Mathematic equation 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 โxโ or any value, algebraic inequation formulas are used. Similarly, when there is a need to calculate a bunch of numbers, the mean and average equation and formulas are used.

## Average vs Mean

**The main difference between average and mean is that Average is calculated for a set of values which are nearly same, whereas Mean is calculated for a set of values which have higher difference or the values are not close at all to each other. Arithmetic mean is referred to as Average, whereas Mean has its three different categories. **

The mean value which is equal to the sum of the ratio of the given set of numbers or values to the total number or values present in the set is defined as 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, 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 Mean in arithmetic. The term Mean is used often in many varied fields like anthropology, history, economics, statistics and it is utilized in almost every field of academics.

For example, Nationโs population is calculated by the mean of the per capita income.

## Comparison Table Between Average and Mean

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 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 is 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 of creating smoother series is in demand. This aid to show primary trends or rather periodic behaviour.

Moving average is one of the easiest ways to calculate periodic behaviour: an individual chooses a number โnโ and creates a fresh series by taking the mathematical mean of the first values of โnโ, 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 generally be used to amplify or vanquish different periodic behavior, very substantial analysis is done of what weightings 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 โmoving averageโ is utilized in digital signaling.

The reason behind this is that the observer is generally interested only in the drift or the periodic behavior. Average also follows a law.

The law of averages is a belief often 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 with 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, mean is the often used as a method to calculate the center of a value set.

Itโs the basic and important part of 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 average value which comes between the maximum and minimum value 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 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 known as an average, whereas the arithmetical average of the group/set of more than two value set is known as mean.
- Average can generally be known as mean or mathematical mean, whereas mean is a way of defining the average of a set.
- Mathematical mean is also considered as an average, whereas mean has multiple types.
- Average is used in day-today life, as a general English word, whereas mean is a very technical or arithmetical term.
- Average can contribute median and mode, whereas mean cannot provide median or mode.

## Conclusion

Average and mean, comparatively are slightly different but both are a very important matter in mathematics, statistics, economics and almost everywhere for bigger calculations.

Average is very commonly used in our day-to-day life as it not only a technical term but also an English term. Mean is generally widely used in calculating the population and it is a very technical term for a daily use.

Both the mathematical derivatives play a pivotal role in our daily lives.

## References

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