Well, the temperature varies all day still how a single temperature can indicate the condition for the entire day? For example; Therefore we need an extra representative value to help reduce this ambiguity.Range, as the word suggests, represents the difference between the largest and the smallest value of data. On the internet, you would find the temperatures for a lot of days, data of the temperature in the past and the data of the temperature in the present and also the predictions of the temperature in the future. In these cases, the operation is sometimes symbolized by a double colon (::) between the two quantities to be averaged.

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. Arithmetic Mean for Ungrouped Data If n numbers, x 1,x 2,…,x n, then their arithmetic mean or their average 2. 1.

This helps us determine the range over which the data is spread. Join us and fall in love with learning.The arithmetic mean is simple to understand and easy to calculate.It is influenced by the value of every item in the series.It has the capability of further algebraic treatment.It is a measured value and not based on the position in the series.It is changed by extreme items such as very small and very large items.In some cases, A.M. does not represent the original item. The arithmetic mean isn't always ideal, especially when a single outlier can skew the mean by a large amount. In a physical sense, the arithmetic mean can be thought of as a centre of gravity. A solution to this problem is to use the optimization formulation (The arithmetic mean is often denoted by a bar, for example as in

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Instead of this long list of data mathematicians decided to use representative values that could take into consideration a wide range of data. Examples of Arithmetic Mean in Statistics. In mathematics and statistics, the arithmetic mean , or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the count of numbers in the collection. Some important properties of the arithmetic mean are as follows:The arithmetic mean of Virat Kohli’s batting scores also called his Batting Average is;The arithmetic mean of his scores in the last 10 innings is 66.1. There are two scenarios here.Why don’t you calculate the Arithmetic mean of both the sets above? If you wanted to find the arithmetic means of the runs scored by Virat Kohli in the last few innings, all you would have to do is sum up his runs to obtain sum total and then divide it by the number of innings.
For calculating the mean of grouped data, we calculate the class mark. Next Page . Arithmetic Mean The arithmetic mean is the amount secured by dividing the sum of values of the items in a series by the number.

There are two scenarios here.The range in the first scenario is represented by the difference between the largest value, 93 and the smallest value, 48.Whereas in the second scenario, the range is represented by the difference between the highest value, 75 and the smallest value, 70.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. Wouldn’t all this be extremely confusing? Taking the previous example into consideration once again. Statistical Measures.

The arithmetic mean has several properties that make it useful, especially as a measure of central tendency.