Total Hours: 25 | Marks: 10
Introduction
Maths plays a very important role in Artificial Intelligence. To make AI smart and accurate, we use some basic concepts from Statistics and Probability.
These maths topics help AI understand data, find patterns, and make predictions.
What is Statistics?
Statistics is a branch of mathematics that deals with collecting, organizing, analyzing, and interpreting data.
In simple words, statistics helps us understand large amounts of data by using numbers.
Important Terms in Statistics
1. Mean (Average)
Mean is the average of a set of numbers.
Formula:
Mean = (Sum of all values) ÷ (Total number of values)
Example:
If marks are 50, 60, 70
Mean = (50 + 60 + 70) / 3 = 180 / 3 = 60
2. Median
Median is the middle value when the numbers are arranged in order.
Example 1 (odd number of values):
50, 60, 70 → Median = 60 (middle value)
Example 2 (even number of values):
40, 50, 60, 70 → Median = (50 + 60)/2 = 55
3. Mode
Mode is the number that appears most often in the data.
Example:
45, 60, 45, 70, 80 → Mode = 45 (because it appears twice)
4. Standard Deviation (SD)
Standard deviation tells us how spread out the numbers are from the mean.
- A small SD means the data is close to the mean.
- A large SD means the data is spread out.
Note for students: We do not need to calculate SD in detail in Class 9. Just understand the concept.
Types of Data in Statistics
1. Numerical Data
Data that involves numbers.
Example:
Marks of students, ages, height, weight
2. Categorical Data
Data that represents categories or groups.
Example:
- Gender (Male/Female)
- Type of transport (Bus, Cycle, Walk)
Graphical Representation of Data
To understand data better, we show it using graphs or charts.
Common graphs include:
- Bar Graph – For comparing categories
- Pie Chart – To show parts of a whole
- Line Graph – To show change over time
- Histogram – To show distribution of data
Graphs make it easy to visualize and analyze the data.
What is Probability?
Probability is the chance or likelihood of an event happening.
It is a number between 0 and 1.
- Probability of 0 means the event will not happen
- Probability of 1 means the event will definitely happen
Formula:
Probability = (Number of favorable outcomes) ÷ (Total number of outcomes)
Example 1: Tossing a Coin
- Total outcomes: 2 (Heads, Tails)
- Probability of getting Heads = 1/2
- Probability of getting Tails = 1/2
Example 2: Rolling a Dice
- Total outcomes: 6 (numbers 1 to 6)
- Probability of getting a 4 = 1/6
- Probability of getting an even number = 3/6 = 1/2 (even numbers: 2, 4, 6)
Types of Probability
1. Theoretical Probability
This is based on logic and known outcomes.
Example: Tossing a coin or rolling a dice
2. Experimental Probability
This is based on real experiments or data collected.
Example: Toss a coin 100 times and note how many times you get heads.
Formula:
Experimental Probability = (Number of times event happened) ÷ (Total number of trials)
Importance of Statistics and Probability in AI
- AI uses statistics to analyze data.
- Probability helps AI to predict what may happen next.
Examples:
- A weather app predicting rain based on past data.
- YouTube suggesting videos based on your watching pattern.
- A self-driving car deciding the best route using traffic data.
Suggested Classroom Activities and Practicals
1. Dice Game
Roll a dice 50 times and record the results.
- Count how many times each number appears.
- Find the experimental probability of getting each number.
2. Mini Survey and Data Analysis
Ask students to collect data on any topic.
Example: Favorite food of classmates.
- Organize the data in a table.
- Find mode (most liked food).
- Show the data using a bar graph or pie chart.
3. Number Pattern Game
Give students sets of numbers and ask them to:
- Find mean, median, and mode
- Discuss which number tells the best “story” about the data
Summary of the Unit
- Statistics helps us understand and organize data.
- Mean, median, and mode are important measures of central tendency.
- Probability tells us how likely something is to happen.
- Theoretical probability uses logic, while experimental probability uses real data.
- Maths is the foundation for AI to analyze data and make predictions.
- Practicing with real-world data helps improve both AI understanding and math skills.