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Basic Average Calculation

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Introduction

In aptitude tests, average questions are very common. The average (arithmetic mean) represents the equal share value of a group.

If you know the total of values and the number of values, you can quickly calculate the average.

Pattern: Basic Average Calculation

Pattern: Basic Average Calculation

The key formula for average is:

Average = (Sum of all items) ÷ (Number of items)

This formula is the foundation for solving all average-related problems. Whether it’s marks, ages, runs, or numbers, the process remains the same.

Step-by-Step Example

Question

Find the average of the numbers 12, 18, 25, 15, and 20.

Options:

  • A) 16
  • B) 18
  • C) 20
  • D) 22

Solution

  1. Step 1: Add all values

    12 + 18 + 25 + 15 + 20 = 90.

  2. Step 2: Count the items

    There are 5 numbers.

  3. Step 3: Apply the average formula

    90 ÷ 5 = 18.

  4. Final Answer:

    18 → Option B

  5. Quick Check:

    5 × 18 = 90 → matches the total ✅

Quick Variations

Common situations:

- Average of marks scored by students.

- Average age of a group.

- Average runs scored in cricket.

Trick to Always Use

  • Add all numbers carefully.
  • Divide by the total count.
  • Verify by multiplying Average × Count.

Summary

  • Always start by adding all values accurately.
  • Use the core formula: Average = Sum ÷ Count.
  • Cross-check the result by multiplying average × number of items.
  • Apply this method to numbers, marks, runs, ages, and more.

Example to remember:
If the sum of 5 values is 90, then average = 90 ÷ 5 = 18.

Practice

(1/5)
1. Find the average of 10, 20, 30, and 40.
easy
A. 25
B. 20
C. 30
D. 35

Solution

  1. Step 1: Calculate the total sum

    Sum = 10 + 20 + 30 + 40 = 100.

  2. Step 2: Count the number of items

    Count of numbers = 4.

  3. Step 3: Apply the average formula

    Average = 100 ÷ 4 = 25.

  4. Final Answer:

    25 → Option A

  5. Quick Check:

    25 × 4 = 100 ✅
Hint: Pair extremes: (10+40) and (20+30) to get totals quickly.
Common Mistakes: Forgetting to divide the sum by the number of items.
2. Find the average of the first 8 natural numbers (1 to 8).
easy
A. 4
B. 4.5
C. 5
D. 3.5

Solution

  1. Step 1: Add all numbers

    Sum = 1+2+3+4+5+6+7+8 = 36.

  2. Step 2: Identify the count

    Count = 8.

  3. Step 3: Compute the average

    Average = 36 ÷ 8 = 4.5.

  4. Final Answer:

    4.5 → Option B

  5. Quick Check:

    For consecutive numbers average = (first + last)/2 = (1+8)/2 = 4.5 ✅
Hint: For consecutive numbers, average = (first + last)/2.
Common Mistakes: Summation errors or forgetting to divide by count.
3. Find the average of 14, 18, 22, and 26.
easy
A. 18
B. 19
C. 20
D. 21

Solution

  1. Step 1: Add all numbers

    Sum = 14 + 18 + 22 + 26 = 80.

  2. Step 2: Count the numbers

    Count = 4.

  3. Step 3: Divide to get the average

    Average = 80 ÷ 4 = 20.

  4. Final Answer:

    20 → Option C

  5. Quick Check:

    (14+26)/2 = 20 and (18+22)/2 = 20 → consistent ✅
Hint: Evenly spaced numbers: average = middle value (or (first+last)/2).
Common Mistakes: Arithmetic slip when summing the numbers.
4. Find the average of 5, 15, 25, 35, and 45.
medium
A. 20
B. 22
C. 24
D. 25

Solution

  1. Step 1: Calculate the sum

    Sum = 5 + 15 + 25 + 35 + 45 = 125.

  2. Step 2: Count all numbers

    Count = 5.

  3. Step 3: Divide sum by count

    Average = 125 ÷ 5 = 25.

  4. Final Answer:

    25 → Option D

  5. Quick Check:

    Middle term of this arithmetic progression is 25 → average = 25 ✅
Hint: For odd count in AP, average = middle term.
Common Mistakes: Miscalculating the sum or misplacing the middle value.
5. The average of 20, 28, 32, and 40 is?
medium
A. 30
B. 29
C. 28
D. 31

Solution

  1. Step 1: Add the numbers

    Sum = 20 + 28 + 32 + 40 = 120.

  2. Step 2: Count the terms

    Count = 4.

  3. Step 3: Compute the average

    Average = 120 ÷ 4 = 30.

  4. Final Answer:

    30 → Option A

  5. Quick Check:

    Group (20+40=60, 28+32=60) → total 120; 120 ÷ 4 = 30 ✅
Hint: Pair numbers to make round sums quickly (20+40, 28+32).
Common Mistakes: Arithmetic slip while adding pairs.