# Arithmetic Mean Definition, Formula, Properties, and Examples

The arithmetic mean is sometimes also called mean, average, or arithmetic average. For ungrouped data, we can easily find the arithmetic mean by adding all the given values in a data set and dividing it by a number of values. The measures of central tendency enable us to make a statistical summary of the enormous organized data.

The difference in the value of range between the two scenarios enables us to estimate the range over which the values are spread, the larger the range, the larger apart the values are spread. This gives us the extra information which is not getting through on average. Arithmetic means utilizes two basic mathematical operations, addition and division to find a central value for a set of values.

Arithmetic mean is the ratio of the summation of all observations to the total number of observations present. Mean in simplistic terms is the arithmetical average of a set of two or more quantities. You will learn about arithmetic mean, formula for ungrouped and grouped data along with solved examples/questions, followed by properties, advantages, disadvantages and so on.

- If the frequency of various numbers in a data set is f1, f2, f3, f4, f5, …, fn for the numbers n1, n2, n3, n4, n5, … nn.
- In such a distribution a lot of people’s earnings fall below the average and a few are way above it.
- To get more ideas students can follow the below links tounderstand how to solve various types of problems using the properties ofarithmetic mean.
- It allows us to know the centre of the frequency distribution by considering all of the observations.

Majorly the mean is defined for the average of the sample, whereas the average represents the sum of all the values divided by the number of values. Mean is nothing but the average of the given values in a data set. In simple terms, the median is the value that lies in the middle of the data with half of the observations above it and the other half below it.

Among all these measures, the arithmetic mean or mean is considered to be the best measure, because it includes all the values of the data set. If any value changes in the data set, this will affect the mean value, but it will not be in the case of median or mode. We see the use of representative value quite regularly in our daily life. When you ask about the mileage of the car, you are asking for the representative value of the amount of distance travelled to the amount of fuel consumed. This doesn’t mean that the temperature in Shimla in constantly the representative value but that overall, it amounts to the average value. Average here represents a number that expresses a central or typical value in a set of data, calculated by the sum of values divided by the number of values.

## Measures of Dispersion – Definition, Formulas & Examples

In the assumed mean method, students need to first assume a certain number within the data as the mean. The arithmetic mean is the simplest and most widely used measure of a mean, or average. The arithmetic mean formula simply involves taking the sum of a group of numbers, then dividing that sum by the count of the numbers used in the series.

## Some Other Properties of Arithmetic Mean

It is commonly referred to as Mean or Average by people in general and is commonly represented by the letter X̄. We can use any of the three methods for finding the arithmetic mean for grouped data depending on the value of frequency and the mid-terms of the interval. Now let’s discuss the three methods for finding the arithmetic mean for grouped data in detail. If the frequency of various numbers in a data set is f1, f2, f3, f4, f5, …, fn for the numbers n1, n2, n3, n4, n5, … nn. The average is a pretty neat tool, but it comes with its set of problems. Say there are 10 students in the class and they recently gave a test out of 100 marks.

At least from the point of view of students scoring 50’s/ 100, the second scenario is quite different. The same applies to the students with 90, in the case of these students in the second set, the marks are reduced. So for both the classes, the results mean something different, but the average for both classes are the same. In the first class, the students are performing very varied, some very well and some not so well whereas in the other class the performance is kind of uniform.

Therefore we need an extra representative value to help reduce this ambiguity. We know that observation with the maximum frequency is called the mode. The arithmetic mean is one of the oldest methods used to combine observations in order to give a unique approximate value. It appears to have been first used by Babylonian astronomers in the third century BC.

## Arithmetic Mean And Range

However, nowadays we have very powerful and very easy ways to show the whole set of data, the whole distribution, so presenting only the arithmetic mean may be a bad practice. See When to Use Mean, Median, or Mode for a deeper discussion on this topic. In some cases a “mean” or an “average” may refer to a weighted average, in which different weights are assigned to different points of the data set based on some characteristic of theirs. This mean calculator does not support weighted averages as they require a more advanced set of inputs. You can, however, use our weighted mean calculator to find the weighted average.

Let’s understand what is arithmetic mean and how it is calculated along with its properties using examples. When the data is presented in the form of class intervals, the mid-point of each class (also called class mark) is considered for calculating the arithmetic mean. To get more ideas students can follow the below links tounderstand how to solve various types of problems using the properties ofarithmetic mean. To solve different types of problemson average we need to follow the properties of arithmetic mean. If the arithmetic mean of the data set, 4, 5, 6, 7, and 8 is 6 and if each value is multiplied by 3 find the new mean. If the arithmetic mean of the data set, 4, 5, 6, 7, and 8 is 6 and if each value is increased by 3 find the new mean.

6) The sum of deviations of the items from the arithmetic mean is always zero. To find the arithmetic mean between 2 numbers, add the two given numbers and then divide the sum by 2. The following steps are used to compute the arithmetic mean by the direct method.

We hope that the above article on Arithmetic Mean is helpful for your understanding and exam preparations. Stay tuned to the Testbook app for more updates on related topics from Mathematics, and various such subjects. Also, reach out to the test series available to examine your knowledge regarding several exams. An Average is a single number that expresses a bunch of numbers in simple terms.

It allows us to know the centre of the frequency distribution by considering all of the observations. In statistics, the Arithmetic Mean (AM) or average is one of the representative figures along with the median and mode. These figures, i.e., arithmetic mean, median, and mode are also called measures of central tendencies. The arithmetic mean is the 5 properties of arithmetic mean ratio of the sum of all observations to the total number of observations. The term “arithmetic mean” is preferred in some mathematics and statistics contexts because it helps distinguish it from other types of means, such as geometric and harmonic. A single value used to symbolise a whole set of data is called the Measure of Central Tendency.

Due to the above qualities, for samples drawn from a population (e.g. a survey) the sample mean is a statistically unbiased estimator for the population mean. These are all reasons to make use of our arithmetic average https://1investing.in/ calculator. We can calculate the arithmetic mean (AM) in three different types of series as listed below. Embibe offers a range of study materials that includes MCQ mock test papers for 2022 and sample papers.