Mathematic equations and formulas are methods through which we can solve or calculate big numbers and inputs in an easier and shortcut way.
When there is a need to find out the value of ‘x’ or any value, algebraic inequation formulas are used. Similarly, when there is a need to calculate a bunch of numbers, the mean and average equations and formulas are used.
Key Takeaways
- The average represents a central value of a data set, calculated by dividing the sum of values by the number of values.
- Mean is a specific type of average, which is the arithmetic mean.
- Both average and mean can be affected by outliers, skewing the representation of central tendency.
Average vs Mean
The term “mean” refers to the arithmetic average of a set of values and is the common type of average. The term “average” can refer to different types of averages, such as the mean, median, or mode, where it represents the central tendency of a set of data.
The mean value, which is equal to the sum of the ratio of the given set of numbers or values to the total number of values present in the set, is defined as the mathematical Average.
For example, the average of 3,5,7 will be (3+5+7)/3 = 5. Therefore, the central value of the set is 3. Hence, the average is the mean value of a set of numbers.
While the central calculated value of a group or set of numbers is defined as the Mean in arithmetic, the term Mean is used in many fields like anthropology, history, economics, and statistics and is utilized in almost every field of academics.
For example, Nation’s population is calculated by the mean of the per capita income.
Comparison Table
| Parameters of Comparison | Average | Mean |
|---|---|---|
| Definition | The sum of the total value divided by the total number of values is known as an average. | The arithmetical average of the group/set of more than two value set is known as mean. |
| Formula | Average= (sum of the numbers/values)/ (total number of units.). | Mean = (sum of total values)/ (number of values). |
| Types | Mathematical mean is also considered as an average. | Mean has multiple types. |
| Contribution in median and mode | Can contribute median and mode. | Cannot provide median or mode. |
| Other names | Average is also known as mean or mathematical mean. | It is a way of defining the average of a set. |
What is Average?
The number of the units present in a set will divide by the sum of all the numbers present in the set, i.e., the ratio of the sum of the numbers or values in a set to the total units in the set.
It is written or formulated as AVERAGE = SUM OF THE NUMBERS/ TOTAL NUMBER OF UNITS. Average=(sum of the numbers/values)/(total number of units.)
In time series, such as regular stock market prices or annual temperatures, the want to create smoother series is in demand. This aid in showing primary trends or rather periodic behaviour.
The moving average is one of the easiest ways to calculate periodic behaviour: an individual chooses a number ‘n’ and creates a fresh series by taking the mathematical mean of the first values of ‘n’, followed by moving forward a place by leaving the oldest value/number and introducing a fresh value/number at the opposite end of the list, and it goes on.
Nothing can be as simple as this form of moving average. Using a weighted average is a bit more complicated form.
The weighting can be used to amplify or vanquish different periodic behaviour, very substantial analysis is done of what weightings are to be used in the literature on straining.
Even when the sum of the weights is not more than or equal to 1.0 (the output series/chain is a scaled type of the averages), the term “moving average” is utilized in digital signalling.
This is because the observer is interested only in the drift or the periodic behaviour. Average also follows the law.
The law of averages is a belief held that a certain outcome or event will, over distinct periods of time, happen at a frequency that is almost equal to its probability.
Based on the context or the sense of application, it can be considered a logical, common-sense observation or a misinterpretation of probability.
What is Mean?
Mean is a mathematical average of a group of values that is calculated by dividing the sum of all the given values by the number of values in the set.
It is a point in a value set that is called the average of all the values in a set/group. In statistics, the mean is used as a method to calculate the centre of a value set.
It’s the basic and important part of the statistical analysis of data. Calculating the average mean of the population is called population mean/mean population.
The population data is vast sometimes, and analysis on that value set cannot be performed. So, in that situation, the average is calculated by taking a sample out of it.
That sample denotes the population set, and the mean of this part of the value is defined as a sample mean. Mean = (sum of total values)/(number of values)
The mean value is also known as the average value, which comes between the maximum and minimum values in a group of data.
The numbers can be the values in the set, but the mean value cannot be. The fundamental formula to calculate the output of the mean is based on the provided data/values. While evaluating the mean, each term in the data set is counted in.
Main Differences Between Average and Mean
- The sum of the total value divided by the total number of values is an average, whereas the arithmetical average of the group/set of more than two value sets is the mean.
- The average can be known as the mean or mathematical mean, whereas the mean is a way of defining the average of a set.
- The mathematical mean is also considered as an average, whereas the mean has multiple types.
- Average is used in day-to-day life as a general English word, whereas mean is a very technical or arithmetical term.
- The average can contribute median and mode, whereas the mean cannot provide the median or mode.
I’ve put so much effort writing this blog post to provide value to you. It’ll be very helpful for me, if you consider sharing it on social media or with your friends/family. SHARING IS ♥️
The discussion of population mean and sample mean is well-articulated. It’s important to distinguish between these concepts, and the article does so effectively.
The explanations of moving averages, weightings, and the law of averages are insightful. They provide additional context and understanding of the practical applications of averages.
The article provides a clear definition and comparison of average and mean, and explains their use in various fields. It is very informative and helpful for understanding statistics.
Completely agree with you, the article does a great job of simplifying the concepts and making them easy to understand.
The distinction between average and mean, especially in terms of outliers and representation of central tendency, is well-explained in this article. It’s a valuable resource for anyone studying statistics.
The article’s breakdown of average and mean is incredibly detailed and provides a solid foundation for understanding these statistical measures. The inclusion of practical examples further enhances comprehension.
I completely agree. The use of examples makes the article engaging and effectively reinforces the theoretical explanations.
Absolutely, the practical examples help readers visualize how average and mean are applied in real-world scenarios.
I appreciate the detailed comparison table that clearly outlines the differences between average and mean. It’s a practical way to summarize the key points of the topic.
This article beautifully illustrates the mathematical concepts behind average and mean. The example calculations provided for both concepts make the learning process easier for readers.
I find the section about the law of averages particularly interesting. It’s fascinating how probability and frequency converge in this concept. The article has done a great job of presenting such a complex topic in a comprehensive manner.