🧰 Python Modules

Do you build your own calculator every time you need a square root? Of course not! Python programmers don't either. Python comes with hundreds of ready-made tools packed into modules — for maths, random numbers, statistics, dates, and much more. You just import a module and use its functions. This chapter explains what a module is, the different ways to import one, the main functions of the math, random and statistics modules, how to predict the possible outputs of a program that uses random numbers, and how to create a module of your own.

13.1 🏁 Introduction

A module is a Python file (.py) that contains ready-made definitions — functions, variables (constants) and classes — which can be reused in other programs by importing it.

import math
print(math.sqrt(81))      # 9.0
print(math.pi)            # 3.141592653589793

Types of modules:

Analogy: Python's standard library is like a school library 📚. Each module is a book on one subject (maths, statistics…). You don't copy the whole book into your notebook — you just borrow (import) it and read the page (function) you need!

13.2 📥 Importing Modules

There are three common ways to import a module.

13.2.1 import <module> — Import the Whole Module

import math
print(math.sqrt(16))       # 4.0
print(math.floor(7.8))     # 7

You must write the module name, a dot, then the function name (math.sqrt). This is called dot notation.

You can also give the module a short alias using as:

import statistics as st
print(st.mean([10, 20, 30]))    # 20

13.2.2 from <module> import <name> — Import Selected Names

from math import sqrt, pi
print(sqrt(25))            # 5.0   ← no "math." needed
print(pi)                  # 3.141592653589793
# print(floor(2.5))        # ❌ NameError — floor was not imported

13.2.3 from <module> import * — Import Everything

from math import *
print(ceil(4.1), floor(4.9))    # 5 4

Comparing the three ways:

13.3 📐 The math Module

The math module provides mathematical functions and constants. Remember to import math first.

13.3.1 Constants

13.3.2 Functions

import math
print(math.ceil(-2.5))        # -2   (−2 is the smallest integer ≥ −2.5)
print(math.floor(-2.5))       # -3   (−3 is the largest integer ≤ −2.5)
print(math.ceil(7))           # 7    (already an integer)
print(math.pow(4, 0.5))       # 2.0
print(2 ** 5, math.pow(2, 5)) # 32 32.0
print(abs(-7), math.fabs(-7)) # 7 7.0

ceil() and floor() on a number line:

   floor(-2.5) = -3      ceil(-2.5) = -2        floor(4.2) = 4   ceil(4.2) = 5
        ↓                     ↓                       ↓               ↓
  ──────┼──────●──────────────┼───────── … ───────────┼──────●────────┼──────
       -3    -2.5            -2                        4    4.2        5

Trigonometric functions use RADIANS, not degrees. Convert degrees with math.radians():

import math
angle = math.radians(90)             # 90° → 1.5707963267948966 radians
print(math.sin(angle))               # 1.0
print(round(math.cos(math.radians(60)), 2))   # 0.5

13.4 🎲 The random Module

The random module generates random (unpredictable) numbers — useful for games, dice, OTPs, quizzes and simulations. Remember to import random first.

import random
print(random.randint(1, 6))           # a dice roll: 1, 2, 3, 4, 5 or 6
print(random.randrange(10, 100, 10))  # 10, 20, … or 90 (never 100)
print(random.random())                # e.g. 0.7319939418114051

Useful tricks with random.random():

import random
# Random integer from 10 to 20 (both included) using random():
n = int(random.random() * 11) + 10
# random() * 11 → 0.0 to 10.999…  →  int() → 0 to 10  →  + 10 → 10 to 20
print(n)

randint() vs randrange() — The Critical Comparison:

13.4.1 Predicting Possible Outputs 🔮

Because random numbers are unpredictable, exams ask: "Which of the given outputs are POSSIBLE?" The method:

1. Find the smallest and largest value each random call can produce.
2. Work out what the program prints for those limits.
3. Check each option against these limits.

Example:

import random
AR = [20, 30, 40, 50, 60, 70]
FROM = random.randint(1, 3)
TO = random.randint(2, 4)
for K in range(FROM, TO + 1):
    print(AR[K], end="#")

Which outputs are possible? (i) 10#40#70# (ii) 30#40#50# (iii) 50#60#70# (iv) 40#50#70#

Indices :   0    1    2    3    4    5
AR      :  20   30   40   50   60   70

FROM can be 1, 2 or 3      TO can be 2, 3 or 4
K runs from FROM to TO → the printed indices are CONSECUTIVE, between 1 and 4
So only values from AR[1] to AR[4] (30, 40, 50, 60) can be printed, in order.
(If FROM = 3 and TO = 2, the range is empty and nothing is printed.)

Maximum values: FROM = 3, TO = 4. Minimum values: FROM = 1, TO = 2.

13.5 📊 The statistics Module

The statistics module calculates measures of central tendency of numeric data. Remember to import statistics first.

import statistics as st
marks = [72, 85, 90, 85, 60, 78]
print(st.mean(marks))        # 78.33333333333333
print(st.median(marks))      # 81.5
print(st.mode(marks))        # 85
print(st.mode(["red", "blue", "red"]))   # red   (mode works on strings too!)

How the median is calculated:

Odd count  → [7, 1, 5]            sorted → [1, 5, 7]            middle = 5
Even count → [72, 85, 90, 85, 60, 78]
             sorted → [60, 72, 78, 85, 85, 90]
             two middle values → 78 and 85 → median = (78 + 85) / 2 = 81.5

13.6 🛠️ Creating Your Own Module

Any .py file you write can be used as a module!

Code Example: geometry.py

# geometry.py — a user-defined module
PI = 3.14159

def circle_area(r):
    return PI * r * r

def rect_area(l, b):
    return l * b

Code Example: main.py

# main.py — saved in the SAME folder as geometry.py
import geometry
print(geometry.circle_area(7))     # 153.93791
print(geometry.rect_area(4, 5))    # 20

13.7 💻 Important Programs Using Modules

Code Example: quadratic_roots.py

# Roots of ax² + bx + c = 0 using math.sqrt()
import math
a = float(input("Enter a: "))
b = float(input("Enter b: "))
c = float(input("Enter c: "))
d = b * b - 4 * a * c
if d > 0:
    r1 = (-b + math.sqrt(d)) / (2 * a)
    r2 = (-b - math.sqrt(d)) / (2 * a)
    print("Real and different roots:", r1, r2)
elif d == 0:
    print("Real and equal roots:", -b / (2 * a))
else:
    print("Roots are imaginary")
# Input a=1, b=-5, c=6 → Real and different roots: 3.0 2.0

Code Example: dice_game.py

# Roll two dice 5 times and count how often they show doubles
import random
doubles = 0
for turn in range(1, 6):
    d1 = random.randint(1, 6)
    d2 = random.randint(1, 6)
    print("Turn", turn, ":", d1, d2)
    if d1 == d2:
        doubles += 1
print("Doubles:", doubles)

Code Example: otp_generator.py

# Generate a random 4-digit OTP
import random
otp = random.randint(1000, 9999)
print("Your OTP is", otp)

Code Example: marks_statistics.py

# Mean, median and mode of marks entered by the user
import statistics
marks = eval(input("Enter a list of marks: "))
print("Mean  :", round(statistics.mean(marks), 2))
print("Median:", statistics.median(marks))
print("Mode  :", statistics.mode(marks))
# Input [45, 67, 89, 67, 90, 55] →
# Mean  : 68.83
# Median: 67.0
# Mode  : 67

Code Example: circle_calc.py

# Area and circumference of a circle using math.pi
from math import pi
r = float(input("Enter radius: "))
print("Area =", round(pi * r ** 2, 2))
print("Circumference =", round(2 * pi * r, 2))
# Input 7 → Area = 153.94
#           Circumference = 43.98

⚠️ Common Errors and Misconceptions

🔑 Quick Revision

Importing:

• import math → math.sqrt(9)
• import statistics as st → st.mean(L)
• from math import sqrt, pi → sqrt(9)
• from math import * → everything (risk of name clashes)

math module: pi, e, sqrt() (float), ceil() (up), floor() (down), pow() (float), fabs() (float), sin() / cos() / tan() (radians)

random module:

statistics module: mean() → average · median() → middle of sorted data · mode() → most frequent

🎯 Sample Exam Questions

Q1: Very Short Answer [1 mark each]

a) What is the output of print(math.ceil(3.01), math.floor(3.99))? → 4 3

b) Which module must be imported to use mode()? → statistics

c) What is the range of values returned by random.randint(5, 10)? → Integers from 5 to 10 (both included)

d) What will math.fabs(-12) return? → 12.0

e) Name the constant in the math module that stores the value of π. → math.pi

Q2: Output Based [2 marks]

Q: Write the output of the following code:

import math
import statistics as st
print(math.sqrt(64) + math.pow(2, 3))
print(math.floor(-4.2), math.ceil(-4.2))
print(st.median([9, 3, 7, 1]), st.mode([4, 2, 4, 6, 2, 4]))

Answer:

16.0
-5 -4
5.0 4

Q3: Possible Output [2 marks]

Q: What are the possible outputs of the following code? Also write the maximum and minimum values that N can take.

import random
COLOURS = ["RED", "GREEN", "BLUE", "PINK", "GOLD"]
N = random.randrange(1, 4)
for i in range(N):
    print(COLOURS[i], end="-")

(i) RED- (ii) RED-GREEN-BLUE-PINK- (iii) GREEN-BLUE- (iv) RED-GREEN-BLUE-

Answer: N can be 1, 2 or 3 → Minimum = 1, Maximum = 3. The loop always starts from index 0 (RED).

• (i) RED- ✅ possible (N = 1)
• (ii) ❌ not possible — needs N = 4, but randrange(1, 4) never gives 4
• (iii) ❌ not possible — the output must start with RED
• (iv) RED-GREEN-BLUE- ✅ possible (N = 3)

Q4: Short Answer [2 marks]

Q: Differentiate between random.randint() and random.randrange() with an example.

randint(a, b) returns a random integer between a and b, including both a and b; e.g. randint(1, 5) can return 1 to 5. randrange(start, stop, step) returns a random integer from range(start, stop, step), so the stop value is excluded; e.g. randrange(1, 5) can return 1 to 4. randrange() also allows a step value.

Q5: Program [3 marks]

Q: Write a program that generates 10 random integers between 1 and 100, stores them in a list, and prints the list along with its mean, median and the largest number.

import random
import statistics
nums = []
for i in range(10):
    nums.append(random.randint(1, 100))
print("Numbers:", nums)
print("Mean:", statistics.mean(nums))
print("Median:", statistics.median(nums))
print("Largest:", max(nums))

✏️ Practice Problems

1. What is a module? Write any three advantages of using modules.

2. Write the output of: (a) math.ceil(-0.5) (b) math.floor(0.5) (c) math.pow(3, 2) (d) math.sqrt(math.pow(3, 2) + math.pow(4, 2))

3. Write a program to input the angle in degrees and print its sine, cosine and tangent, rounded to 3 decimal places.

4. Write a program to simulate tossing a coin 20 times and count the number of heads and tails.

5. Write a program to input 5 numbers into a list and print their mean, median and mode using the statistics module.

6. What are the minimum and maximum values that x can take? x = random.randrange(5, 50, 5) + 1

7. What are the possible outputs of the following code?

   import random
   L = [10, 20, 30, 40, 50]
   start = random.randint(0, 2)
   for i in range(start, start + 2):
      print(L[i], end=" ")

   (i) 10 20 (ii) 30 40 (iii) 40 50 (iv) 20 30

8. Write a program to generate a random 6-character password made up of capital letters only (hint: chr(random.randint(65, 90))).

9. Differentiate between import math and from math import *. Which one is safer and why?

10. Write a program that asks the user to guess a random number between 1 and 20, and tells them whether each guess is too high, too low or correct, until they guess it.