Infographic: Averages | Quantitative Aptitude (Quant) - CAT PDF Download

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Infographic: Averages
Basic Definition
Central value in a data set
Average = Sum of values ÷ Total 
number of values
Key Formulae
Simple Average = (a¡ + a¢ + ... + a¹) 
/ n
Mode = 3 × Median - 2 × Mean
Median & Mode
Median: Middle value when 
arranged
Mode: Most frequently occurring 
value
Essential Formulae
Natural Numbers
First n natural numbers: (n+1)/2
First n even numbers: n + 1
First n odd numbers: n
Squares of first n natural numbers: (n+1)(2n+1)/6
Important Points
Sum of first n natural numbers: n(n+1)/2
In AP: odd terms ³ middle term is average
In AP: even terms ³ average of two middle terms
Shortcut Techniques
01
Finding New Average
Take difference: New score - Old 
average
Divide by total innings
Add to old average
02
When Average Changes
Calculate change in average
Multiply by sample size
Add/subtract from base average
03
Deviation Method
Use assumed mean to simplify
Calculate deviations from assumed 
value
Adjust final result
Person Replacement Rules
1
Average Increases
New person age = Left person age + 
(Increase × Total persons)
2
Average Decreases
New person age = Left person age - 
(Decrease × Total persons)
3
Person Joins
New member = Previous average ± 
(Change × Members including new)
Weighted Average
Weighted Mean = (x¡w¡ + x¢w¢ + ... + x¹w¹) / (w¡ + w¢ + ... + w¹)
Where x = values and w = respective weights
Quick Tips & Tricks
Tip 1
If each number increases/decreases by n, average also 
changes by n
Tip 2
If each number multiplied/divided by n, average also 
multiplied/divided by n
Tip 3
Average of consecutive series = middle term (median)
Tip 4
Same value added to half & subtracted from half = no 
change in average
EduRev Tip: To maximise players with high scores, balance with minimum scores. Use deviation method for complex 
weighted averages to save time!