Arithmetic Mean Geometric Mean Harmonic Mean AM and GM

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How to Find Arithmetic Mean for Grouped Data?

1. In statistics, the Arithmetic Mean (AM) or called average is the ratio of the sum of all observations to the total number of observations.
2. 5) The presence of extreme observations has the least impact on it.
3. The Arithmetic Mean (AM), often known as average in statistics, is the ratio of the sum of all observations to the total number of observations.
4. Particularly, the arithmetic mean is sensitive to extreme values or outliers, which can distort the mean, making it less representative of the data as a whole.
5. It appears to have been first used by Babylonian astronomers in the third century BC.

The Harmonic mean is calculated as n divided by reciprocals of rates (r). Below formulae is used for Harmonic mean H, n is the no. of observations. Let’s first understand where does the word or concept of Harmonic comes from?

The drawback of A.P and Weighted Arithmetic Mean

The deviations of the observations from arithmetic mean (x – x̄) are -20, -10, 0, 10, 20. If all the observations assumed by a variable are constants, say “k”, then arithmetic mean is also “k”. The arithmetic mean or mean is the simplest way to calculate the average for the given set of numbers. It is classified into two different types, namely simple arithmetic mean and weighted arithmetic mean.

Chapter 3: Pair of Linear equations in two variables

It is calculated by adding all the numbers in a given data set and then dividing it by the total number of items within that set. The arithmetic mean (AM) for evenly distributed numbers is equal to the middlemost number. Further, the AM is calculated using numerous methods, which is based on the amount of the data, and the distribution of the data. In the assumed mean method, students need to first assume a certain number within the data as the mean. The arithmetic mean accounts for every value in the data set, which makes it a comprehensive measure of central tendency. This is in contrast to other measures like median and mode, which do not take into account every individual data point.

The arithmetic mean of the observations is calculated by taking the sum of properties of arithmetic mean all the observations and then dividing it by the total number of observations. In statistics, arithmetic mean (AM) is defined as the ratio of the sum of all the given observations to the total number of observations. For example, if the data set consists of 5 observations, the AM can be calculated by adding all the 5 given observations divided by 5.

Follow this page for any further details related to NCERT examinations. One of the main disadvantages of the arithmetic mean is that it is sensitive to extreme values, or outliers, in the data set. A single extremely large or small value can distort the mean, making it an inaccurate representation of the data.

For example, mean income is typically skewed upwards by a small number of people with very large incomes, so that the majority have an income lower than the mean. By contrast, the median income is the level at which half the population is below and half is above. The mode income is the most likely income and favors the larger number of people with lower incomes. Instead of this long list of data, mathematicians decided to use representative values which could take into consideration a wide range of data. Instead of weather for every particular day, we use terms such as average (mean), median and mode to describe weather over a month or so.

Listed below are some of the major advantages of the arithmetic mean. 5) It is least affected by the presence of extreme observations. For example, if the height of every student in a group of 10 students is 170 cm, the mean height is, of course 170 cm. Here we will learn about all the properties andproof the arithmetic mean showing the step-by-step explanation. Whereas in the second scenario, the range is represented by the difference between the highest value, 75 and the smallest value, 70. The range in the first scenario is represented by the difference between the largest value, 93 and the smallest value, 48.

This means that 50 kg is the one value that represents the average weight of the class and the value is closer to the majority of observations, which is called mean. In real life, the importance of displaying a single value for a huge amount of data makes it simple to examine and analyse a set of data and deduce necessary information from it. It’s important to note, however, that while it is a useful and versatile tool, it isn’t always the best measure of central tendency for every set of numbers. It can be greatly affected by outliers, or numbers that are much larger or smaller than the others in the data set.