Mean Formula

 

The mean formula is a fundamental concept in statistics used to determine the average of a set of numbers. It is one of the most basic measures of central tendency, helping us understand the general trend in a dataset. Whether you’re analyzing exam scores, daily temperatures, or survey data, the mean in statistics gives a clear picture of the “typical” value.

This article covers the definition, formula of mean for both grouped and ungrouped data, and includes solved examples and practice questions.

 

Table of Contents

• What is Mean in Statistics?
• Mean Formula for Ungrouped Data
• Mean Formula for Grouped Data
• How to Calculate Mean
• Solved Examples on Mean Formula
• Practice Problems on Mean Formula
• Applications of Mean in Real Life
• Conclusion
• FAQs on Mean Formula

 

What is Mean in Statistics?

The mean in statistics is the average of a set of values. It is calculated by dividing the total sum of the values by the number of values in the dataset.

In simple terms:
Mean = (Sum of all values) / (Number of values)

It is represented by the symbol x̄ (x-bar).

 

Mean Formula for Ungrouped Data

Mean (x̄) = Σx / n
Where:
x̄ = mean
Σx = sum of all values
n = number of values

 

Mean Formula for Grouped Data

Mean (x̄) = Σfx / Σf
Where:
f = frequency
x = midpoint of class interval
Σfx = sum of frequency multiplied by midpoint
Σf = total frequency

 

How to Calculate Mean

For Ungrouped Data:

1. Add all the values

2. Count the number of values

3. Divide the total by the number of values
   
   

For Grouped Data:

1. Find midpoints: (lower limit + upper limit) / 2

2. Multiply each midpoint by its frequency (fx)

3. Add all fx values

4. Divide by total frequency
   
   

 

Solved Examples on Mean Formula

Example 1 (Ungrouped Data):
Find the mean of 5, 7, 9, 10, 14
Mean = (5 + 7 + 9 + 10 + 14) / 5 = 45 / 5 = 9

Example 2 (Grouped Data):

Class Interval | Frequency
0 - 10 | 4
10 - 20 | 6
20 - 30 | 5
30 - 40 | 3

Midpoints: 5, 15, 25, 35
fx: 4×5=20, 6×15=90, 5×25=125, 3×35=105
Mean = (20 + 90 + 125 + 105) / (4 + 6 + 5 + 3) = 340 / 18 = 18.89

 

Practice Problems on Mean Formula

1. Find the mean of: 6, 10, 15, 25, 30
   
   

2. Use the mean formula to calculate the average marks from this table:
   Marks | Frequency
   0-20 | 2
   20-40 | 3
   40-60 | 5
   60-80 | 4
   
   

3. If the mean of 4, x, 10 is 8, find x
   
   

4. The following data shows scores of students. Find the arithmetic mean:
   Score Range | Frequency
   0–50 | 7
   50–100 | 13
   
   

5. Mean of 5 consecutive numbers is 20. What is the largest number?
   
   

 

Applications of Mean in Real Life

• Academics: Average marks and scores

• Business: Average sales, revenue, or profits

• Healthcare: Mean patient age, mean diagnosis time

• Sports: Batting or scoring averages

• Weather: Average temperatures or rainfall
  
  

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Conclusion

The mean formula is essential in statistical analysis for understanding data behavior. Whether using the formula of mean for grouped or ungrouped data, it's a versatile tool in academics, economics, research, and more.

 

Frequently Asked Questions on Mean Formula

1.What is the formula of mean in statistics?

Ans. Mean = Σx / n or Mean = Σfx / Σf

2.What is the difference between mean and average?

Ans. There is no difference; they are used interchangeably.

3.What symbol is used for mean?

Ans. The symbol is x̄ (x-bar).

4.How do you calculate mean from grouped data?

Ans.  Use the formula: Mean = Σfx / Σf, where x is the midpoint.

5.When is mean not reliable?

 Ans. Mean is not reliable when the data has outliers or extreme values. In such cases, median may be a better measure.

 

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