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Most Frequently Asked NumPy Interview Questions and Answers [For Freshers]

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Most Frequently Asked NumPy Interview Questions and Answers [For Freshers]

If you are looking to have a glorious career in the technological sphere, you already know that a qualification in NumPy is one of the most sought-after skills out there. After all, NumPy is built on the de facto standards of computing arrays. 

NumPy is one of the commonly used libraries of Python for working with arrays. It is broadly used for performing the vast majority of advanced mathematical calculations on a large scale of data. The NumPy arrays are much faster and more compact than Python lists.

There are various advantages of using NumPy as well such as the utilization of lesser storage space. This lesser storage space allows the users to specify the data types. The feature of specifying the data type allows the further optimization of code.

A common apprehension is that “Why should we use NumPy rather than Matlab, octave or yorick?” To answer, NumPy supports the operations on arrays of homogenous data. This makes Python act as a really advanced programming language that manipulates numerical data. It increases the functionality and operability of NumPy.

Although many relevant questions have been discussed in the article a few basic things should also be known in case the interviewer asks during the NumPy coding questions.

  1. Arrays- Arrays in NumPy are a grid of values. All of these values are of the same type. 
  2. Function in NumPy-  Some of the functions are mentioned below-
  1. numpy.linspace
  2. numpy.digitize
  3. numpy.random
  4. Numpy.nan
  5. numpy.repeat

Sometimes the interviewer can also ask about the founding year of NumPy, one should be prepared with a brief answer. This can be asked even during numpy interview questions for data science.  NumPy was created in the year 2005 by Travis Oliphant.

So, here’s a listing of some commonly asked NumPy interview questions and answers you might want to look up before you appear for your next interview. 

Top 15 NumPy Interview Questions and Answers

Question 1: What is NumPy?

NumPy is an open-source, versatile general-purpose package used for array-processing. It is short on Numerical Python. It is known for its high-end performance with powerful N-dimensional array objects and the tools it is loaded with to work with arrays. The package is an extension of Python and is used to perform scientific computations and other broadcasting functions.

NumPy is easy to use, well-optimized, and highly flexible. It is compared with MATLAB on the basis of their functionalities as both of them facilitate writing fast programs as long as most of the functions work on the arrays. NumPy is closely integrated with Python and makes it a much more sophisticated programming language.

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Question 2: What are the uses of NumPy?

The open-source numerical library on Python supports multi-dimensional arrays and contains matrix data structures. Different types of mathematical operations can be performed on arrays using NumPy. This includes trigonometric operations as well as statistical and algebraic computations. Numeric and Numarray are extensions of NumPy. 

Another answer for NumPy data science interview questions could be – “NumPy is used for scientific computing, deep learning, and financial analysis. Various functions can be performed with the aid of NumPy such as the arithmetic operations, stacking, matrix operations, broadcasting, linear algebra, etc.”

Question 3: Why is NumPy preferred to other programming tools such as IDL, Matlab, Octave, Or Yorick?

NumPy is a high-performance library in the Python programming language that allows scientific calculations. It is preferred to Idl, Matlab, Octave, Or Yorick because it is open-source and free. Also, since it uses Python which is a general-purpose programming language, it scores over a generic programming language when it comes to connecting Python’s interpreter to C/C++ and Fortran code. 

NumPy supports multi-dimensional arrays and matrices and helps to perform complex mathematical operations on them. 

Question 4: What are the various features of NumPy?

As a powerful open-source package used for array-processing, NumPy has various useful features. They are:

  1. Contains an N-dimensional array object
  2. It is  interoperable; compatible with many hardware and computing platforms
  3. Works extremely well with array libraries; sparse, distributed or GPU
  4. Ability to perform complicated (broadcasting) functions
  5. Tools that enable integration with C or C++ and Fortran code 
  6. Ability to perform high-level mathematical functions like statistics, Fourier transform, sorting, searching, linear algebra, etc 
  7. It can also behave as a multi-dimensional container for generic data
  8. Supports scientific and financial calculations.
  9. Can work with various types of databases
  10. Provides multi-dimensional arrays
  11. Indexing, Slicing, or Masking with other arrays facilitate sin accessing the specific pixels of an image.

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Question 5: How can you Install NumPy on Windows?

To install NumPy on Windows, you must first download and install Python on your computer.

Follow the steps given below to install Python: 

Step 1: Visit the official page of Python and download Python and Python executable binaries on your Windows 10/8/7

Step 2: Open Python executable installer and press Run

Step 3: Install pip on your Windows system

Using pip, you can install NumPy in Python. Below is the Installation Process of NumPy: 

Step 1: Start the terminal

Step 2: Type pip 

Step 3: install NumPy

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Question 6. List the advantages NumPy Arrays have over (nested) Python lists?

Python’s lists, even though hugely efficient containers capable of a number of functions, have several limitations when compared to NumPy arrays. It is not possible to perform vectorised operations which includes element-wise addition and multiplication. 

They also require that Python store the type information of every element since they support objects of different types. This means a type dispatching code must be executed each time an operation on an element is done. Also, each iteration would have to undergo type checks and require Python API bookkeeping resulting in very few operations being carried by C loops. 

This makes for one of the commonly asked numpy questions, where the advantages are required to enlist. Another advantage could be the less memory space that is utilized to store the data which helps in further optimization of the code. Scientific computing and array-oriented computing are more aligned advantages of NumPy.

Question 7: List the steps to create a 1D array and 2D array

A one-dimensional array is created as follows: 

num=[1,2,3]

num = np.array(num)

print(“1d array : “,num) 

A two-dimensional array is created as follows: 

num2=[[1,2,3],[4,5,6]]

num2 = np.array(num2)

print(“\n2d array : “,num2)

A 1-D array stands for a one-dimensional array that creates the array in one dimension. Whereas the 2D arrays have a collection of rows and columns.

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Question 8: How do you create a 3D array?

A three-dimensional array is created as follows: 

num3=[[[1,2,3],[4,5,6],[7,8,9]]]

num3 = np.array(num3)

print(“\n3d array : “,num3)

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Question 9: What are the steps to use shape for a 1D array, 2D array and 3D/ND array respectively?

1D Array:

num=[1,2,3] if not added

print(‘\nshpae of 1d ‘,num.shape)

2D Array:

num2=[[1,2,3],[4,5,6]] if not added

print(‘\nshpae of 2d ‘,num2.shape)

3D or ND Array: 

num3=[[[1,2,3],[4,5,6],[7,8,9]]] if not added

print(‘\nshpae of 3d ‘,num3.shape)

Question 10: How can you identify the datatype of a given NumPy array?

Use the following sequence of codes to identify the datatype of a NumPy array. 

print(‘\n data type num 1 ‘,num.dtype)

print(‘\n data type num 2 ‘,num2.dtype)

print(‘\n data type num 3 ‘,num3.dtype)

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Question 11. What is the procedure to count the number of times a given value appears in an array of integers?

You can count the number of times a given value appears using the bincount() function. It should be noted that the bincount() function accepts positive integers or boolean expressions as its argument. Negative integers cannot be used. 

Use NumPy.bincount(). The resulting array is

>>> arr = NumPy.array([0, 5, 4, 0, 4, 4, 3, 0, 0, 5, 2, 1, 1, 9])

>> NumPy.bincount(arr)

 

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Question 12. How do you check for an empty (zero Element) array?

If the variable is an array, you can check for an empty array by using the size attribute. However, it is possible that the variable is a list or a sequence type, in that case, you can use len().

The preferable way to check for a zero element is the size attribute. This is because: 

>>> a = NumPy.zeros((1,0))

>>> a.size

0

whereas

>>> len(a)

1

Question 13: What is the procedure to find the indices of an array on NumPy where some condition is true?

You may use the function numpy.nonzero() to find the indices or an array. You can also use the nonzero() method to do so. 

In the following program, we will take an array a, where the condition is a > 3. It returns a boolean array. We know False on Python and NumPy is denoted as 0. Therefore, np.nonzero(a > 3) will return the indices of the array a where the condition is True. 

>>> import numpy as np

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

>>> a > 3

array([[False, False, False],

       [ True,  True,  True],

       [ True,  True,  True]], dtype=bool)

>>> np.nonzero(a > 3)

(array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))

You can also call the nonzero() method of the boolean array.

>>> (a > 3).nonzero()

(array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))

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Question 14: Shown below is the input NumPy array. Delete column two and replace it with the new column given below.

import NumPy

sampleArray = NumPy.array([[34,43,73],[82,22,12],[53,94,66]]) 

newColumn = NumPy.array([[10,10,10]])
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Expected Output:

Printing Original array

[[34 43 73]

 [82 22 12]

 [53 94 66]]

Array after deleting column 2 on axis 1

[[34 73]

 [82 12]

 [53 66]]

Array after inserting column 2 on axis 1

[[34 10 73]

 [82 10 12]

 [53 10 66]]

Solution:

import NumPy

print(“Printing Original array”)

sampleArray = NumPy.array([[34,43,73],[82,22,12],[53,94,66]]) 

print (sampleArray)

print(“Array after deleting column 2 on axis 1”)

sampleArray = NumPy.delete(sampleArray , 1, axis = 1) 

print (sampleArray)

arr = NumPy.array([[10,10,10]])

print(“Array after inserting column 2 on axis 1”)

sampleArray = NumPy.insert(sampleArray , 1, arr, axis = 1) 

print (sampleArray)

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Question 15: Create a two 2-D array. Plot it using matplotlib

Solution:

import NumPy

print(“Printing Original array”)

sampleArray = NumPy.array([[34,43,73],[82,22,12],[53,94,66]]) 

print (sampleArray)

print(“Array after deleting column 2 on axis 1”)

sampleArray = NumPy.delete(sampleArray , 1, axis = 1) 

print (sampleArray)

arr = NumPy.array([[10,10,10]])

print(“Array after inserting column 2 on axis 1”)

sampleArray = NumPy.insert(sampleArray , 1, arr, axis = 1) 

print (sampleArray)

Advanced NumPy Concepts

In NumPy, advanced concepts like broadcasting, universal functions (ufuncs), and advanced indexing play important roles in enhancing the efficiency and readability of code. Broadcasting is a feature that enables NumPy to easily operate on arrays of varying shapes, eliminating the need for explicit loops. This simplifies operations such as element-wise addition, subtraction, multiplication, and division. 

 

Universal functions, or ufuncs, operate element-wise on arrays, optimizing computations without explicit looping. They include functions like np.add(), np.subtract(), np.multiply(), and np.divide(). Moreover, advanced indexing has techniques like boolean indexing, integer array indexing, and multidimensional slicing, providing powerful tools for selective data manipulation.

NumPy in Data Science Applications

Nowadays, NumPy is quite essential in various data science applications, particularly in machine learning. Its role in data representation, numerical computations for model training and optimization, and easy integration with machine learning frameworks underscore its importance. 

 

Additionally, NumPy’s statistical capabilities, including descriptive statistics and hypothesis testing, make it important for proper data analysis. Integration with other data science libraries like Pandas for data manipulation, Matplotlib for visualization, and Scikit-learn for machine learning further solidifies NumPy’s position in the data science ecosystem.

NumPy Performance Optimization

Optimizing the performance of NumPy code involves exploring various strategies. Algorithmic improvements, profiling, and benchmarking are crucial for identifying bottlenecks and enhancing efficiency. 

 

Moreover, NumPy-specific optimization tools, such as np. Vectorize () and np. fromiter(), provide targeted approaches to improve code performance. Understanding the internal memory layout of NumPy arrays, including C-order (row-major) and F-order (column-major), allows developers to choose the appropriate layout based on access patterns, optimizing for cache efficiency. 

 

Vectorization, a key concept, involves expressing operations in terms of arrays rather than individual elements, leading to parallelized execution and leveraging hardware capabilities for faster computations.

NumPy in Data Science Applications

  1. NumPy in Machine Learning Algorithms:

Machine learning algorithms depend heavily on NumPy due to their ability to handle arrays, enabling easy implementation of complex models. In the world of data preprocessing, NumPy provides an exceptional foundation for manipulating datasets. Its array operations allow for efficient cleaning, transformation, and normalization of data, ensuring that inputs to machine learning models are in a suitable form.

Feature engineering is a crucial step in enhancing model performance and often involves creating new features from existing ones. NumPy’s array operations and mathematical functions facilitate these transformations, empowering data scientists to derive meaningful features contributing to model accuracy. The ability to express these transformations concisely through NumPy arrays expedites the feature engineering process.

Also, when it comes to model training, NumPy plays an important role in the showing and manipulation of numerical data. Machine learning algorithms often involve iterative processes that demand efficient numerical computations. NumPy’s array-centric approach and vectorized operations contribute to the speed and efficiency of these computations, making it a preferred choice for implementing algorithms.

Moreover, exploring NumPy’s integration with popular machine learning frameworks like TensorFlow and PyTorch showcases its adaptability across diverse ecosystems. These frameworks, known for their flexibility and scalability, leverage NumPy-like arrays, enabling seamless interchangeability between data science tools and machine learning frameworks.

  1. NumPy for Statistical Analysis:

NumPy stands as a powerhouse for statistical analysis, offering an extensive suite of functions for computing various descriptive statistics. From calculating mean and median to determining standard deviation and percentiles, NumPy provides a comprehensive toolkit for gaining insights into data distributions.

Statistical hypothesis testing, a fundamental component of rigorous data analysis, finds a natural ally in NumPy. Through functions like np. ttest and np. zscore, data scientists can conduct hypothesis tests and assess the significance of observed patterns. This capability is vital for making informed decisions and drawing reliable conclusions from datasets.

Additionally, probability distributions, a cornerstone in statistical modeling, are well-supported by NumPy. The library includes functions for generating random numbers from different distributions, calculating probability density functions, and performing various statistical operations. This versatility makes NumPy an invaluable asset in the hands of statisticians and data scientists navigating the intricacies of probability theory.

  1. Integration of NumPy with Other Data Science Libraries:

NumPy’s easy integration with other data science libraries helps its utility in real-world applications. Its partnership with Pandas, another influential library in the data science world, is particularly noteworthy. Pandas DataFrames, built on NumPy arrays, get through NumPy’s efficient numerical operations for data manipulation and cleaning. The connection between NumPy and Pandas forms a foundation for exploratory data analysis and preprocessing tasks.

However, visualization is a key aspect of data interpretation and benefits from NumPy’s integration with Matplotlib. 

Matplotlib is a powerful plotting library that readily accepts NumPy arrays for creating insightful plots and graphs. This synergy enables data scientists to visually represent patterns, trends, and relationships within datasets, fostering a deeper understanding of the underlying information.

In machine learning, NumPy collaborates easily with Scikit-learn, which is a prominent library for building and evaluating machine learning models. NumPy arrays serve as the input format for Scikit-learn algorithms, ensuring a standardized and efficient interface. Additionally, this interoperability facilitates the smooth transition from data manipulation and preprocessing, executed with NumPy, to model building and evaluation using Scikit-learn.

Techniques for Optimizing NumPy Code

Algorithmic Improvements:

Optimizing NumPy code starts with algorithmic improvements, where the focus is on enhancing the time and space complexity of operations. Efficient algorithms lay the foundation for a performant system. For instance, replacing a quadratic-time algorithm with a linear one or minimizing unnecessary operations can significantly enhance the overall efficiency of the code.

Moreover, algorithmic improvements are particularly critical in scenarios where large datasets or complex computations are involved. By strategically selecting or designing algorithms, data scientists and developers can achieve substantial gains in runtime and memory utilization.

Profiling and Benchmarking:

Profiling and benchmarking tools, such as Python’s Timeit module and dedicated profilers, play a crucial role in identifying bottlenecks and areas for improvement in NumPy code. Profiling provides a detailed breakdown of the time each part of the code takes to execute, offering insights into which functions or operations consume the most resources.

Additionally, benchmarking involves comparing the performance of different implementations or versions of a particular operation. This allows developers to select the most efficient approach based on empirical evidence rather than intuition.

NumPy-Specific Optimization Tools:

NumPy provides specific tools for optimization, such as np.vectorize() and np.fromiter(). The np. vectorize() function converts a Python function into a NumPy ufunc (universal function), allowing for vectorized operations on arrays. This is especially beneficial when dealing with element-wise computations where traditional loops can be a bottleneck.

On the other hand, np.fromiter() creates a new 1-dimensional array from an iterable object, providing a memory-efficient way to build NumPy arrays. This function is helpful when dealing with large datasets, and its careful application can result in significant performance gains.

NumPy’s Internal Memory Layout (C-order vs F-order)

  1. Memory Layout:

Understanding how NumPy arranges data in memory is crucial for optimizing array performance. NumPy arrays are contiguous blocks of memory, and the way elements are stored can impact access times. The default memory layout is C-order (row-major), meaning elements in the last dimension change fastest in memory, for pandas and numpy interview questions.

  1. C-order (Row-Major) vs. F-order (Column-Major):

Choosing the appropriate memory layout based on access patterns is essential for optimizing NumPy code. C-order is suitable when operations involve accessing elements along rows, while F-order is preferable for column-wise access. This decision depends on the computational tasks at hand and the predominant access patterns.

Optimizing for cache efficiency is a key consideration in this context. By aligning memory layout with access patterns, developers can reduce cache misses, leading to faster data retrieval and improved overall performance.

Vectorization and Its Impact on Performance:

Vectorization involves writing operations in terms of arrays rather than individual elements, enabling parallelized execution. NumPy’s vectorized operations are implemented in C, making use of low-level optimizations and parallelism. This approach is more efficient than traditional Python loops and results in code that is concise, readable, and high-performing.

Vectorized operations take advantage of hardware capabilities, such as SIMD (Single Instruction, Multiple Data) instructions in modern processors. This allows NumPy to process multiple data elements simultaneously, contributing to a significant boost in computational efficiency.

Benefits of Vectorization

The benefits of vectorization are quite vast.

  • Firstly, vectorized code is more concise and expressive, making it easier to understand and maintain.
  • Secondly, it leads to improved code efficiency, as operations are delegated to highly optimized C and Fortran libraries.
  • Thirdly, vectorization reduces the reliance on Python loops, which can be inherently slow, especially when dealing with large datasets.

Thus, we can say that the nature of vectorized operations aligns with the hardware trends towards multi-core processors. As a result, vectorized NumPy code can get hold of these impressive capabilities for faster computations. This makes it a crucial aspect of performance optimization for numpy practice questions.

How NumPy and Pandas Revolutionized Data Analysis

In the world of data analysis and manipulation, NumPy and Pandas have emerged as two powerful tools that have transformed the way professionals handle and process data. These libraries provide adaptable and efficient solutions to a variety of data-related problems. Let’s look more closely at how NumPy and Pandas have transformed data analysis.

  1. Streamlined Data management: Before NumPy and Pandas, data management and manipulation were generally time-consuming and tedious processes. Analysts and data scientists had to resort to intricate loops and complex code to perform even basic operations. NumPy introduced the concept of arrays, enabling vectorized operations that significantly expedited tasks like element-wise calculations, array transformations, and aggregations. Pandas further elevated this by introducing DataFrames, simplifying the representation and manipulation of tabular data. This simplified method improved performance while also making the code more readable and maintained.
  2. Bridging the Domain Gap: NumPy and Pandas have played critical roles in bridging the domain gap within the data environment. Data analysis, scientific computing, and machine learning often require a seamless integration of mathematical operations and data processing. NumPy’s array-based operations allowed professionals from diverse backgrounds to leverage their domain-specific knowledge while efficiently performing mathematical computations. Similarly, Pandas’ tabular data structure facilitated collaboration between analysts, data engineers, and domain experts, as it provided a standardized and intuitive way to work with data across disciplines.
  3. Accelerating Innovation: The introduction of NumPy and Pandas sparked innovation by enabling faster experimentation and development. Researchers, analysts, and data scientists could focus more on formulating hypotheses, designing experiments, and extracting insights, rather than getting entangled in intricate data manipulation code. This acceleration in the data analysis process led to quicker iterations and facilitated the discovery of patterns, trends, and correlations within datasets. As a result, these libraries played a significant role in driving advancements in fields such as scientific research, finance, healthcare, and more.

Embracing the Power of NumPy and Pandas in Your Career

In today’s data-driven world, knowing NumPy and Pandas can boost your professional chances and open doors to new opportunities. These libraries have become indispensable resources for professionals involved in data analysis, machine learning, research, and a variety of other fields. Let’s look at how using NumPy and Pandas may help you advance in your profession.

  1. Enhanced Employability: Proficiency in NumPy and Pandas is highly valued by employers seeking candidates with strong data analysis and manipulation skills. Whether you’re applying for a data analyst, data scientist, or research position, showcasing your ability to efficiently handle and process data using these libraries can give you a competitive edge in the job market. Many job descriptions explicitly mention these skills as prerequisites, underscoring their importance.
  2. Lifelong Learning and Growth: NumPy and Pandas remain at the forefront of data analysis and manipulation as the data environment evolves. You are going on a path of lifetime learning and progress by devoting time and effort to mastering these resources. Their vast documentation, active forums, and ongoing development guarantee that there is always something new to learn and apply to your skill set. As you gain a deeper grasp of NumPy and Pandas, you will be better prepared to adapt to future data technologies and approaches.

Conclusion

We hope the above-mentioned NumPy interview questions will help you prepare for your upcoming interview sessions. If you are looking for courses that can help you get a hold of Python language, upGrad can be the best platform.

If you are curious to learn about data science, check out IIIT-B & upGrad’s Online Data Science Programs which are created for working professionals and offer 10+ case studies & projects, practical hands-on workshops, mentorship with industry experts, 1-on-1 with industry mentors, 400+ hours of learning and job assistance with top firms.

 We hope this helps. Good luck for with your Interview!

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Rohit Sharma

Blog Author
Rohit Sharma is the Program Director for the UpGrad-IIIT Bangalore, PG Diploma Data Analytics Program.

Frequently Asked Questions (FAQs)

1How do I practice NumPy?

Going through a step-by-step procedure can make any topic easy to learn. By performing a few basic exercises, you will get a grip of the library and also understand its usage. Firstly, begin with the installation process of the NumPy library in your system. Later on, continue with the below exercises that are recommended for beginners to practice NumPy: Addition of 2 NumPy arrays Multiplying a NumPy array with a scalar Identity matrix Array re-dimensioning Array datatype conversion Obtaining Boolean array from any Binary array Horizontal stacking of NumPy arrays Generation of custom sequences With the help of these tasks, you will be able to practice NumPy and get the hang of it. These are some of the basics that will help you to get a command over the same.

2Why is NumPy so fast?

NumPy is considered to be faster than other Python libraries. The main reasons behind the extremely fast speed of NumPy are: NumPy arrays are formed only with a collection of elements that have similar data-types. These elements are all densely packed in memory. On the other hand, a Python list can consist of different data-types. Due to this reason, there are plenty of constraints while computing Python lists. NumPy can divide a single task into several sub-tasks and process all of them in parallel. All the functions of NumPy are implemented in C. This is another reason why the processing becomes faster in NumPy as compared to the Python lists.

3Should I use Pandas or NumPy?

If you are a data scientist, then both pandas and NumPy are essential tools for you in Python. Both the libraries have their own set of benefits. If you want efficient vector and matrix operations, then NumPy is the best option to go with. At the same time, Pandas efficiently provides R-like data frames to allow the users to receive intuitive tabular data analysis. Based on several tests by developers, it has been seen that NumPy is more optimized when it comes to arithmetic computations. Other than that, NumPy is memory efficient compared to Pandas, while Pandas are better performing when there are 500K or more rows to deal with. So, one can say that the usage of both libraries will completely depend upon your usage.

4How many dimensions can a NumPy array have?

NumPy arrays can have more than one dimension.

5What is the difference between NumPy and Pandas?

NumPy has homogenous data whereas Pandas can have different types of data. NumPy has multiple dimensions whereas Pandas can be two-dimensional. NumPy is faster and Pandas is a little slower.

6How do I practice NumPy?

The beginners can practice NumPy by being strategic in their approach, such as- Element-wise addition of 2 NumPy arrays. Multiplication of matrix (NumPy array) by a scalar Conversion of array data type Sequence generation

7What is a NumPy array?

A NumPy array is an N-dimensional array that is used for various elements such as linear algebra, Fourier transform, etc. This is array is arranged in a grid manner, this grid has values of the homogenous type.

8What is the difference between a NumPy array and a Python array?

The size at the time of the creation of arrays of NumPy is fixed, which is not the same for Python lists.NumPy arrays have a homogenous data type whereas the Python arrays do not have a homogenous but rather heterogeneous data type. NumPy arrays have many functions, elements, and operations for complex computation.

9 Is NumPy a module or library?

NumPy is a library for Python that is sued to work with arrays. It has various functions that allow working with linear algebra, Fourier transform, etc.

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