviation along the column, i.e., axis=1. This results in three standard deviation values – one per each day.

Clearly, on the third day, we have observed the highest standard deviation.

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Test your skills now!

Related Video 1

Related Video 2

The post How to Calculate the Standard Deviation in NumPy? appeared first on Be on the Right Side of Change.

Here’s another practical example:

import numpy as np

# stock prices (3x per day)
# [morning, midday, evening]
APPLE = np.array(
[[50,60,55], # day 1
[60,60,65]]) # day 2

# midday variance
y = np.var(APPLE, axis=0)[1]

print(int(y))

What is the output of this puzzle?
*Advanced Level* (solution below)

Numpy is a popular Python library for data science focusing on arrays, vectors, and matrices.

This puzzle introduces a new feature of the numpy library: the variance function. When applied to a 1D numpy array, this function returns the variance of the array values. The variance is the average squared deviation from the mean of the values in the array.
When applied to a 2D numpy array, numpy simply flattens the array. The result is the variance of the flattened 1D array.

In the puzzle, we have a matrix with two rows and three columns. The matrix gives the stock prices of the Apple stock. Each row represents the prices for one day. The first column specifies the morning price, the second the midday price, and the third the evening price.

Now, we do not want to know the variance of the flattened matrix but the variance of the price in the midday. In both days, the midday price was $60. Therefore, the variance is 0.

Numpy provides this functionality via the axis parameter. In a 2D matrix, the row is specified as axis=0 and the column as axis=1. We want to know three variances, for the morning, midday, and evening. Hence, we calculate the variance along the row, i.e., axis=0. This results in three variance values. Now we take the second element to get the midday variance.

Are you a master coder?
Test your skills now!

Related Video

Solution

0

The post Python Numpy 101: How to Calculate the Row Variance of a Numpy 2D Array? appeared first on Be on the Right Side of Change.