AVERAGE

Average is one of the most important and frequently applied concepts in CSAT. Though it looks mathematically simple, CSAT questions test whether the aspirant understands the logic behind average, not just the formula. Average-based reasoning is widely used in questions related to marks, age, income, temperature, speed, data interpretation, and even logical estimation.

MEANING OF AVERAGE

• Average represents a single value that describes the central tendency of a group of values
• It gives an overall idea of the data rather than exact details

Basic Definition
• Average = Sum of observations / Number of observations

Example
• Marks of 5 students = 40, 50, 60, 70, 80
• Average = (40+50+60+70+80)/5 = 60

Interpretation
• Average does not mean all values are equal
• It only represents a balance point

TYPES OF AVERAGE (CSAT CONTEXT)

Simple Arithmetic Mean
• Most commonly used average
• Formula:
  Average = Total / Number

Weighted Average (Conceptual Introduction)
• Used when values have different importance
• Frequently applied in:
  – Speed problems
  – Marks with different weightage
  – Price variation problems

AVERAGE AND TOTAL RELATION

Very Important Concept
• Total = Average × Number of observations

This relation is heavily used in CSAT to:
• Find missing values
• Handle replacement questions
• Solve multi-group problems

AVERAGE WHEN A VALUE IS ADDED

Concept
• When a new value is added, total increases and number increases by 1

Formula Approach
• New Average = (Old Total + New Value) / New Number

CSAT Logic Tip
• Compare new value with old average:
  – If new value > old average → average increases
  – If new value < old average → average decreases

AVERAGE WHEN A VALUE IS REMOVED

Concept
• When a value is removed, both total and count reduce

CSAT Trick
• If removed value is less than average → new average increases
• If removed value is more than average → new average decreases

REPLACEMENT CONCEPT (VERY IMPORTANT)

Replacement means:
• One value is removed
• Another value is added
• Total changes but number remains same

Formula
• Change in average = (New value − Old value) / Number

AVERAGE OF TWO GROUPS

Concept
• Combined average lies between individual averages

Formula
• Combined Average =
  (Avg₁ × n₁ + Avg₂ × n₂) / (n₁ + n₂)

Logical Insight
• Group with larger size has greater influence

AVERAGE SPEED (INTRODUCTION)

Definition
• Average speed = Total distance / Total time

Important Insight
• Average of speeds is not simple average unless distances are equal

This concept is crucial for:
• Train problems
• Round-trip problems

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Subject: CSAT

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