# What Is The Formula Of Arithmetic Mean? (Perfect answer)

The arithmetic mean is calculated by adding up all the values and dividing the sum by the total number of values. For example, the mean of 7, 4, 5 and 8 is 7+4+5+84=6.

## What is arithmetic mean write the formula?

Arithmetic mean is the sum of all observations divided by a number of observations. Arithmetic mean formula = {Sum of Observation}÷{Total numbers of Observations} Arithmetic mean formula = X=ΣXin X = Σ X i n, where i varies from 1 to n.

## What is the formula of arithmetic mean Class 11?

The formula to calculate the arithmetic mean is: Arithmetic Mean, AM = Sum of all Observations/Total Number of Observations.

## What is the arithmetic mean between 10 and 24?

Using the average formula, get the arithmetic mean of 10 and 24. Thus, 10+24/2 =17 is the arithmetic mean.

## How do you solve mean economics?

Mean is a point in a data set which is the average of all the data point we have in a set. It is basically arithmetic average of the data set and can be calculated by taking a sum of all the data points and then dividing it by the number of data points we have in data set.

## What is the formula of mean in class 10th?

To find the mean, we divide the sum of the observations by the total number of observations. The mean of a given set of data is equal to the sum of the numerical values of each and every observation divided by the total number of observations.

## How do you find the arithmetic mean of an 11th class?

Arithmetic Mean is the number which is obtained by adding the values of all the items of a series and dividing the total by the number of items.

## How do you find the arithmetic mean of Class 9?

Sum of all of the numbers of a group, when divided by the number of items in that list is known as the Arithmetic Mean or Mean of the group. For example, the mean of the numbers 5, 7, 9 is 4 since 5 + 7 + 9 = 21 and 21 divided by 3 [there are three numbers] is 7.

## What is the arithmetic mean between 19 and 7?

Solution:Arithmetic mean between 7 and 19 is 13.

## What is the arithmetic mean of 4 and 9?

What is the geometric mean of 4 and 9? The geometric mean of 4 and 9 is 6.

## What is the formula for finding the mean?

The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.

## Why do we calculate mean?

The mean is essentially a model of your data set. It is the value that is most common. That is, it is the value that produces the lowest amount of error from all other values in the data set. An important property of the mean is that it includes every value in your data set as part of the calculation.

## Arithmetic Mean Formula – What Is Arithmetic Mean Formula? Examples

The arithmetic mean formula is used to compute the mean or average of a set of numbers, which is then used to determine the central tendency of the data. It may alternatively be defined as the ratio of the total number of observations to the sum of all the observations that have been provided. Let us look at several cases of the arithmetic mean formula that have been solved.

## What Is Arithmetic Mean Formula?

If you want to determine the arithmetic mean of a set of data, you simply add all of the observations together and divide the total number of observations by the number of observations in question. The following is the arithmetic mean formula, which may be used to compute the mean set of observations:

### Arithmetic Mean Formula

It is defined as the total of all observations divided by a certain number of observations (the arithmetic mean). The arithmetic mean formula is (X=Sigma frac n), where I is a number ranging from 1 to n, and the arithmetic mean formula is Simple hints helped students learn a lot in high school. If you engage in rote learning, you are more prone to lose important information. Cuemath is a visual learning tool that will leave you startled by what you learn. Schedule a No-Obligation Trial Class.

## Examples on Arithmetic Mean Formula

Example 1: Eight students took a class test and received the following scores: 10, 19, 12, 21, 18, 20, 11, and 19. What is the arithmetic mean of the grades that the pupils received? Solution: To calculate: the arithmetic mean of the grades received by the students With the use of this formula, arithmetic mean Equals Arithmetic mean = ((10+19+12+21+18+20+11+19) x 8= 16.25 Answer: The arithmetic mean of the grades earned by the students is 16.25 points. The heights of five pupils are 164 cm, 134 cm, 155 cm, 156 cm, and 172 cm, respectively, as shown in the table below.

Solution: To determine the following: the mean height of the students Using the arithmetic mean formula,Arithmetic mean =/ Arithmetic mean = (164 + 134 + 155 + 156 + 172)/5 = 781/5 = 156.2 cm Arithmetic mean = (164 + 134 + 155 + 156 + 172)/5 = 781/5 = 156.2 cm The average height of the pupils was 156.2 centimeters.

One new employee has been added to the group, earning a monthly pay of \$1550.

Solution: With n = 5, x = 1400, and the arithmetic mean formula, x = xi/nxi = xi nxi = xi nxi = 7000xi = nxi = 1400nxi = 7000xi The total wage for five employees is \$7000.

The average wage of six employees is 8550/6 = 1425.

## FAQs on Arithmetic Mean Formula

According to statistical theory, the arithmetic mean formula is defined as the total of all observations divided by the number of observations.

The arithmetic mean formula in general is =. In statistics, the arithmetic mean formula is written as (X=Sigma frac n), where I is a number ranging from 1 to n.

### How To Calculate the Arithmetic Mean Using Arithmetic Mean Formula?

It is simple to determine the average of a collection of observations if just the total number of observations (n) is known. This may be accomplished by using an algebraic mean formula, such as Arithmetic Mean =n.

### How To Use the Arithmetic Mean Formula?

Calculating the generic arithmetic mean formula may be represented numerically as Arithmetic Mean = Consider the following example to better understand how to utilize the arithmetic mean formula. Example: Calculate the arithmetic mean of the following data: (1, 2, 3, 4, 5). Solution: The total number of observations was five. Formula for calculating the arithmetic mean = In mathematics, the Arithmetic Mean is defined as ((1 + 2 + 3 + 4 + 5) 5 = 15/5 = 3. The arithmetic mean of the numbers (1, 2, 3, 4, 5) is 3.

### What Will Be the Arithmetic Mean Formula for n Observations?

n observations is represented by the arithmetic mean formula, which is stated as Arithmetic mean of n observations Equals

## What is the Arithmetic Mean Formula?

The word “arithmetic mean” refers to the mathematical average of two or more integers, and it is most commonly used in mathematics. Calculating the arithmetic mean can be accomplished in a variety of ways depending on the frequency of each variable in the data set, including using a simple average (equally weighted) or a weighted average. When dealing with equally weighted variables, it is possible to get the formula for the arithmetic mean by adding all of the variables in the data set and then dividing the result by the number of variables in the data set.

+ x n) / n or Arithmetic Mean = x i/ nArithmetic Mean = (x 1+ x 2+.

+ x n) / n

• X I equals the I th variable
• N equals the number of variables in the data collection

For unequally weighted variables, the arithmetic mean formula may be determined by adding the products of each variable and its frequency, and then dividing the result by the total of all the frequencies in the population. Arithmetic Mean = (f 1 *x 1+f 2 *x 2+. + f n *x n) / (f 1+ f 2+. + f n) or Arithmetic Mean = (f I x I / (f I x I or Arithmetic Mean = (f I x I or Arithmetic Mean = (f I x I /

• X I equals the I th variable
• F I equals the frequency of the I th variable

### Examples of Arithmetic Mean Formula (With Excel Template)

Let’s look at an example to better understand how to calculate the Arithmetic Mean in a more straightforward method.

#### Arithmetic Mean Formula – Example1

Take, for example, a hitter who scored the following runs in his last ten innings during the course of the previous year: 45, 65, 7, 10, 43, 35, 25, 17, 78, and 91 runs in his last ten innings. Calculate the batsman’s batting average throughout his past ten innings of play. Solution: The Arithmetic Mean is determined with the help of the formula shown below. The Arithmetic Mean is defined as x I / n.

• Arithmetic Mean = (45 + 65 + 7 + 10 + 43 + 35 + 25 + 17 + 78 + 91) / 10
• Arithmetic Mean =41.60

As a result, the batsman’s average runs per innings in his last ten innings stayed at 41.60 runs per innings.

#### Arithmetic Mean Formula – Example2

For illustration purposes, let us use a class of 45 pupils. Recently, a weekly scientific test was administered, and the students were graded on a scale of 1 to 10, depending on their performance.

Calculate the average score in the test based on the information in the following table. Solution: The Arithmetic Mean is determined with the help of the formula shown below. The Arithmetic Mean is defined as (f I x I / f i.

• Arithmetic Mean = ((3 * 3) + (4 * 9) + (6 * 18) + (7 * 12) + (9 * 3) / 45
• Arithmetic Mean = 264 / 45
• Arithmetic Mean = 5.87

Thus, the average scientific exam result for the class was 5.87 out of a possible 6.

#### Arithmetic Mean Formula – Example3

Let us consider the case of two data sets with two distinct arithmetic means as an illustration. The first data set has 10 variables with a mean of 45, whereas the second data set contains 7 variables with a mean of 42, as seen in the table. Calculate the arithmetic mean of the two data sets after they’re all joined. Solution: Arithmetic This formula is used to compute the means of the merged data set. Arithmetic Mean = ((m 1 *n 1) + (m 2 *n 2)) / (n 1 +n 2) Arithmetic Mean = ((m 1 *n 1) + (m 2 *n 2) Arithmetic Mean = ((m 1 *n 1) Arithmetic Mean = ((m 1 *n 1) Arithmetic Mean = ((m 1 *n 1) Arithmetic Mean = ((m 1 *n 1) Arithmetic Mean = ((m 1 *n

• Calculate the Arithmetic Mean by dividing (45 * 10 + 42 * 7) by (10 + 7)
• The Arithmetic Mean is 43.76
• The Arithmetic Mean is 43.76.

This results in an average arithmetic mean of 43.76 for the combined data set.

### Explanation

The formula for arithmetic mean may be computed by following the steps outlined below: 1. Step 1: To begin, gather and arrange the variables for which the arithmetic mean must be determined in the appropriate order. The variables are symbolized by the letters x and i. After that, find the total number of variables in the data set, which is indicated by the letter “n” when all variables are equal in importance (as in a random sample). Alternatively, calculate the frequency of each variable, which is indicated by f I and the number of variables is equal to the total of the frequencies of the variables.

Step 3: The Arithmetic Mean is defined as x I / n.

The Arithmetic Mean is defined as f I x i/f i.

### Relevance and Uses of Arithmetic Mean Formula

The idea of the arithmetic mean is quite straightforward and rudimentary in nature. However, it is still extremely essential since it is frequently employed as a statistical indicator to analyze the average outcome of a data collection. In reality, it allows you to determine which of the variables is better or worse than the average of the entire collection of variables. It may also be used as a metric to indicate the average value throughout an entire data series, which is known as the mean.

### Arithmetic Mean Formula Calculator

You can use the Arithmetic Mean Calculator that is provided below.

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### Recommended Articles

This page contains information on the Arithmetic Mean Formula.

We will go through how to calculate the arithmetic mean, as well as provide some practical examples. In addition, we give an Arithmetic Mean Calculator that may be downloaded as an Excel spreadsheet template. You may also read the following articles to find out more information –

1. Detailed instructions on how to compute Harmonic Mean
2. A guide to the population mean formula
3. Examples of the mean formula
4. And more.

## Arithmetic mean

Thearithmetic mean is sometimes referred to as themean in some circles. It is an average, which is a measure of the center of a collection of data points. In order to get the arithmetic mean, add up all of the values and divide the total number of values by the entire number of values. For example, the mean of the numbers (7), (4), (5), and (8), is (frac=6). For example, if the data values are (x 1), (x 2),., (x n), then we have (bar =fracsum_ n x i), where (bar =fracsum_ n x i) is a symbol indicating the mean of the data values ((x i)).

As a result, the sum of a collection of numbers may be thought of as a “average” of those numbers.

The arithmetic mean is highly sensitive to outlier values in a distribution.

A function’s “sum” over an interval is the function’s integral over the interval, as illustrated in the following sketch: As a result, the mean (M) is defined as (M(b-a)=int ab f(x),dx), while the standard deviation (S) is defined as This means that the integral “averages” out the function.

## Arithmetic Mean

Arithmetic The mean, which is an often used word in statistics, is the average of the numerical values in a set. It is derived by first computing the sum of the numbers in the set and then dividing the resulting by the number of numbers in the set, as shown in the example below.

### Arithmetic Mean Formula

The following is a representation of the formula: The Arithmetic Mean is defined as x1 + x2 + x3 +.+ xn / n. You are allowed to use this image on your website, in templates, or in any other way you see fit. Please credit us by include a link to this page. Hyperlinking an article link will be implemented. As an illustration: The Arithmetic Mean is the source of this information (wallstreetmojo.com) Where,

• The following is how the formula is expressed: It is calculated as follows: Arithmetic Mean = 1 plus 2 plus 3 plus.+ xn / n You are allowed to use this picture on your website, in templates, or in any other way you see fit. However, please provide a link to this page as a source of inspiration. Hyperlinking an article link will be done. As an illustration, Arithmetic Mean is the source of this information (wallstreetmojo.com) Where,

Alternatively, it may be represented graphically as illustrated below- The symbol sigma is used in the preceding Equation to represent the symbol sigma. It denotes the addition of all of the values.

### Steps to Calculate Arithmetic Mean

• Step 1: Compute the total of all of the observations
• Step 2:
• Arithmetic Mean = x1+x2+x3+.+xn/n
• Arithmetic Mean = x1+x2+x3+.+xn/n If you want to think in symbolic terms, the Arithmetic Mean Formula is expressed as follows:

### Examples

There are five points to consider. These are the numbers 56, 44, 20, 50, and 80. Calculate the arithmetic mean of the data. Solution

• The observations in this case are 56, 44, 20, 50, and 80
• N = 5

As a result, the following is the calculation:

#### Example2

Franklin Inc. is a manufacturing company with a staff of 10 people. Wage discussions are now taking place between the management of Franklin Inc.

and the company’s labor union. This is why the CEO of Franklin Inc. is interested in finding out what the arithmetic mean of the salaries of the company’s employees is. The pay, as well as the names of the employees, are shown in the following table.

Name of the Worker Wages (\$)
Jeffery Gates 100
George Clinton 120
Thomas Smith 250
Kamala Sanders 90
Steve Roosevelt 110
Martha Smith 40
Clara Truman 50
Nicholas Obama 150
Michael Carlin 70
Arnold Smith 100
Number of Observations (n) 10

Make an estimate of the arithmetic mean of the CEO’s pay. Solution As a result, the following is the calculation:

#### Example3

It is the Principal of a school who summons two teachers to his office. One of the teachers teaches Division A, and the other teacher teaches Division B, respectively. Both of them believe that their techniques of teaching are superior to the other’s. After considering all of the data, the Principal determines that the Division with the higher arithmetic mean of marks will have had a superior instructor. The following are the grades of seven students from each of the two Divisions who studied together.

Sr. No Division A Division B
Student 1 56 70
Student 2 60 65
Student 3 56 60
Student 4 64 65
Student 5 70 75
Student 6 55 55
Student 7 50 65

Look up in the table to see which Division has a greater arithmetic mean. Division A is in charge of the solution. As a result, the following is the calculation: Division B is comprised of the following: As a result, the following is the calculation: Division A’s arithmetic mean is 58.71 points, while Division B’s arithmetic mean is 65 points (higher)

### Arithmetic Mean in Excel

Grandsoft Inc. is a publicly traded corporation that is traded on the stock markets. A stock exchange is a market that facilitates the buying and selling of listed securities such as public company stocks, exchange-traded funds, debt instruments, options, and so on, in accordance with the standard regulations and guidelines—for example, the NYSE and NASDAQ—in accordance with the standard regulations and guidelines. Continue reading for more information. Various experts have set a target price for the company, which they believe will be reached.

When it comes to investing, a price target represents the price at which an investor is willing to purchase or sell a company at a specific point in time, or the price at which they will be willing to leave their current position.

Calculate the arithmetic mean of the stock prices using the formula below.

Analyst Target Price
A 1000
B 1200
C 900
D 900
E 1500
F 750
G 750

Solution The mean may be calculated using an Excel formula that is pre-installed. The first step is to choose a blank cell and type =AVERAGE (B2: B8) Step 2 – To obtain the answer, press the Enter key.

### Relevance and Uses

Arithmetic mean is one of the most significant statistics and is most usually employed as a measure of central tendency, which is a measure of how much something has changed over time. The Central Tendency of a Data Distribution is a statistical metric that depicts the point in the middle of the complete Data Distribution. It may be discovered using three distinct measurements, namely the mean, median, and mode. Continue reading for more information. It is simple to compute and does not need a thorough understanding of high-level statistics.

Data, whether qualitative or quantitative, can be used to make more informed and effective decisions that are more relevant to the situation.

Continue reading for more information. It is employed when all of the observations in a data collection are of equal significance. It is necessary to employ a weighted mean when certain claims are more significant than others.

### Recommended Articles

Arithmetic Mean Formula has been explained in this article. Practical examples and a downloadable Excel template are provided to help you understand how to calculate the arithmetic mean using the formula provided in this section. Several articles about excel modeling are available online, including the ones below.

• Calculating exponents in Excel
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16 Courses; 15+ Projects; 90+ Hours; Full Lifetime Access; Certificate of Completion

## Arithmetic Mean Definition

It is the simplest and most generally used measure of amean, or average, since it is the most straightforward to calculate. It is as simple as taking the total of a set of numbers and dividing that sum by the amount of numbers that were used in the series to arrive at the answer. Let’s say you have the numbers 34, 44, 56, and 78 on your hands. The total comes to 212. The arithmetic mean is equal to 212 divided by four, which equals 53. Additionally, people employ a variety of different sorts of means, such as thegeometric mean and theharmonic mean, which come into play in a variety of scenarios in finance and investment.

### Key Takeaways

• Arithmetic mean: The simple average, also known as the total sum of a series of numbers, divided by the number of numbers in that series of numbers
• Because of this, arithmetic mean is not always the most appropriate approach of computing an average in the financial sector, especially when a single outlier might distort the average by a significant amount. Other averages that are more widely employed in finance include the geometric mean and the harmonic mean
• However, the geometric mean is not utilized in finance.

## How the Arithmetic Mean Works

The arithmetic mean retains its significance in the field of finance as well. To give an example, mean earnings predictions are often calculated using the arithmetic mean. Consider the following scenario: you want to know the average earnings projection of the 16 analysts covering a specific stock. To find the arithmetic mean, just add up all of the estimations and divide the total by 16. The same is true if you wish to figure out what a stock’s average closing price was for a specific month.

To find the arithmetic mean, just add up all of the costs and divide by 23 to arrive at the final figure.

As a measure of central tendency, it’s also valuable because it tends to produce relevant findings even when dealing with big groupings of numbers.

## Limitations of the Arithmetic Mean

The arithmetic mean isn’t always the best choice, especially when a single outlier has the potential to significantly distort the mean. Consider the following scenario: you need to estimate the allowance for a group of ten children. Nine of them are given a weekly stipend ranging between \$10 and \$12. The tenth child is entitled to a \$60 stipend. Because of that one outlier, the arithmetic mean will be \$16, not \$16 + \$1. This is not a particularly representative sample of the group. In this specific instance, the medianallowance of ten points could be a more appropriate metric.

It is also not commonly utilized to compute present and future cash flows, which are employed by analysts in the preparation of their forecasts. It is almost certain that doing so will result in erroneous data.

### Important

When there are outliers or when looking at past returns, the arithmetic mean might be deceiving to the investor. In the case of series that display serial correlation, the geometric mean is the most appropriate choice. This is particularly true in the case of investment portfolios.

## Arithmetic vs. Geometric Mean

The geometric mean, which is determined in a different way, is frequently used in these applications by analysts. When dealing with series that demonstrate serial correlation, the geometric mean is the most appropriate choice. This is particularly true in the case of investment portfolios. The majority of returns in finance are connected, including bond yields, stock returns, and market risk premiums, among other things. Because of this, the use of crucial compounding and the geometric mean becomes increasingly important as the time horizon grows.

Taking the product of all the numbers in the series, the geometric mean increases it by the inverse of the length of the series, yielding the geometric mean.

The geometric mean varies from the arithmetic mean in that it takes into consideration the compounding that occurs from one period to the next.

## Example of the Arithmetic vs. Geometric Mean

Suppose the returns on an investment during the previous five years were 20 percent, 6 percent, 10 percent, -1 percent, and 6 percent, respectively. The arithmetic mean would simply put them all together and divide by five, yielding an annualized rate of return of 4.2 percent on average. The geometric mean, on the other hand, would be computed as (1.2 x 1.06 x 0.9 x 0.99 x 1.06) 1/5-1 = 3.74 percent per year average return on the investment. It is important to note that the geometric mean, which is a more accurate computation in this circumstance, will always be less than the arithmetic mean in this situation.

## Appendix 6. Calculation of arithmetic and geometric means

It is possible to measure the central tendency of a set of numbers using a variety of ways. Calculating thearithmetic mean is one approach of doing so. Adding up all of the values and dividing the total by the number of values is how you achieve this. Consider the following example: If there is a collection of “n” integers, add the numbers together, for instance: a + b + c + d, and so on. Then divide the total by the number “n.” One issue with the arithmetic mean is that its value will be disproportionately impacted by a single extreme number, which might be problematic.

1. Take the “n th ” root of the values after multiplying them together.
2. The effect of single extreme values is reduced as a result.
3. To multiply, all you have to do is add the log indices together.
4. Exemplification in Action In a serological test, you have documented the results of the following set of values.

2 3= 82 4= 162 2 3= 82 4= 162 4= 162 6= 64 4= 162 6= 64 Formula for calculating the geometric mean =4 (8 16 16 ) =4 (131072) = 19 When the log indices are used to get the geometric mean, the geometric mean equals = 2 4.3= 19.7.

## Arithmetic mean – Wikipedia

See Mean for a more in-depth discussion of this subject. Generally speaking, in mathematics and statistics, thearithmetic mean (pronounced air-ith-MET -ik) or arithmetic average (sometimes known as simply themean or theaverage when the context is obvious) is defined as the sum of a collection of numbers divided by the number of items in the collection. A collection of results from an experiment or an observational research, or more typically, a collection of results from a survey, is commonly used.

In addition to mathematics and statistics, the arithmetic mean is commonly employed in a wide range of subjects, including economics, anthropology, and history, and it is employed to some extent in virtually every academic field.

Because of skewed distributions, such as the income distribution, where the earnings of a small number of people exceed the earnings of most people, the arithmetic mean may not correspond to one’s conception of the “middle,” and robust statistics, such as the median, may provide a more accurate description of central tendency.

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## Definition

The arithmetic mean (also known as the mean or average), indicated by the symbol (readbar), is the mean of a data collection. Among the several measures of central tendency in a data set, the arithmetic mean is the most widely used and easily comprehended. The term “average” refers to any of the measures of central tendency used in statistical analysis. The arithmetic mean of a collection of observed data is defined as being equal to the sum of the numerical values of each and every observation divided by the total number of observations in the set of data being considered.

The arithmetic mean is defined as A statistical population (i.e., one that contains every conceivable observation rather than merely a subset of them) is marked by the Greek letter m, and the mean of that population is denoted by the letter m.

Not only can the arithmetic mean be computed for scalar values, but it can also be defined for vectors in many dimensions; this is referred to as the centroid.

More generally, because the arithmetic mean is an aconvex combination (i.e., the coefficients add to 1), it may be defined on any convex space, not only a vector space, according to the definition above.

## Motivating properties

The arithmetic mean has a number of characteristics that make it particularly helpful as a measure of central tendency, among other things. These are some examples:

## Contrast with median

The arithmetic mean and the median can be compared and contrasted. The median is defined as the point at which no more than half of the values are greater than and no more than half are less than the median. If the elements of the data grow arithmetically when they are arranged in a particular order, then the median and arithmetic average are the same. Take, for example, the data sample described above. The average and the median are both correct. When we take a sample that cannot be structured in such a way that it increases arithmetically, such as the median and arithmetic average, the differences between the two can be considerable.

As a rule, the average value can deviate greatly from the majority of the values in the sample, and it can be significantly greater or lower than the majority of them.

Because of this, for example, median earnings in the United States have climbed at a slower rate than the arithmetic average of earnings since the early 1980s.

## Generalizations

If certain data points count more highly than others, then the average will be a weighted average, or weighted mean. This is because some data points are given greater weight in the computation. In the case ofandis, for example, the arithmetic mean, or equivalently An alternative method would be to compute a weightedmean, in which the first number is given more weight than the second (maybe because it is believed to appear twice as frequently in the broader population from which these numbers were sampled) and the result would be.

Arithmetic mean (also known as “unweighted average” or “equally weighted average”) can be thought of as a specific instance of the weighted average in which all of the weights are equal to each other in a given set of circumstances (equal toin the above example, and equal toin a situation withnumbers being averaged).

### Continuous probability distributions

Whenever a numerical property, and any sample of data from it, can take on any value from a continuous range, instead of just integers for example, the probability of a number falling into some range of possible values can be described by integrating a continuous probability distribution across this range, even when the naive probability of a sample number taking one specific value from an infinitely many is zero.

Themean of the probability distribution is the analog of a weighted average in this context, in which there are an infinite number of possibilities for the precise value of the variable in each range, and is referred to as the weighted average in this context.

The normal distribution is also the most commonly encountered probability distribution. Other probability distributions, such as the log-normal distribution, do not follow this rule, as seen below for the log-normal distribution.

### Angles

When working with cyclic data, such as phases or angles, more caution should be exercised. A result of 180° is obtained by taking the arithmetic mean of one degree and three hundred fifty-nine degrees. This is false for two reasons: first, it is not true.

• Angle measurements are only defined up to an additive constant of 360° (or 2 in the case of inradians) for several reasons. Due to the fact that each of them produces a distinct average, one may just as readily refer to them as the numbers 1 and 1, or 361 and 719, respectively. Second, in this situation, 0° (equivalently, 360°) is geometrically a better average value because there is less dispersion around it (the points are both 1° from it and 179° from 180°, the putative average)
• Third, in this situation, 0° (equivalently, 360°) is geometrically a better average value because there is less dispersion around it (the points are both 1° from it and 179° from 180°, the putative average

An oversight of this nature will result in the average value being artificially propelled towards the centre of the numerical range in general use. Using the optimization formulation (i.e., defining the mean as the central point: that is, defining it as the point about which one has the lowest dispersion), one can solve this problem by redefining the difference as a modular distance (i.e., defining it as the distance on the circle: the modular distance between 1° and 359° is 2°, not 358°).

## Symbols and encoding

The arithmetic mean is frequently symbolized as a bar (also known as a vinculumormacron), as in the following example: (readbar). In some applications (text processors, web browsers, for example), the x sign may not be shown as expected. A common example is the HTML code for the “x” symbol, which is made up of two codes: the base letter “x” and a code for the line above (772; or “x”). When a text file, such as a pdf, is transferred to a word processor such as Microsoft Word, the x symbol (Unicode 162) may be substituted by the cent (Unicode 162) symbol (Unicode 162).