🗺️ Chapter Roadmap
1 & 2 Average & The Universal Formula
Finding an average means gathering everything together and then distributing it equally. In statistics, this is formally called the "Mean".
(Add all the numbers together, then divide by how many numbers there are)
🏏 The Cricket Example:
A batsman scores the following runs in his 3 matches:
Step 1 (Find the Sum): 50 + 100 + 0 = 150 total runs
Step 2 (Divide): The number of matches is 3. So, 1503 = 50
Batsman's Average = 50 runs per match
3 The "Sum" Trick (Working Backwards)
In many competitive exams, they don't ask you to find the average. Instead, they give you the average and ask you to find the total sum. Just multiply the average by the number of items!
💡 Sum = Average × Number of Items
Exam Question: The average weight of 5 students is 40 kg. What is their total combined weight?
4 Finding the Missing Number
Once you understand the "Sum Trick" above, finding a missing number becomes very easy.
Exam Example: The average of three numbers is 20. If two of the numbers are 15 and 25, what is the third number?
-
Step 1: Find the Total Sum
3 numbers × Average of 20 = 60 (This must be the total sum) -
Step 2: Find the Sum of known numbers
We know two numbers: 15 + 25 = 40 -
Step 3: Subtract to find the missing piece
Total Sum (60) - Known Sum (40) = 20
The third number is 20.
5 ⚡ Speed Trick for Consecutive Numbers
Sometimes tests ask long questions like: "Find the average of the first 100 natural numbers". If you try to add 1 + 2 + 3... up to 100, you will run out of time!
The First/Last Shortcut Rule:
If the numbers form a continuous sequence with an equal gap between them (Like 1, 2, 3... or Even numbers 2, 4, 6... or Multiples of five 5, 10, 15...), you do not need to add all of them!
Just add the First number and the Last number, and divide by 2.
(Numbers: 1, 2, 3 ... 100)
First = 1, Last = 100
1 + 1002 = 1012 = 50.5
(Numbers: 2, 4, 6, 8, 10)
First = 2, Last = 10
2 + 102 = 122 = 6