Python Numerical Thinking

1. Overview

Before Machine Learning, Artificial Intelligence, or data analysis, we must become comfortable with numerical data. A model does not directly understand stories. It understands numbers, arrays, rows, columns, shape, and patterns.

2. Indexing

Indexing means selecting one item from a sequence. Python indexing starts from 0.

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

print(numbers[0])   # 10
print(numbers[1])   # 20
print(numbers[4])   # 50

Negative indexing

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

print(numbers[-1])  # 50
print(numbers[-2])  # 40
print(numbers[-5])  # 10

3. Slicing

Slicing means selecting a range of values.

The start value is included. The stop value is not included.

numbers = [10, 20, 30, 40, 50, 60]

print(numbers[1:4])    # [20, 30, 40]
print(numbers[:3])     # [10, 20, 30]
print(numbers[3:])     # [40, 50, 60]
print(numbers[::2])    # [10, 30, 50]
print(numbers[::-1])   # [60, 50, 40, 30, 20, 10]

Slicing strings

name = "Champak"

print(name[0])      # C
print(name[1:4])    # ham
print(name[::-1])   # kapmahC

4. Dictionaries

A dictionary stores data as key-value pairs. It is useful when data has names.

student = {
    "name": "Aarav",
    "math": 86,
    "science": 91,
    "english": 78
}

print(student["name"])
print(student["math"])

Dictionary operations

student = {
    "name": "Aarav",
    "math": 86,
    "science": 91
}

print(student["math"])

student["english"] = 78
student["math"] = 90

print(student.get("history", "Not found"))

for key, value in student.items():
    print(key, "=", value)

5. NumPy Arrays

NumPy means Numerical Python. It gives us arrays that are powerful for numerical work.

import numpy as np

marks = np.array([70, 80, 90, 60])

print(marks)

List multiplication vs array multiplication

numbers = [1, 2, 3]
print(numbers * 2)

# Output:
# [1, 2, 3, 1, 2, 3]

import numpy as np

numbers = np.array([1, 2, 3])
print(numbers * 2)

# Output:
# [2 4 6]

6. Creating NumPy Arrays: zeros, ones, random, arange and linspace

So far, we created NumPy arrays manually using np.array(). But in real numerical work, we often need to create arrays automatically. NumPy gives us many useful functions for this.

np.zeros()

np.zeros() creates an array filled with zeroes.

import numpy as np

a = np.zeros(5)

print(a)

Output:

[0. 0. 0. 0. 0.]

Two-dimensional zeros array

import numpy as np

a = np.zeros((3, 4))

print(a)
print("Shape:", a.shape)

This creates an array with 3 rows and 4 columns.

np.ones()

np.ones() creates an array filled with ones.

import numpy as np

a = np.ones(5)

print(a)

Output:

[1. 1. 1. 1. 1.]

Two-dimensional ones array

import numpy as np

a = np.ones((2, 3))

print(a)
print("Shape:", a.shape)

np.full()

np.full() creates an array filled with a value of our choice.

import numpy as np

a = np.full((3, 3), 7)

print(a)

Output:

[[7 7 7]
 [7 7 7]
 [7 7 7]]

np.arange()

np.arange() creates numbers in a range. It is similar to Python's range(), but it creates a NumPy array.

import numpy as np

a = np.arange(1, 11)

print(a)

Output:

[ 1  2  3  4  5  6  7  8  9 10]

arange with step

import numpy as np

even_numbers = np.arange(2, 21, 2)

print(even_numbers)

Output:

[ 2  4  6  8 10 12 14 16 18 20]

np.linspace()

np.linspace() creates evenly spaced values between a starting value and an ending value.

import numpy as np

a = np.linspace(0, 1, 5)

print(a)

Output:

[0.   0.25 0.5  0.75 1.  ]

np.random.rand()

np.random.rand() creates random decimal numbers between 0 and 1.

import numpy as np

a = np.random.rand(5)

print(a)

Two-dimensional random array

import numpy as np

a = np.random.rand(3, 4)

print(a)
print("Shape:", a.shape)

np.random.randint()

np.random.randint() creates random integers.

import numpy as np

marks = np.random.randint(40, 101, size=10)

print(marks)

This creates 10 random marks from 40 to 100. The ending value 101 is not included.

Random marks table

import numpy as np

marks = np.random.randint(40, 101, size=(5, 3))

print(marks)
print("Shape:", marks.shape)

print("Subject-wise mean:", np.mean(marks, axis=0))
print("Student-wise mean:", np.mean(marks, axis=1))

Quick reference table

7. Shape

Shape tells us the structure of an array.

One-dimensional array

import numpy as np

a = np.array([10, 20, 30, 40])

print(a.shape)

(4,)

Two-dimensional array

import numpy as np

marks = np.array([
    [80, 85, 90],
    [70, 75, 65],
    [92, 88, 95]
])

print(marks.shape)

(3, 3)

8. Axis

Axis tells NumPy the direction of calculation.

import numpy as np

marks = np.array([
    [80, 85, 90],
    [70, 75, 65],
    [92, 88, 95]
])

axis = 0

axis=0 calculates column-wise.

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

axis = 1

axis=1 calculates row-wise.

print(np.mean(marks, axis=1))

9. Mean and Median

import numpy as np

data = np.array([12, 18, 20, 25, 30, 35, 40])

mean_value = np.mean(data)
median_value = np.median(data)

print("Mean:", mean_value)
print("Median:", median_value)

Mean is the average. Median is the middle value after sorting.

10. Minimum, Maximum and Range

import numpy as np

data = np.array([12, 18, 20, 25, 30, 35, 40])

min_value = np.min(data)
max_value = np.max(data)
range_value = max_value - min_value

print("Minimum:", min_value)
print("Maximum:", max_value)
print("Range:", range_value)

11. Two-dimensional Statistics

import numpy as np

marks = np.array([
    [80, 85, 90],
    [70, 75, 65],
    [92, 88, 95],
    [60, 72, 68]
])

print("Marks:")
print(marks)

print("Shape:", marks.shape)

print("Overall mean:", np.mean(marks))
print("Subject-wise mean:", np.mean(marks, axis=0))
print("Student-wise mean:", np.mean(marks, axis=1))

print("Subject-wise minimum:", np.min(marks, axis=0))
print("Subject-wise maximum:", np.max(marks, axis=0))
print("Subject-wise range:", np.max(marks, axis=0) - np.min(marks, axis=0))

12. Output: Basic Numerical Thinking Notebook

Copy this into the editor and run it.

"""
Basic Numerical Thinking Notebook
Programmer's Picnic by Champak Roy
"""

import numpy as np

print("=" * 60)
print("BASIC NUMERICAL THINKING NOTEBOOK")
print("=" * 60)

# 1. Indexing

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

print("\n1. INDEXING")
print("Numbers:", numbers)
print("First value:", numbers[0])
print("Second value:", numbers[1])
print("Last value:", numbers[-1])

# 2. Slicing

print("\n2. SLICING")
print("First three values:", numbers[:3])
print("Values from index 1 to 3:", numbers[1:4])
print("Every second value:", numbers[::2])
print("Reverse list:", numbers[::-1])

# 3. Dictionary

student = {
    "name": "Aarav",
    "math": 80,
    "science": 85,
    "english": 90
}

print("\n3. DICTIONARY")
print("Student dictionary:", student)
print("Name:", student["name"])
print("Math marks:", student["math"])

# 4. NumPy Array

marks = np.array([80, 85, 90, 70, 75, 65])

print("\n4. NUMPY ARRAY")
print("Marks array:", marks)
print("Marks multiplied by 2:", marks * 2)
print("Marks plus 5:", marks + 5)

# 4B. Creating NumPy arrays automatically

print("\n4B. CREATING ARRAYS AUTOMATICALLY")

zeros_array = np.zeros(5)
ones_array = np.ones(5)
full_array = np.full((2, 3), 7)
range_array = np.arange(1, 11)
even_array = np.arange(2, 21, 2)
line_array = np.linspace(0, 1, 5)
random_decimal_array = np.random.rand(5)
random_marks = np.random.randint(40, 101, size=10)

print("Zeros array:", zeros_array)
print("Ones array:", ones_array)
print("Full array:")
print(full_array)
print("Range array:", range_array)
print("Even numbers:", even_array)
print("Linspace array:", line_array)
print("Random decimal array:", random_decimal_array)
print("Random marks:", random_marks)

print("Mean of random marks:", np.mean(random_marks))
print("Median of random marks:", np.median(random_marks))
print("Minimum random mark:", np.min(random_marks))
print("Maximum random mark:", np.max(random_marks))
print("Range of random marks:", np.max(random_marks) - np.min(random_marks))

# 5. Basic Statistics

print("\n5. BASIC STATISTICS")
print("Mean:", np.mean(marks))
print("Median:", np.median(marks))
print("Minimum:", np.min(marks))
print("Maximum:", np.max(marks))
print("Range:", np.max(marks) - np.min(marks))

# 6. Two-dimensional Array

class_marks = np.array([
    [80, 85, 90],
    [70, 75, 65],
    [92, 88, 95],
    [60, 72, 68]
])

print("\n6. TWO-DIMENSIONAL ARRAY")
print("Class marks:")
print(class_marks)
print("Shape:", class_marks.shape)

# 7. Axis

print("\n7. AXIS THINKING")

subject_names = np.array(["Math", "Science", "English"])

subject_mean = np.mean(class_marks, axis=0)
student_mean = np.mean(class_marks, axis=1)

print("Subject names:", subject_names)
print("Subject-wise mean:", subject_mean)
print("Student-wise mean:", student_mean)

print("Subject-wise min:", np.min(class_marks, axis=0))
print("Subject-wise max:", np.max(class_marks, axis=0))
print("Subject-wise range:", np.max(class_marks, axis=0) - np.min(class_marks, axis=0))

# 8. Dictionary + NumPy together

report = {
    "subjects": subject_names,
    "subject_mean": subject_mean,
    "student_mean": student_mean,
    "overall_mean": np.mean(class_marks),
    "overall_median": np.median(class_marks),
    "overall_min": np.min(class_marks),
    "overall_max": np.max(class_marks),
    "overall_range": np.max(class_marks) - np.min(class_marks)
}

print("\n8. FINAL REPORT DICTIONARY")

for key, value in report.items():
    print(key, ":", value)

print("\n" + "=" * 60)
print("NOTEBOOK COMPLETE")
print("=" * 60)

13. Python Editor

Run the notebook here. Change the arrays and observe how the results change.

14. Practice Tasks

import numpy as np

temperatures = [24, 26, 29, 31, 30, 28, 25]

print("Temperatures:", temperatures)

print("First:", temperatures[0])
print("Third:", temperatures[2])
print("Last:", temperatures[-1])

print("First three:", temperatures[:3])
print("Last three:", temperatures[-3:])
print("Reverse:", temperatures[::-1])

city_weather = {
    "city": "Varanasi",
    "morning_temp": 24,
    "afternoon_temp": 31,
    "evening_temp": 28
}

print("City weather:", city_weather)

temp_array = np.array(temperatures)

print("Mean:", np.mean(temp_array))
print("Median:", np.median(temp_array))
print("Min:", np.min(temp_array))
print("Max:", np.max(temp_array))
print("Range:", np.max(temp_array) - np.min(temp_array))

print("\nArray creation practice")

zeros_array = np.zeros(5)
ones_array = np.ones((2, 3))
range_array = np.arange(1, 11)
line_array = np.linspace(0, 1, 5)
random_array = np.random.randint(20, 41, size=(3, 3))

print("Zeros:", zeros_array, "Shape:", zeros_array.shape)
print("Ones:")
print(ones_array)
print("Shape:", ones_array.shape)
print("Arange:", range_array, "Shape:", range_array.shape)
print("Linspace:", line_array, "Shape:", line_array.shape)
print("Random integers:")
print(random_array)
print("Shape:", random_array.shape)

weekly_weather = np.array([
    [24, 31, 28],
    [25, 32, 29],
    [26, 33, 30],
    [24, 30, 27],
    [23, 29, 26],
    [25, 31, 28],
    [26, 32, 29]
])

print("Weekly weather:")
print(weekly_weather)

print("Shape:", weekly_weather.shape)

print("Mean of morning, afternoon, evening:")
print(np.mean(weekly_weather, axis=0))

print("Mean of each day:")
print(np.mean(weekly_weather, axis=1))

15. Final Challenge

Create a marks analysis notebook for 5 students and 4 subjects.

• Print the full marks array.
• Print the shape of the array.
• Print mean, median, minimum, maximum and range.
• Print subject-wise mean using axis=0.
• Print student-wise mean using axis=1.
• Create a random marks array using np.random.randint() and analyze it.

import numpy as np

marks = np.array([
    [80, 85, 90, 88],
    [70, 75, 65, 72],
    [92, 88, 95, 91],
    [60, 72, 68, 70],
    [85, 89, 84, 87]
])

# Write your code below

import numpy as np

marks = np.array([
    [80, 85, 90, 88],
    [70, 75, 65, 72],
    [92, 88, 95, 91],
    [60, 72, 68, 70],
    [85, 89, 84, 87]
])

print("Marks:")
print(marks)

print("Shape:", marks.shape)
print("Mean:", np.mean(marks))
print("Median:", np.median(marks))
print("Minimum:", np.min(marks))
print("Maximum:", np.max(marks))
print("Range:", np.max(marks) - np.min(marks))

print("Subject-wise mean:", np.mean(marks, axis=0))
print("Student-wise mean:", np.mean(marks, axis=1))

print("\nRandom marks analysis")

random_marks = np.random.randint(40, 101, size=(5, 4))

print("Random marks:")
print(random_marks)

print("Shape:", random_marks.shape)
print("Mean:", np.mean(random_marks))
print("Median:", np.median(random_marks))
print("Minimum:", np.min(random_marks))
print("Maximum:", np.max(random_marks))
print("Range:", np.max(random_marks) - np.min(random_marks))

print("Subject-wise mean:", np.mean(random_marks, axis=0))
print("Student-wise mean:", np.mean(random_marks, axis=1))