How to Find the Average? All You Need to Know

The average, also referred to as the arithmetic mean, is a fundamental metric in mathematics that is used to describe a set of numbers using a single value that represents the data's central tendency. It provides a simple and effective way to understand the overall trend of a dataset.

The average is calculated by dividing the sum of all values in a dataset by the number of values present. It is expressed as:

Average = Sum of Values/Number of Values

Example:

Let’s say we have these numbers: 4, 6, 8, and 12

1. Add them up: 4 + 6 + 8 + 12 = 30
2. Count how many numbers: 4
3. Divide: 30 ÷ 4 = 7.5

So, the average is 7.5.

Types of Averages

1. Arithmetic Mean (Simple Average)

This is what most people mean when they say “average.”

How to do it:
 

Add all the numbers together, then divide by how many numbers there are.

Example:
 

Numbers: 5, 10, 15
 

Add: 5 + 10 + 15 = 30
 

Divide: 30 ÷ 3 = 10
 

So, the average is 10

2. Median (Middle Number):

The median is the number in the middle when all the numbers are in order.

How to do it:

• Put the numbers in order.
• If there’s an odd number of values, pick the middle one.
• If there’s an even number, add the two middle ones and divide by 2.
  
  Read More – How to Calculate Average Percentage
  
  

Example 1 (odd amount):
 

Numbers: 3, 5, 7
 

Middle number = 5

Example 2 (even amount):
 

Numbers: 2, 4, 6, 8
 

Middle two: 4 and 6
 

(4 + 6) ÷ 2 = 5

3. Mode (Most Often)

The mode is the number that appears the most.

Example:
 

Numbers: 2, 3, 3, 5, 6
 

3 appears the most, so the mode is 3

If no number repeats, there’s no mode.
 

If two or more numbers appear the same most times, it’s multi-mode.

4. Weighted Average

This is used when some numbers are more important than others.

How to do it:

• Multiply each number by its weight.
  
• Add those results.
• Divide by the total of the weights.

Example:
 

Scores: 80 (weight 2), 90 (weight 3)
 

(80×2 + 90×3) = 160 + 270 = 430
 

Total weight = 2 + 3 = 5
 

430 ÷ 5 = 86
 

So, the weighted average is 86

5. Trimmed Mean

This average removes the smallest and largest numbers to avoid extreme values messing things up.

How to do it:

• Take away the lowest and highest numbers.
• Find the average of what’s left.

Example:
 

Numbers: 1, 2, 3, 4, 100
 

Remove 1 and 100
 

Left: 2, 3, 4
 

(2 + 3 + 4) ÷ 3 = 3

Also Read - How to Calculate Percentage of Marks
 

How to Calculate the Average?

Formula:  Average = Number of values/Total of the numbers​

Real-World Applications

Calculating averages is useful in various areas:

• Education: Determining the average score of students in a class.
  
  
• Finance: Calculating average monthly expenses or income.
  
  
• Health: Monitoring average daily steps or calorie intake.

Tips for Accurate Calculation

• Ensure all numbers are included: Missing numbers can skew the average.
  
  
• Be cautious with large datasets: For large datasets, consider using tools like Excel or Google Sheets to automate the calculation.
  
  
• Understand the context: The average provides a central value, but it may not represent all data points equally, especially if there are outliers.

Real-Life Applications of Averages

Average Marks in Geography Class 
 

• Scenario: In a class of 50 students, the average mark scored in Geography is 72 out of 100.
  
  
• Calculation: To find the total marks scored by all students, multiply the average by the number of students:
  
  
• Total Marks = Average × Number of Students = 72 × 50 = 3600

The total marks obtained by all 50 students combined is 3600.

Average Percentage of Marks in Mathematics

• Scenario: Jyoti secured 35 marks out of 50 in English and 25 marks out of 30 in Mathematics.
  
  
• Calculation: To compare her performance across subjects, calculate the percentage for each:

English:

• Percentage = (Marks Obtained/ Total Marks) × 100 = (30 / 50) × 100 = 70%

Mathematics:

• Percentage = (Marks Obtained/ Total Marks) × 100 = (25 / 30) × 100 = 83.33%

Jyoti performed better in Mathematics with a percentage of approximately 83.33%, compared to 70% in English.

Interactive Problems to Reinforce Understanding

Problem 1:

In a class of 50 students, the average mark scored in Mathematics is 65 out of 100. The total marks scored by all students except Karan and Arjun is 3080. If the marks scored by Karan and Arjun are the same, what are the marks scored by Arjun?

Solution:
 

 Let the marks scored by Karan and Arjun be x.

The total marks scored by all 50 students is:

65 × 50 = 3250

The total marks scored by Karan and Arjun is:

3250 − 3080 = 170

Since Karan and Arjun scored the same marks:

2x = 170 ⇒ x = 85

Arjun scored 85 marks.

The Average of Negative Numbers

Average = Total number of numbers / Sum of all numbers

Example: All Negative Numbers

Numbers: -4, -6, -8

• Step 1: Add them

 − 4 + (−6) + (−8) =−18

• Step 2: Count them
   There are 3 numbers
  
  
• Step 3: Divide
   − 18 ÷ 3 = − 6

Average = -6

Tips and Tricks

1. Use Rounding for Quick Estimates

If you need a rough average quickly, round the numbers to the nearest 10 or 100, calculate the average, and then adjust if needed.

Example:
 

 Instead of averaging 98, 102, and 97 directly, estimate with 100 for each →
 (100 + 100 + 100) ÷ 3 = 100 (rough estimate)

2. Average of Consecutive Numbers

The average of consecutive numbers is always the middle number.

Example:
 

Average of 5, 6, 7 = 6

For an even set, it's the average of the two middle numbers.
 

Example: 4, 5, 6, 7 → (5 + 6) / 2 = 5.5

3. Use the Formula Backwards

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

Sum= Average × Number of Values

Example: If the average score of 8 students is 75, the total marks = 75 × 8 = 600

4. Use Excel or a Calculator for Large Sets

For large datasets, save time by using:

• Excel: Use the formula =AVERAGE(A1:A10)
  
  
• Scientific calculator: Add all numbers and divide

5. Remove Extremes for Better Context

Outliers can distort your average. Try calculating a trimmed mean by removing the highest and lowest values.

Example:
 

 1, 3, 4, 5, 100 → Trim 1 and 100 → Average of 3, 4, 5 = 4

6. Know When NOT to Use the Average

Use median instead of average when:

• Data has extreme outliers
  
  
• Values are not normally distributed

7. Break the Data into Chunks

When working with large or mixed numbers, break them into smaller groups, average each, and then find the overall average using the weighted average technique if needed.

Conclusion

Calculating and understanding averages is an important academic and life skill. When assessing grades, costs, or trends, the average gives a quick and reliable way to summarise data. You can improve your ability to decide and numerical cognition by learning basic average forms and applying simple methods. Use examples from everyday life to develop your confidence and accuracy.

Faqs

Q. What is the average? Give an example.

The middle value in a given set of variables is called the average. For instance, (3+5)/2 = 8/2 = 4 is the average of 3 and 5. Thus, the central value for 3 and 5 is 4.

Q. What is the average formula?

The average of the provided numbers can be found by dividing the total number of values by the sum of all the values. (Sum of Values/Number of Values) = Average.

Q. Is the average and mean of numbers, the same?

The term "average" in basic mathematics refers to the mean of values. Consequently, it makes sense that the terms mean and average are similar.

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