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# Averages

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Averages: In colloquial language, an average is a single number taken as representative of a list of numbers. Different concepts of average are used in different contexts. Often “average” refers to the arithmetic mean, the sum of the numbers divided by how many numbers are being averaged. In statistics, mean, median, and mode are all known as measures of central tendency, and in colloquial usage, any of these might be called an average value.

• # Averages

Averages are a means of finding the central or the typical value of a set of data. Through the average, we can avoid taking each data point into consideration and instead focus on the average value that represents the typical magnitude of the data points. Let us learn more about averages and average formula.
• ## Average Of Data

Let us understand the concept of averages first. Let us say that you want to buy shoes for your friend but you don’t know their fit. What will you do? You can guess the size and see if your guess was accurate or not. What is the chance that you will be right? It is very small considering that there are a lot of sizes and only one range is true. Now let us say that you want to buy shoes for every kid in your state. You can only select one size though. There will be thousands of such kids with a range of sizes. If you buy say size 8 shoes, what is the chance that those shoes will fit some kid? The chances are very high. How will you know which size will fit the most number of students? The answer is the concept of averages. Out of a large set of data, the average is the number that represents most of the data values. Thus it is a measure of the “central” tendency. If you know the average of a data set, you will be able to know the behaviour or the approximate value of most of the data points.
• ## Formula For Average

For a given set of data, each data point corresponds to an observation. In any number of ‘n’ observations, the average value is found out by finding the sum of the observations and dividing it by the number of observations i.e. n. For example, let a, b, c, … represent ‘n’ number of observations. Then the average of these observations will be given by: Average value = (a + b + c + … )/n ;where n is the total number of observations. Let us see an example and then move on to the application of this concept.

1. Example 1: The shoe sizes of 12 students of a class are 7, 8, 6, 8, 9, 6, 7, 8, 6, 9, 7, 8. Out of the following, which shoe will fit the most number of people?
•  7
• 6
• 8
• 9
• Answer: To find the shoe size that represents the most number of students, we can use the concept of averages. For that, we will have to sum the observations or the data points and divide them by the number of data points. Let us see:  (7 + 8 + 6 + 8 + 9 + 6 + 7 + 8 + 6 + 9 + 7 + 8)/12 = 7.41
• This size is closer to 7 than 8, so the answer should be A) 7.

Notice that the average is a measure of central tendency. It doesn’t guarantee that the average will always represent the maximum number of data points.