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Basic Average Calculation

Introduction

Aptitude tests में average questions काफी common होते हैं। Average (arithmetic mean) किसी group का equal share value बताता है।

अगर आपको values का total और number of values पता हो, तो average बहुत जल्दी निकाला जा सकता है।

Pattern: Basic Average Calculation

Pattern

Average का मुख्य formula:

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

यही formula सभी average-related problems की foundation है। चाहे marks हों, ages हों, runs हों या simple numbers - process हमेशा वही रहता है।

Step-by-Step Example

Question

Numbers 12, 18, 25, 15, और 20 का average निकालिए।

Options:

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

Solution

  1. Step 1: सभी values जोड़ें

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

  2. Step 2: Total items गिनें

    Numbers की संख्या = 5.

  3. Step 3: Average formula apply करें

    90 ÷ 5 = 18.

  4. Final Answer:

    18 → Option B

  5. Quick Check:

    5 × 18 = 90 → total match करता है ✅

Quick Variations

Common situations:

- Students के marks का average

- किसी group की average age

- Cricket में average runs

Trick to Always Use

  • सभी numbers ध्यान से जोड़ें।
  • Total count से divide करें।
  • Average × Count करके verify करें।

Summary

Summary

  • हमेशा values को accurately add करें।
  • Core formula उपयोग करें: Average = Sum ÷ Count.
  • Result check करने के लिए average × number of items multiply करें।
  • इस method को numbers, marks, runs, ages आदि पर apply कर सकते हैं।

याद रखने लायक example:
अगर 5 values का sum 90 है, तो 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.

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