Average and Mean

The average is determined for sets of data that are almost identical, i.e. the difference between the sets of data is very minimal. While the mean is determined for those groups of numbers that differ or are near to one another.

Average

The sum of the specified numbers divided by the total number of numbers that are required to be averaged is defined as the average. 

The mathematical formula to arrive at average = sum of all the terms/Total number of terms

An average is a single specific number chosen to represent a set of numbers. Average is frequently used to refer to the mathematical mean. In the field of statistics, Average is always interchangeably used with Mean.

Let’s look at an example to better comprehend about Average.

The given set of numbers: 2,4,6,8,10,12

Sum of the given numbers = 2+4+6+8+10+12

Hence, Sum of the given numbers/ terms in the given set = 42

Total number of numbers in the set provided/ total number of terms = 6

Average = sum of all the terms/Total number of terms

Average = 42/6

Hence, Average = 7

Mean

The mean is the midpoint of a sequence of values or terms. It is referred to as the mean of the values in the data collection. In statistics, the value of mean is the centre value that is recognized as the average value in mathematics.

Mean is commonly used to refer to the arithmetic mean, but it may also refer to the Harmonic Mean, Geometric Mean, and so on. These types of means are utilised in various contexts depending on the composition and nature of the values & information.

It is also termed as the sum of the smallest and greatest values in the provided data set divided by two.

The mathematical formula to arrive at Mean is as follows:

Mean = (smallest value in the data set + largest value in the data set)2

Let’s look at an example to better comprehend about Mean.

The given set of numbers: 2,5,7,9,11,14

Smallest value in the data set = 2

Largest value in the data set = 14

Mean = (smallest value in the data set + largest value in the data set)2

Mean = (2+14)/2

Mean = (16)/2

Hence, Mean = 8

We may assert that average implies mean, but not the other way around.

Types of Mean

There are three kinds of means:

The Arithmetic Mean – It is the sum of the provided set’s values divided by the entire number of set’s values.

The Geometric Mean – It is identical to the arithmetic mean, except that instead of summing, we multiply the numbers and obtain the square root in the case of two numbers, the cube root in the case of three numbers, and so on.

The Harmonic Mean – The reciprocal of the arithmetic mean is the harmonic mean.

Average And Mean: Difference 

Average

• It is the total of the numbers divided by the number of numbers averaged
• Average is determined for groups of data that are almost identical
• An average is a specific number chosen to represent a set of numbers

Mean

• It is the sum of the smallest and biggest values in the supplied data set divided by two
• The mean is computed for those groups of data that differ the most or are not at all near to each other
• The mean is the midpoint of a group of values

Also See:

• Difference Between Atomic mass and Atomic weight
• Difference Between Atom and Ion
• Difference Between Ammeter And Galvanometer
• Difference Between AM and FM
• Difference Between Alternator and Generator
• Difference Between Alcohol and Phenol

Conclusion

We discussed Average, Mean, types of Mean, Difference between Average and Mean, and other related topics through the study material notes on the Difference between Average and Mean. 

The average is calculated by taking the total of all values and dividing it by the number of values. It is also referred to as mean at times. The mean in statistics is the average of a particular sample or data collection. It is calculated by dividing the total number of observations by the number of data points.