NCERT Textbook: Introduction to NumPy | Informatics Practices for Class 11 - Humanities/Arts PDF Download

 Page 1


6.1 Introduct Ion NumPy stands for ‘Numerical Python’. It is a 
package for data analysis and scientific computing 
with Python. NumPy uses a multidimensional 
array object, and has functions and tools 
for working with these arrays. The powerful 
n-dimensional array in NumPy speeds-up data 
processing. NumPy can be easily interfaced with 
other Python packages and provides tools for 
integrating with other programming languages 
like C, C++ etc.
Introduct Ion to n um Py 
Chapter 
6 
“The goal is to turn data into information, 
and information into insight.” 
—  Carly Fiorina
In this chapter
 » Introduction 
 » Array
 » NumPy Array
 » Indexing and Slicing
 » Operations on Arrays
 » Concatenating Arrays
 » Reshaping Arrays
 » Splitting Arrays
 » Statistical Operations 
on Arrays
 » Loading Arrays from 
Files
 » Saving NumPy Arrays 
in Files on Disk
Chap 6.indd   95 19-Jul-19   3:43:32 PM
2024-25
Page 2


6.1 Introduct Ion NumPy stands for ‘Numerical Python’. It is a 
package for data analysis and scientific computing 
with Python. NumPy uses a multidimensional 
array object, and has functions and tools 
for working with these arrays. The powerful 
n-dimensional array in NumPy speeds-up data 
processing. NumPy can be easily interfaced with 
other Python packages and provides tools for 
integrating with other programming languages 
like C, C++ etc.
Introduct Ion to n um Py 
Chapter 
6 
“The goal is to turn data into information, 
and information into insight.” 
—  Carly Fiorina
In this chapter
 » Introduction 
 » Array
 » NumPy Array
 » Indexing and Slicing
 » Operations on Arrays
 » Concatenating Arrays
 » Reshaping Arrays
 » Splitting Arrays
 » Statistical Operations 
on Arrays
 » Loading Arrays from 
Files
 » Saving NumPy Arrays 
in Files on Disk
Chap 6.indd   95 19-Jul-19   3:43:32 PM
2024-25
96
Informat Ics Pract Ices – c lass XI
Installing NumPy 
NumPy can be installed by typing following command:
 pip install NumPy 
6.2 Arr Ay We have learnt about various data types like list, tuple, 
and dictionary. In this chapter we will discuss another 
datatype ‘Array’. An array is a data type used to store 
multiple values using a single identifier (variable name). 
An array contains an ordered collection of data elements 
where each element is of the same type and can be 
referenced by its index (position). 
The important characteristics of an array are:
• Each element of the array is of same data 
type, though the values stored in them may be 
different.
• The entire array is stored contiguously in 
memory. This makes operations on array fast.
• Each element of the array is identified or 
referred using the name of the Array along with 
the index of that element, which is unique for 
each element. The index of an element is an 
integral value associated with the element, 
based on the element’s position in the array. 
For example consider an array with 5 numbers:    
           [ 10, 9, 99, 71, 90 ] 
Here, the 1st value in the array is 10 and has the 
index value [0] associated with it; the 2
nd
 value in the 
array is 9 and has the index value [1] associated with 
it, and so on. The last value (in this case the 5
th
 value) 
in this array has an index [4]. This is called zero based 
indexing. This is very similar to the indexing of lists in 
Python. The idea of arrays is so important that almost 
all programming languages support it in one form or 
another.
6.3 n um Py Arr Ay NumPy arrays are used to store lists of numerical data, 
vectors and matrices. The NumPy library has a large set of 
routines (built-in functions) for creating, manipulating, 
and transforming NumPy arrays. Python language also 
has an array data structure, but it is not as versatile, 
efficient and useful as the NumPy array. The NumPy 
Contiguous memory 
allocation:
The memory space 
must be divided 
into the fined sized 
position and each 
position is allocated 
to a single data only.
Now Contiguous 
Memory Allocation:
Divide the data into 
several blocks and 
place in different 
parts of the memory 
according to the 
availability of memory 
space. 
Chap 6.indd   96 19-Jul-19   3:43:32 PM
2024-25
Page 3


6.1 Introduct Ion NumPy stands for ‘Numerical Python’. It is a 
package for data analysis and scientific computing 
with Python. NumPy uses a multidimensional 
array object, and has functions and tools 
for working with these arrays. The powerful 
n-dimensional array in NumPy speeds-up data 
processing. NumPy can be easily interfaced with 
other Python packages and provides tools for 
integrating with other programming languages 
like C, C++ etc.
Introduct Ion to n um Py 
Chapter 
6 
“The goal is to turn data into information, 
and information into insight.” 
—  Carly Fiorina
In this chapter
 » Introduction 
 » Array
 » NumPy Array
 » Indexing and Slicing
 » Operations on Arrays
 » Concatenating Arrays
 » Reshaping Arrays
 » Splitting Arrays
 » Statistical Operations 
on Arrays
 » Loading Arrays from 
Files
 » Saving NumPy Arrays 
in Files on Disk
Chap 6.indd   95 19-Jul-19   3:43:32 PM
2024-25
96
Informat Ics Pract Ices – c lass XI
Installing NumPy 
NumPy can be installed by typing following command:
 pip install NumPy 
6.2 Arr Ay We have learnt about various data types like list, tuple, 
and dictionary. In this chapter we will discuss another 
datatype ‘Array’. An array is a data type used to store 
multiple values using a single identifier (variable name). 
An array contains an ordered collection of data elements 
where each element is of the same type and can be 
referenced by its index (position). 
The important characteristics of an array are:
• Each element of the array is of same data 
type, though the values stored in them may be 
different.
• The entire array is stored contiguously in 
memory. This makes operations on array fast.
• Each element of the array is identified or 
referred using the name of the Array along with 
the index of that element, which is unique for 
each element. The index of an element is an 
integral value associated with the element, 
based on the element’s position in the array. 
For example consider an array with 5 numbers:    
           [ 10, 9, 99, 71, 90 ] 
Here, the 1st value in the array is 10 and has the 
index value [0] associated with it; the 2
nd
 value in the 
array is 9 and has the index value [1] associated with 
it, and so on. The last value (in this case the 5
th
 value) 
in this array has an index [4]. This is called zero based 
indexing. This is very similar to the indexing of lists in 
Python. The idea of arrays is so important that almost 
all programming languages support it in one form or 
another.
6.3 n um Py Arr Ay NumPy arrays are used to store lists of numerical data, 
vectors and matrices. The NumPy library has a large set of 
routines (built-in functions) for creating, manipulating, 
and transforming NumPy arrays. Python language also 
has an array data structure, but it is not as versatile, 
efficient and useful as the NumPy array. The NumPy 
Contiguous memory 
allocation:
The memory space 
must be divided 
into the fined sized 
position and each 
position is allocated 
to a single data only.
Now Contiguous 
Memory Allocation:
Divide the data into 
several blocks and 
place in different 
parts of the memory 
according to the 
availability of memory 
space. 
Chap 6.indd   96 19-Jul-19   3:43:32 PM
2024-25
Introduct Ion to n um Py 
97
array is officially called ndarray but commonly known 
as array. In rest of the chapter, we will be referring to 
NumPy array whenever we use “array”. following are few 
differences between list and Array.
6.3.1 Difference Between List and Array
List Array
List can have elements of different data 
types for example, [1,3.4, ‘hello’, ‘a@’]
All elements of an array are of same data type for 
example, an array of floats may be: [1.2, 5.4, 2.7]
Elements of a list are not stored  
contiguously in memory.
Array elements are stored in contiguous memory 
locations. This makes operations on arrays faster than 
lists. 
Lists do not support element wise operations, 
for example, addition, multiplication, etc. 
because elements may not be of same type.
Arrays support element wise operations. For example, 
if A1 is an array, it is possible to say A1/3 to divide 
each element of the array by 3.
Lists can contain objects of different 
datatype that Python must store the type 
information for every element along with its 
element value. Thus lists take more space 
in memory and are less efficient.
NumPy array takes up less space in memory as 
compared to a list because arrays do not require to 
store datatype of each element separately. 
List is a part of core Python. Array (ndarray) is a part of NumPy library.
6.3.2 Creation of NumPy Arrays from List
There are several ways to create arrays. To create an 
array and to use its methods, first we need to import the 
NumPy library.
#NumPy is loaded as np (we can assign any 
#name), numpy must be written in lowercase
>>> import numpy as np  
The NumPy’s array() function converts a given list 
into an array. For example,
#Create an array called array1 from the 
#given list.
>>> array1 = np.array([10,20,30]) 
#Display the contents of the array
>>> array1      
array([10, 20, 30])   
• Creating a 1-D Array
An array with only single row of elements is called 
1-D array. Let us try to create a 1-D array from 
a list which contains numbers as well as strings. 
>>> array2 = np.array([5,-7.4,'a',7.2])
>>> array2
Chap 6.indd   97 19-Jul-19   3:43:32 PM
2024-25
Page 4


6.1 Introduct Ion NumPy stands for ‘Numerical Python’. It is a 
package for data analysis and scientific computing 
with Python. NumPy uses a multidimensional 
array object, and has functions and tools 
for working with these arrays. The powerful 
n-dimensional array in NumPy speeds-up data 
processing. NumPy can be easily interfaced with 
other Python packages and provides tools for 
integrating with other programming languages 
like C, C++ etc.
Introduct Ion to n um Py 
Chapter 
6 
“The goal is to turn data into information, 
and information into insight.” 
—  Carly Fiorina
In this chapter
 » Introduction 
 » Array
 » NumPy Array
 » Indexing and Slicing
 » Operations on Arrays
 » Concatenating Arrays
 » Reshaping Arrays
 » Splitting Arrays
 » Statistical Operations 
on Arrays
 » Loading Arrays from 
Files
 » Saving NumPy Arrays 
in Files on Disk
Chap 6.indd   95 19-Jul-19   3:43:32 PM
2024-25
96
Informat Ics Pract Ices – c lass XI
Installing NumPy 
NumPy can be installed by typing following command:
 pip install NumPy 
6.2 Arr Ay We have learnt about various data types like list, tuple, 
and dictionary. In this chapter we will discuss another 
datatype ‘Array’. An array is a data type used to store 
multiple values using a single identifier (variable name). 
An array contains an ordered collection of data elements 
where each element is of the same type and can be 
referenced by its index (position). 
The important characteristics of an array are:
• Each element of the array is of same data 
type, though the values stored in them may be 
different.
• The entire array is stored contiguously in 
memory. This makes operations on array fast.
• Each element of the array is identified or 
referred using the name of the Array along with 
the index of that element, which is unique for 
each element. The index of an element is an 
integral value associated with the element, 
based on the element’s position in the array. 
For example consider an array with 5 numbers:    
           [ 10, 9, 99, 71, 90 ] 
Here, the 1st value in the array is 10 and has the 
index value [0] associated with it; the 2
nd
 value in the 
array is 9 and has the index value [1] associated with 
it, and so on. The last value (in this case the 5
th
 value) 
in this array has an index [4]. This is called zero based 
indexing. This is very similar to the indexing of lists in 
Python. The idea of arrays is so important that almost 
all programming languages support it in one form or 
another.
6.3 n um Py Arr Ay NumPy arrays are used to store lists of numerical data, 
vectors and matrices. The NumPy library has a large set of 
routines (built-in functions) for creating, manipulating, 
and transforming NumPy arrays. Python language also 
has an array data structure, but it is not as versatile, 
efficient and useful as the NumPy array. The NumPy 
Contiguous memory 
allocation:
The memory space 
must be divided 
into the fined sized 
position and each 
position is allocated 
to a single data only.
Now Contiguous 
Memory Allocation:
Divide the data into 
several blocks and 
place in different 
parts of the memory 
according to the 
availability of memory 
space. 
Chap 6.indd   96 19-Jul-19   3:43:32 PM
2024-25
Introduct Ion to n um Py 
97
array is officially called ndarray but commonly known 
as array. In rest of the chapter, we will be referring to 
NumPy array whenever we use “array”. following are few 
differences between list and Array.
6.3.1 Difference Between List and Array
List Array
List can have elements of different data 
types for example, [1,3.4, ‘hello’, ‘a@’]
All elements of an array are of same data type for 
example, an array of floats may be: [1.2, 5.4, 2.7]
Elements of a list are not stored  
contiguously in memory.
Array elements are stored in contiguous memory 
locations. This makes operations on arrays faster than 
lists. 
Lists do not support element wise operations, 
for example, addition, multiplication, etc. 
because elements may not be of same type.
Arrays support element wise operations. For example, 
if A1 is an array, it is possible to say A1/3 to divide 
each element of the array by 3.
Lists can contain objects of different 
datatype that Python must store the type 
information for every element along with its 
element value. Thus lists take more space 
in memory and are less efficient.
NumPy array takes up less space in memory as 
compared to a list because arrays do not require to 
store datatype of each element separately. 
List is a part of core Python. Array (ndarray) is a part of NumPy library.
6.3.2 Creation of NumPy Arrays from List
There are several ways to create arrays. To create an 
array and to use its methods, first we need to import the 
NumPy library.
#NumPy is loaded as np (we can assign any 
#name), numpy must be written in lowercase
>>> import numpy as np  
The NumPy’s array() function converts a given list 
into an array. For example,
#Create an array called array1 from the 
#given list.
>>> array1 = np.array([10,20,30]) 
#Display the contents of the array
>>> array1      
array([10, 20, 30])   
• Creating a 1-D Array
An array with only single row of elements is called 
1-D array. Let us try to create a 1-D array from 
a list which contains numbers as well as strings. 
>>> array2 = np.array([5,-7.4,'a',7.2])
>>> array2
Chap 6.indd   97 19-Jul-19   3:43:32 PM
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98
Informat Ics Pract Ices – c lass XI
array(['5', '-7.4', 'a', '7.2'],     
dtype='<U32')
Observe that since there is a string value in the 
list, all integer and float values have been promoted to 
string, while converting the list to array.
Note: U32 means Unicode-32 data type.
• Creating a 2-D Array
We can create a two dimensional (2-D) arrays by 
passing nested lists to the array() function. 
Example 6.1 
>>> array3 = np.array([[2.4,3],   
             [4.91,7],[0,-1]])
>>> array3
array([[ 2.4 ,  3.  ],
       [ 4.91,  7.  ],
       [ 0.  , -1.  ]])
Observe that the integers 3, 7, 0 and -1 have been 
promoted to floats.
6.3.3 Attributes of NumPy Array
Some important attributes of a NumPy ndarray object are:
i) ndarray.ndim: gives the number of dimensions  
of the array as an integer value. Arrays can be 
1-D, 2-D or n-D. In this chapter, we shall focus 
on 1-D and 2-D arrays only. NumPy calls the 
dimensions as axes (plural of axis). Thus, a 2-D 
array has two axes. The row-axis is called axis-0 
and the column-axis is called axis-1. The number 
of axes is also called the array’s rank. 
Example 6.2 
>>> array1.ndim
1
>>> array3.ndim
2
ii) ndarray.shape: It gives the sequence of integers 
indicating the size of the array for each dimension. 
Example 6.3 
# array1 is 1D-array, there is nothing  
# after , in sequence 
>>> array1.shape
(3,)
>>> array2.shape
(4,)
>>> array3.shape
(3, 2)
A common mistake 
occurs while passing 
argument to array() if 
we forget to put square 
brackets. Make sure 
only a single argument 
containing list of 
values is passed.
#incorrect way 
>>> a = 
np.array(1,2,3,4)    
#correct way
>>> a = 
np.array([1,2,3,4])  
A list is called nested 
list when each 
element is a list itself.
Chap 6.indd   98 19-Jul-19   3:43:32 PM
2024-25
Page 5


6.1 Introduct Ion NumPy stands for ‘Numerical Python’. It is a 
package for data analysis and scientific computing 
with Python. NumPy uses a multidimensional 
array object, and has functions and tools 
for working with these arrays. The powerful 
n-dimensional array in NumPy speeds-up data 
processing. NumPy can be easily interfaced with 
other Python packages and provides tools for 
integrating with other programming languages 
like C, C++ etc.
Introduct Ion to n um Py 
Chapter 
6 
“The goal is to turn data into information, 
and information into insight.” 
—  Carly Fiorina
In this chapter
 » Introduction 
 » Array
 » NumPy Array
 » Indexing and Slicing
 » Operations on Arrays
 » Concatenating Arrays
 » Reshaping Arrays
 » Splitting Arrays
 » Statistical Operations 
on Arrays
 » Loading Arrays from 
Files
 » Saving NumPy Arrays 
in Files on Disk
Chap 6.indd   95 19-Jul-19   3:43:32 PM
2024-25
96
Informat Ics Pract Ices – c lass XI
Installing NumPy 
NumPy can be installed by typing following command:
 pip install NumPy 
6.2 Arr Ay We have learnt about various data types like list, tuple, 
and dictionary. In this chapter we will discuss another 
datatype ‘Array’. An array is a data type used to store 
multiple values using a single identifier (variable name). 
An array contains an ordered collection of data elements 
where each element is of the same type and can be 
referenced by its index (position). 
The important characteristics of an array are:
• Each element of the array is of same data 
type, though the values stored in them may be 
different.
• The entire array is stored contiguously in 
memory. This makes operations on array fast.
• Each element of the array is identified or 
referred using the name of the Array along with 
the index of that element, which is unique for 
each element. The index of an element is an 
integral value associated with the element, 
based on the element’s position in the array. 
For example consider an array with 5 numbers:    
           [ 10, 9, 99, 71, 90 ] 
Here, the 1st value in the array is 10 and has the 
index value [0] associated with it; the 2
nd
 value in the 
array is 9 and has the index value [1] associated with 
it, and so on. The last value (in this case the 5
th
 value) 
in this array has an index [4]. This is called zero based 
indexing. This is very similar to the indexing of lists in 
Python. The idea of arrays is so important that almost 
all programming languages support it in one form or 
another.
6.3 n um Py Arr Ay NumPy arrays are used to store lists of numerical data, 
vectors and matrices. The NumPy library has a large set of 
routines (built-in functions) for creating, manipulating, 
and transforming NumPy arrays. Python language also 
has an array data structure, but it is not as versatile, 
efficient and useful as the NumPy array. The NumPy 
Contiguous memory 
allocation:
The memory space 
must be divided 
into the fined sized 
position and each 
position is allocated 
to a single data only.
Now Contiguous 
Memory Allocation:
Divide the data into 
several blocks and 
place in different 
parts of the memory 
according to the 
availability of memory 
space. 
Chap 6.indd   96 19-Jul-19   3:43:32 PM
2024-25
Introduct Ion to n um Py 
97
array is officially called ndarray but commonly known 
as array. In rest of the chapter, we will be referring to 
NumPy array whenever we use “array”. following are few 
differences between list and Array.
6.3.1 Difference Between List and Array
List Array
List can have elements of different data 
types for example, [1,3.4, ‘hello’, ‘a@’]
All elements of an array are of same data type for 
example, an array of floats may be: [1.2, 5.4, 2.7]
Elements of a list are not stored  
contiguously in memory.
Array elements are stored in contiguous memory 
locations. This makes operations on arrays faster than 
lists. 
Lists do not support element wise operations, 
for example, addition, multiplication, etc. 
because elements may not be of same type.
Arrays support element wise operations. For example, 
if A1 is an array, it is possible to say A1/3 to divide 
each element of the array by 3.
Lists can contain objects of different 
datatype that Python must store the type 
information for every element along with its 
element value. Thus lists take more space 
in memory and are less efficient.
NumPy array takes up less space in memory as 
compared to a list because arrays do not require to 
store datatype of each element separately. 
List is a part of core Python. Array (ndarray) is a part of NumPy library.
6.3.2 Creation of NumPy Arrays from List
There are several ways to create arrays. To create an 
array and to use its methods, first we need to import the 
NumPy library.
#NumPy is loaded as np (we can assign any 
#name), numpy must be written in lowercase
>>> import numpy as np  
The NumPy’s array() function converts a given list 
into an array. For example,
#Create an array called array1 from the 
#given list.
>>> array1 = np.array([10,20,30]) 
#Display the contents of the array
>>> array1      
array([10, 20, 30])   
• Creating a 1-D Array
An array with only single row of elements is called 
1-D array. Let us try to create a 1-D array from 
a list which contains numbers as well as strings. 
>>> array2 = np.array([5,-7.4,'a',7.2])
>>> array2
Chap 6.indd   97 19-Jul-19   3:43:32 PM
2024-25
98
Informat Ics Pract Ices – c lass XI
array(['5', '-7.4', 'a', '7.2'],     
dtype='<U32')
Observe that since there is a string value in the 
list, all integer and float values have been promoted to 
string, while converting the list to array.
Note: U32 means Unicode-32 data type.
• Creating a 2-D Array
We can create a two dimensional (2-D) arrays by 
passing nested lists to the array() function. 
Example 6.1 
>>> array3 = np.array([[2.4,3],   
             [4.91,7],[0,-1]])
>>> array3
array([[ 2.4 ,  3.  ],
       [ 4.91,  7.  ],
       [ 0.  , -1.  ]])
Observe that the integers 3, 7, 0 and -1 have been 
promoted to floats.
6.3.3 Attributes of NumPy Array
Some important attributes of a NumPy ndarray object are:
i) ndarray.ndim: gives the number of dimensions  
of the array as an integer value. Arrays can be 
1-D, 2-D or n-D. In this chapter, we shall focus 
on 1-D and 2-D arrays only. NumPy calls the 
dimensions as axes (plural of axis). Thus, a 2-D 
array has two axes. The row-axis is called axis-0 
and the column-axis is called axis-1. The number 
of axes is also called the array’s rank. 
Example 6.2 
>>> array1.ndim
1
>>> array3.ndim
2
ii) ndarray.shape: It gives the sequence of integers 
indicating the size of the array for each dimension. 
Example 6.3 
# array1 is 1D-array, there is nothing  
# after , in sequence 
>>> array1.shape
(3,)
>>> array2.shape
(4,)
>>> array3.shape
(3, 2)
A common mistake 
occurs while passing 
argument to array() if 
we forget to put square 
brackets. Make sure 
only a single argument 
containing list of 
values is passed.
#incorrect way 
>>> a = 
np.array(1,2,3,4)    
#correct way
>>> a = 
np.array([1,2,3,4])  
A list is called nested 
list when each 
element is a list itself.
Chap 6.indd   98 19-Jul-19   3:43:32 PM
2024-25
Introduct Ion to n um Py 
99
The output (3, 2) means array3 has 3 rows and 2 
columns.
iii) ndarray.size: It gives the total number of 
elements of the array. This is equal to the product 
of the elements of shape.
Example 6.4 
>>> array1.size
3
>>> array3.size
6
iv) ndarray.dtype: is the data type of the elements 
of the array. All the elements of an array are of 
same data type. Common data types are int32, 
int64, float32, float64, U32, etc.
Example 6.5 
>>> array1.dtype
dtype('int32')
>>> array2.dtype
dtype('<U32>')
>>> array3.dtype
dtype('float64')
v) ndarray.itemsize: It specifies the size in bytes 
of each element of the array. Data type int32 and 
float32 means each element of the array occupies 
32 bits in memory. 8 bits form a byte. Thus, an 
array of elements of type int32 has itemsize 32/8=4 
bytes. Likewise, int64/float64 means each item 
has itemsize 64/8=8 bytes.
Example 6.6 
>>> array1.itemsize
4     # memory allocated to integer 
>>> array2.itemsize
128     # memory allocated to string
>>> array3.itemsize
8     #memory allocated to float type
6.3.4 Other Ways of Creating NumPy Arrays 
1.  We can specify data type (integer, float, etc.) while 
creating array using dtype as an argument to 
array(). This will convert the data automatically 
to the mentioned type. In the following example, 
nested list of integers are passed to the array 
function. Since data type has been declared 
as float, the integers are converted to floating  
point numbers.
n otes Chap 6.indd   99 19-Jul-19   3:43:32 PM
2024-25