In mathematics and statistics, the definition of "mean" is critical. The mean is the most common or average value in a set of numbers. It is a measure of **the central tendency** of a probability distribution, along with the median and mode, in statistics. It is also known as the "anticipated value." For example, if a survey asks how much people expect to earn in their job, then the mean salary is what they expect will be earned by **most people**.

There are different types of means. If the values in the set are all positive, then the absolute mean is given by abs(average) where average is the average of **the absolute values** of the numbers in the set. If some values are negative, then the positive mean is given by avg(positive numbers only). There are similar definitions for **the other types** of means.

In mathematics, the word "mean" has several other meanings. The first two that come to mind are the arithmetic mean and the geometric mean. As defined above, they are both ways of averaging the values in a set.

Yet another meaning of the word "mean" in mathematics relates to the concept of center. If we look at a number line, we can see that it has a "mean" or "central point". This mean corresponds to the average of the integers (or real numbers) from -10 to 10.

The mean is calculated by dividing the sum of the numbers in a data set by the total number of values in the data set. The mean is sometimes referred to as the average. The mean may be used to acquire an overall image or concept of the data collection. The mean is best used to a data set with closely spaced integers. For example, if you were to calculate the mean for the list [10, 20, 30, 40], you would get 35. This makes sense because the sum of the numbers is 70 and there are only four numbers so the mean must be divided by four.

Mean has many applications in mathematics and science. It is used in statistics to measure central tendency. That is, where multiple measurements are taken from the same object, mean is used to describe **what type** of value they tend to fall around. For example, the mean weight of students at a school was found to be 52 kg by taking weights of 50 students and calculating **their average**. Mean is also used in probability theory to describe the expected value of **a random variable**. For example, the mean height of students at a school was found to be 1.70 m by taking heights of 95 students and calculating their average. In both cases, the mean fell between the extremes of the data set.

There are several ways to find the mean of a data set. The most direct method is to add up all the numbers in the data set and divide by the number of items in the data set.

The mean is simply a data set model. It is the most commonly used value. That is, it is the value in the data set that creates the least degree of error when compared to **all other values** in the data set. The mean has the critical virtue of include every value in your data collection as part of the calculation. There are no values excluded because they are too extreme.

Another advantage of the mean is its simplicity. All you need to do to calculate it is add up **all the numbers** in **your data** set and divide by the number of items in your data set. There are no long equations or difficult procedures to perform.

Yet another advantage of the mean is its universality. Any method for calculating a single number that represents an entire data set will give you the same result as the mean. This means that if you want to know what number best describes your data set, then the mean is the answer. There is no better or worse method depending on the data set; any method will work about as well as any other method.

Finally, the mean is accurate. If my data set consists only of positive numbers, then the mean is still positive. It cannot tell you anything about the distribution of the data set unless I specify how many positive and negative numbers there are in the data set. But even so, there are methods you can use to determine this information from the mean alone.