Essential array operations with Numpy

Shape and stats with Numpy

Learning Outcomes

5

Array with loop

4

Array Operations and Functions

3

How to create an 1D, 2D, and 3D array

2

Installation of Numpy

1

What is an array and Numpy

Previously, we learned Python fundamentals 

  • We worked with Python Lists to Store multiple values.
  • Lists allowed us to:

Store collections of data

Access elements using indexing

Modify values

Now we move from Python Lists → NumPy Arrays

Imagine a room filled with many boxes

  • Each box contains different types of items

This is like a Python List

➡ Flexible but scattered

➡ Mixed items stored together

Each When you need something, you must:

1

Look at different boxes

2

Search carefully

3

Spend more time

Now imagine a room with only one type of box

  • All boxes contain similar items
  • This is like a NumPy Array

Organized

Consistent

Easy to process

From Lists to NumPy Arrays

  • But numerical operations become:
  • Python Lists allow storing different data types.

Slower

Less efficient

  • NumPy Arrays store same-type elements

Faster computations

Better performance

Optimized for mathematics

Let’s understand NumPy Arrays

Introduction to NumPy?

NumPy Stand for Numerical Python

What is NumPy?

A library designed for fast numerical computing/Calculations

Provides a powerful array object (ndarray)

Why NumPy?

Faster calculations

Memory efficient

Supports multi-dimensional arrays

Key Features:

ndarray → N-dimensional array for numerical data

Vectorization → Perform operations on entire arrays

(no need for explicit loops)

High Performance → Optimized using C under the hood

Mathematical Tools → Built-in functions for:

  • Statistics
  • Linear algebra
  • Aggregations

Shape & Reshaping → Easily change array dimensions

NumPy is the foundation for data science & ML

How to Install NumPy

Install Using pip

Open Command Prompt / Terminal:

pip install numpy

Verify Installation

Open Python and run:

import numpy as np
print(np.__version__)

If the version prints successfully. NumPy is installed.

NumPy Array

An array stores multiple values in a single structure

Elements are usually of the same data type

Each element has a position (index)

What is an Array?

Key Characteristics

Homogeneous → Same type of data

Ordered → Elements have fixed positions

Efficient Access → Quick retrieval using index

Example:

Creating an Array in Numpy

Steps:

First, Import NumPy:

Import numpy as np

Create a NumPy array using np.array():

arr = np.array([1, 2, 3, 4])

View the array:

print(arr)

     Key Idea:

      Use np.array()

      Pass a list / sequence

      NumPy converts it into an ndarray

1D Array (One-Dimensional)

A 1D array is a simple list of elements, similar to a traditional Python list

Syntax:

a1=np.array([val1,val2,-----])

Example:

import numpy as np

arr_1d = np.array([1, 2, 3, 4, 5])

Shape

arr_1d.shape

output:
(5,)

5 columns, 1 row

Real-life example

  • Marks of one student

  • Daily temperatures

  • Prices list

2D Array (Two-Dimensional)

A 2D array represents a table or matrix, with rows and columns. Each element occupies a specific position

Syntax:

a2=np.array([[v1,v2,v3---],[v4,v5,---]])

Example:

Example:
arr_2d = np.array([
    [1, 2, 3],
    [4, 5, 6]
])

Shape

arr_2d.shape

output:
(2, 3)

2 rows ,3 columns

Real-life example

  • Students × subjects marks

  • Excel sheet data

  • Image (black & white)

3D Array (Three-Dimensional)

A 3D array adds a third dimension to the table, often representing a cube or

a volume of data

Syntax:

 a3=np.array([[[v1,v2,v3--],[v4,v5,v6---],[v6,v7,v8,---],[v9,v10,v11,--]]])

Example:

arr_3d = np.array([
    [
        [1, 2, 3],
        [4, 5, 6]
    ],
    [
        [7, 8, 9],
        [10, 11, 12]
    ]
])

Shape

arr_3d.shape

output:
(2, 2, 3)

2 layers, 2 rows in each layer, 3 columns

Visual Representation of NumPy Array Dimensions

Operations on array:

import numpy as np

a = np.array([1, 2, 3, 4])

b = np.array([5, 6, 7, 8])

Sample Array

Element-wise arithmetic operations

1

These happen element by element, no loops needed.

a + b

a - b        

a * b        

a / b

a ** b

addition

subtraction    

multiplication  

division

power

Syntax:-

[ 6 8 10 12]

[-4 -4 -4 -4]   

[ 5 12 21 32]  

[0.2 0.33333333 0.42857143 0.5 ]

[ 1 4 9 16]

output:

Scalar operation

2

The scalar is applied to every element.

a + 10

a * 3        

a / 2        

Syntax:-

[11 12 13 14]

[ 3 6 9 12]    

[0.5 1.  1.5 2. ]

output:

3

Comparison & logical operations

These return boolean arrays.

a > 2

a == 3        

a != b      

[False False True True]

[False False True False]     

[ True True True True]

Syntax:-

output:

Aggregation (statistical operations)

4

Operate on the whole array or along an axis.

a.sum()

a.mean()

a.max()        

a.min()

a.std()    

Syntax:-

np.int64(10)
np.float64(2.5)
np.int64(4)
np.int64(1)
np.float64(1.118033988749895)

output:

For 2D arrays:

Sample code:

arr.sum(axis=0)

arr = np.array([[1, 2], [3, 4]])

arr.sum(axis=1)

--- #column-wise

--- #row-wise

Shape & restructuring operations

5

a.shape

Syntax:-

output:

(4,)

a.reshape(2,2)

array([[1, 2],

         [3, 4]])

a.flatten()

array ( [1, 2, 3, 4])

a.flatten()

array ( [1, 2, 3, 4])

# transpose (mainly for 2D)

Mathematical functions

6

np.sqrt(a)

Computes the square root of each element in array

np.log(a)

Computes the natural logarithm (base e) of each element in a.

np.exp(a)

Computes e raised to the power of each element in a.

np.sin(a)

Computes the sine of each element in a.

Broadcasting

7

Allows operations between arrays of different shapes.

arr = np.array([[1, 2, 3],
               [4, 5, 6]])
print(arr + np.array([10, 20, 30]))

output:
[[11 22 33]
 [14 25 36]]

Each row gets [10, 20, 30] added automatically.

+10 +20 +30

Matrix operations

8

element-wise

import numpy as np

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

ouput:
np.int64(70)
import numpy as np

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

ouput:
array([ 5, 12, 21, 32])
import numpy as np

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

ouput:
np.int64(70)
import numpy as np

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

ouput:
array([ 5, 12, 21, 32])

matrix multiplication

[5 + 12 + 21 + 32]

For 2D matrices:

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

A @ B

output:
array([[19, 22],
       [43, 50]])

Sorting & Searching

9

Sort() Method

import numpy as np
A = np.array([25, 1, 89, 60, 90])
np.sort(A)

output:
array([ 1, 25, 60, 89, 90])

argsort() Method

import numpy as np
A = np.array([25, 1, 89, 60, 90])
np.argsort(A)

output:
array([1, 0, 3, 2, 4])

It returns indices that sort an array.

25 is on 0th index

where() method

import numpy as np
A = np.array([25, 1, 89, 60, 90])
np.where(A > 30)

output:
(array([2, 3, 4]),)

Example: Student Marks Analysis

(Real world UseCase)

A teacher has marks of 3 students in 3 subjects and wants to:

1. Store the data

2. Find each student’s average

3. Find subject-wise average

4. Highest marks

Let’s see how to perform all these operations using Numpy.

Step 1: Store marks in a NumPy array

General structure:

  • Each row = one student
  • Each column = one subject

Code Example:

marks = np.array([

    [80, 85, 90],       # Student 1

    [70, 75, 78],       # Student 2

    [88, 92, 95]        # Student 3

])

So the array looks like:

Student 1 → 80  85  90

 

Student 2 → 70  75  78

 

Student 3 → 88  92  95

Step 2: Average marks of each Student

  • We calculate row-wise average → axis = 1

Code:

student_average = np.mean(marks, axis=1)
print(student_average)
output:
[85.         74.33333333 91.66666667]

Student1

Student2

Student3

80

85

90

70

75

78

88

92

95

85.0

74.333

91.667

Step 3: Average marks of each Subject

  • We calculate column-wise average → axis = 0

Code:

subject_average = np.mean(marks, axis=0)
print(subject_average)
output:
[79.33333333 84.         87.66666667]

Subject1

Subject2

Subject3

80

85

90

70

75

78

88

92

95

79.33

84.0

87.66

Step 4: Find highest marks

import numpy as np
marks = np.array([
    [80, 85, 90],   # Student 1
    [70, 75, 78],   # Student 2
    [88, 92, 95]    # Student 3
])

print(np.max(marks, axis=1))
import numpy as np
marks = np.array([
    [80, 85, 90],   # Student 1
    [70, 75, 78],   # Student 2
    [88, 92, 95]    # Student 3
])

print(np.max(marks, axis=0))

Output:- [90 78 95]

Output:- [88 92 95]

Arrays with Loop

# Using range() and len()

a = [10, 20, 30, 40, 50]

for i in range(len(a)):
    print(f"Index {i}: {a[i]}")

Output:
Index 0: 10
Index 1: 20
Index 2: 30
Index 3: 40
Index 4: 50

# Using enumerate()

a = [10, 20, 30, 40, 50]

for i, val in enumerate(a):
    print(i, val)

Output:
0 10
1 20
2 30
3 40
4 50
  • range(len(a)) → Gives index values (0 to 4).

  • enumerate(a) → Gives both index and value directly (cleaner & recommended).

Modifying array elements using a loop

a = [10, 20, 30, 40, 50]

for i in range(len(a)):
  a[i] = a[i]*2
print(a)

Output:
[20, 40, 60, 80, 100]
  • This code loops through the list using its index and multiplies each element by 2, updating the original list to [20, 40, 60, 80, 100].

Using list comprehension → NumPy array

a = [10, 20, 30, 40, 50]
b = np.array([x**2 for x in a])
print(b)

Output:
[ 100  400  900 1600 2500]
  • This code creates a new NumPy array b by squaring each element of list a using list comprehension, resulting in [100, 400, 900, 1600, 2500].

Summary

5

Array with Loop

4

Array Operations and Functions

3

How to create an 1D, 2D and 3D array

2

Installation of Numpy

1

What is an array and Numpy

Quiz

Which attribute gives the shape of a NumPy array arr

A. arr.size

B. arr.length

C. arr.shape

D. arr.dim

Quiz-Answer

C. arr.shape

Which attribute gives the shape of a NumPy array arr

A. arr.size

B. arr.length

D. arr.dim

Numpy - Shape and stats with Numpy

By Content ITV

Numpy - Shape and stats with Numpy

  • 7

More from Content ITV