What is a module in Python?

A .py file containing reusable functions and variables, loaded into a program with import or from … import.

What is the difference between randint() and randrange()?

randint(a, b) includes both a and b; randrange(start, stop, step) excludes stop and can skip values by step.

What does the statistics module do?

It gives functions like mean(), median() and mode() to find averages of numeric data.

Python Modules Class 11 – math, random, statistics

A module is a Python file (.py) containing ready-made functions, constants and classes. You load it with import module_name (then call module.function()), import module as alias, or from module import name1, name2 (then call the name directly); from module import * loads everything (not recommended). The math module gives sqrt(), pow(), ceil(), floor(), fabs(), factorial(), gcd(), log(), log10(), sin(), cos(), tan() and constants pi and e. The random module gives random() (0 ≤ x < 1), randint(a, b) (a to b, both included) and randrange(start, stop, step) (stop excluded). The statistics module gives mean(), median() and mode().

What is a module? import and from

A module is a .py file with functions and variables we can reuse. Python's standard library has many modules (math, random, statistics, datetime…).

import math → use math.sqrt(25).
import math as m → use m.sqrt(25).
from math import sqrt, pi → use sqrt(25), pi directly.
from math import * → loads all names (can clash with your own names; avoid).

help(math) or dir(math) lists what a module contains.

The math module

Function	Example → result
sqrt(x)	math.sqrt(49) → 7.0
pow(x, y)	math.pow(2, 5) → 32.0 (always float)
ceil(x)	math.ceil(4.1) → 5; ceil(-4.1) → -4
floor(x)	math.floor(4.9) → 4; floor(-4.1) → -5
fabs(x)	math.fabs(-3) → 3.0
factorial(n)	math.factorial(5) → 120
gcd(a, b)	math.gcd(12, 18) → 6
log(x, base), log10(x)	math.log10(1000) → 3.0
sin(x), cos(x), tan(x)	x in radians: math.sin(math.pi/2) → 1.0
pi, e	3.14159…, 2.71828…

The random module

random.random() → a float with 0 ≤ x < 1.
random.randint(a, b) → an integer from a to b, both included.
random.randrange(start, stop, step) → an integer from range(start, stop, step), stop excluded. randrange(10) → 0 to 9.

Random number between 10 and 20 as a float: 10 + random.random() * 10. Outputs change every run.

The statistics module

statistics.mean(data) → average (sum ÷ count).
statistics.median(data) → middle value after sorting; for an even count, the average of the two middle values.
statistics.mode(data) → the most frequent value.

import statistics as st
d = [3, 5, 5, 2, 7]
print(st.mean(d), st.median(d), st.mode(d))   # 4.4 5 5

Board exam focus

Expect: output of math functions (ceil, floor, sqrt, pow), the possible outputs of a random-number statement (a favourite 2-mark question), import vs from, and mean/median/mode of a small list.

Key formulas and definitions

import m → m.f() · from m import f → f()
ceil ↑, floor ↓; pow and sqrt give float
randint(a, b): a..b included; randrange(a, b): b excluded
random() → 0 ≤ x < 1
mean = sum/n; median = middle; mode = most frequent

Worked examples

1. Output? import math; print(math.ceil(2.3), math.floor(-2.3), math.sqrt(81), math.pow(3, 2))

3 -3 9.0 9.0

2. Which of these can print(random.randint(3, 5)) show? 2, 3, 4, 5, 6

3, 4 or 5 (both ends included).

3. What are the possible outputs of random.randrange(1, 10, 3)?

range(1, 10, 3) = 1, 4, 7, so any one of 1, 4, 7.

4. Write a statement to get a random even number between 10 and 20 (both included).

random.randrange(10, 21, 2) → 10, 12, 14, 16, 18 or 20.

5. d = [4, 8, 6, 8, 2, 9]. Find mean, median and mode.

mean = 37/6 ≈ 6.17. Sorted [2, 4, 6, 8, 8, 9] → median = (6 + 8)/2 = 7.0. mode = 8.

6. Fix the error: from math import sqrt; print(math.sqrt(4))

With from-import, the name math is not defined. Write sqrt(4), or use import math.

7. Find the area of a circle of radius 7 using the math module.

import math r = 7 print(math.pi * r ** 2) # 153.938…

Common mistakes

Calling sqrt() after import math without writing math.sqrt().
Thinking randint(1, 6) never gives 6. Both ends are included.
Thinking randrange(1, 6) can give 6. The stop value is excluded.
Expecting math.pow(2, 3) to give 8. It gives 8.0 (a float).

Practice quiz

Practice: answer these yourself

Type or choose your answer, then press Check. Use a hint if you are stuck; the full solution appears after you answer.

Canada (Ontario)	Grade 12	A. Programming Concepts and Skills
CBSE (India)	Class 11	Computational Thinking and Programming - 1

Python Modules: math, random and statistics

🎬 Step-by-step story

🤔 Common doubts, cleared

Why not have all functions ready without importing?

If I use from math import sqrt, can I still use math.pi?

Why does math.pow give 8.0 but 2 ** 3 give 8?

Are random numbers really random?

When is median better than mean?