Chapter: Average

“The average (or arithmetic mean) gives us the central value of a set of numbers. It is frequently tested in SSC, RRB, Banking, and other exams.”

1. Basic Concepts and Formulas

  • Average (AM) = Sum of terms / Number of terms
  • Sum = Average × Number of terms
  • For equal weight items, AM is used; for weighted values, use Weighted Average

2. Type-Wise Questions

  • Type 1: Simple Average
    Example: Find the average of 10, 20, 30, 40, 50.
    Solution: (10+20+30+40+50)/5 = 150/5 = 30
  • Type 2: Average of Consecutive Numbers
    Example: Find the average of first 10 natural numbers.
    Solution: (1+2+...+10)/10 = 55/10 = 5.5
  • Type 3: Average After Replacement
    Example (SSC CGL 2021): Average of 10 numbers is 30. One number (40) is replaced by 60. New average?
    Solution: Total increase = 20 ⇒ Avg increase = 20/10 = 2 ⇒ New Avg = 32
  • Type 4: Average Speed
    Formula: 2xy / (x + y) for two equal distances
    Example: A car goes at 60 km/h and returns at 40 km/h. Find average speed.
    Solution: 2×60×40 / (60+40) = 4800/100 = 48 km/h
  • Type 5: Weighted Average
    Example: A boy scores 80 in test (weight 2), 90 in another (weight 3). Find average.
    Solution: (80×2 + 90×3)/(2+3) = (160+270)/5 = 86

3. Previous Year Exam Questions

  • (RRB ALP 2018): The average of 5 numbers is 72. Average of first 4 is 70. Find 5th number.
    Solution: Total = 5×72 = 360; First 4 = 4×70 = 280 ⇒ Fifth = 360 - 280 = 80
  • (SSC CHSL 2020): Average age of 4 members is 36. New member joins, avg becomes 35. Find new member’s age.
    Solution: Old total = 4×36 = 144; New total = 5×35 = 175 ⇒ New = 175 - 144 = 31
  • (SSC CGL 2019): Average of 10, 20, x is 25. Find x.
    Solution: (10+20+x)/3 = 25 ⇒ x = 45

4. Tips to Remember

  • To find a missing number, work with total sum first.
  • In average speed problems, don't take simple mean. Use correct formula.
  • For weighted averages, multiply each value with its weight.
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