Arithmetic Mean of Grouped & Ungrouped Data with Formula

If xi and fi are sufficiently small, the direct method will work. But, if they are numerically large, we use the assumed arithmetic mean method or step-deviation method. In this section, we will be studying all three methods along with examples. To calculate the central tendency for the given data set, we use different measures like mean, median, mode and so on. 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.

  • Where,n is number of itemsA.M is arithmetic meanai are set values.
  • The arithmetic mean, which is defined as the sum of all observations divided by the number of observations, is one of the measures of central tendency.
  • In business and finance, arithmetic mean is used to calculate various financial indicators, such as stock prices, bond yields, and return on investment.
  • In this respect, completely relying on arithmetic mean can be occasionally misleading.
  • The arithmetic mean is one of the oldest methods used to combine observations in order to give a unique approximate value.

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. To find the arithmetic mean between 2 numbers, add the two given numbers and then divide the sum by 2. In a data set, if some observations have more importance as compared to the other observations then taking a simple average Is misleading.

Arithmetic Mean: 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.

  • The same applies to the students with 90, in the case of these students in the second set, the marks are reduced.
  • But in day-to-day life, people often skip the word arithmetic or simply use the layman term “average”.
  • 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.

The marks obtained by 3 candidates (A, B, and C) out of 100 are given below. If the candidate getting the average score is to be awarded the scholarship, who should get it. It is because it is highly skewed by the outliers, values relatively very high or lower than the rest of the data. But in day-to-day life, people often skip the word arithmetic or simply use the layman term “average”.

Examples of Arithmetic Mean in Statistics

Its formula is derived from the arithmetic mean and that is why, both A.P and W.M are learned together. Also, the arithmetic mean fails to give a satisfactory average of the grouped data. The mid-range is the arithmetic mean of the highest and lowest values of a set. The most frequently occurring number in a list is called the mode. It may happen that there are two or more numbers which occur equally often and more often than any other number.

General properties

The arithmetical average of a group of two or more quantities is known as the mean. With this article you will be able to answer questions like what is the arithmetical mean. The formula for ungrouped and grouped data along with solved examples/ questions. After calculating the class mark, the mean is calculated as discussed earlier. This method of calculating the mean is known as the direct method. Central Tenancies are measures of location that summarise a dataset by giving a “single quantitative value” within the range of the data values.

There are different approaches that can be used to calculate arithmetic mean and students need to gain the knowledge of when to use which approach. Arithmetic mean is one of the most important chapters of Maths. It is introduced in lower grades and is referred to as average however, in 10th boards, students are taught different approaches to calculate the arithmetic mean. Statistics is a vital part of the syllabus in 12th boards and students need to have basic knowledge of arithmetic mean to be able to attend the sums appropriately. This article will include all the details like definition, properties, formulae and examples related to the chapter of arithmetic mean.

Example – Ungrouped data

Angles, times of day, and other cyclical quantities require modular arithmetic to add and otherwise combine numbers. For example, the times an https://1investing.in/ hour before and after midnight are equidistant to both midnight and noon. Consider a color wheel—there is no mean to the set of all colors.

Average: Definition, Formulas, Questions and More

Let n be the number of observations in the operation and n1, n2, n3, n4, …, nn be the given numbers. Now as per the definition, the arithmetic means formula can be defined as the ratio of the sum of all numbers of the group by the number of items. 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. Let us understand the arithmetic mean of ungrouped data with the help of an example. We know that to find the arithmetic mean of grouped data, we need the mid-point of every class.

Comparing different data sets

The arithmetic mean in statistics, is nothing but the ratio of all observations to the total number of observations in a data set. Some of the examples include the average rainfall of a place, the average income of employees in an organization. We often come across statements like “the average monthly income of a family is ₹15,000 or the average monthly rainfall of a place is 1000 mm” quite often. The arithmetic mean, which is defined as the sum of all observations divided by the number of observations, is one of the measures of central tendency.

In education, arithmetic mean is used to calculate student grades, class averages, and grade point averages (GPAs). It is also used to track student progress over time and identify areas of improvement. 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.

Arithmetic mean and Average are different names for the same thing. It is obtained by the sum of all the numbers divided by the number of observations. You would probably have heard your teacher saying “ this time the average score of the class is 70” or your friend saying “I get 10 bucks a month on average”. Outside probability and statistics, a wide range of other notions of mean are often used in geometry and mathematical analysis; examples are given below. If all numbers in a list are the same number, then their average is also equal to this number.

It is widely used in various fields, such as finance, economics, and business, to make decisions and predict future trends. However, it is important to consider its limitations, such as sensitivity to outliers and skewed data, when using arithmetic mean in data analysis. For example, if we want to compare the average income of people in two different cities, we can calculate the arithmetic mean of the income in each city and compare them. The sum of this product is obtained and finally, by dividing the sum of this product by the sum of frequencies we will obtain the arithmetic mean of the continuous frequency distribution.