Average

Averages are used to represent a large set of numbers with a single number. It is a representation of all the numbers available in the data set. The average is calculated by adding all the data values and dividing it by the number of the data point. The age of the students in a class is taken and an average is calculated to give a single value of the average age of the students of a class. Average has numerous applications in our day to day life. For quantities with changing values, the average is calculated and a unique value is used to represent the values. 

Learning about average helps us to quickly summarize the available data. The large set of marks of the students, the changing price of the stocks, the weather data of a place, the income of different people in a city, are all examples for which we can calculate an average. Let us explore the page, to know more about average.

Table of Contents

What is Average?

The average is a numeric value which is a single representation of a large amount of data. The marks of the students of a class in a particular subject are averaged to give the average mark of the class. There is a need to know the performance of the entire class rather than the performance of each individual student. Here, the average is helpful. The average of a set of values is equal to the sum of the values divided by the individual values. Also, average is used in situations of changing values. The temperature of a place across the season is averaged to indicate the temperature of a place. The incomes of different employees in a company are averaged to know the income of the employees in a company.

It is sometimes difficult to make decisions based on one single data or a large set of data. Hence, the average value is taken and it helps to represent all the values in a single value

Definition of Average: 

The average is known as the arithmetic mean which is the sum of all numbers in a collection, divided by the count of the numbers present in the collection.

In other words, the average is the ratio of the sum of all given observations to the total number of observations.

Average = Sum of the Observations/Number of Observations

Average Formula

Calculation of Average 

The calculation of average follows three simple steps. Further, it includes the arithmetic operations: addition and division.

  • Step 1: Sum of the Numbers: The first step in the process of finding average is to find the sum of the given numbers. As an example, let us take the weight of six children. Find the sum of all the individual weights of the 6 children. 20lb, 25lb, 21lb, 30lb, 25lb, 26lb

  • Step 2: Number of Observations. Here we need to know the count or the data points. Here in our example of weights of children, we have 6 children. Count the total number of observations. Here, in this case, Zoe has a total of 6 observations which includes the weight of Zoe and her 5 friends. A total number of observations 6

  • Step 3: Average Calculation: Substituting the values from step 1 and step 2 in the average formula, we have the following expression. ​​

Average = Sum of the Observations/Number of Observations = 147/6 = 24.5lbs

Can Median Be Considered as Average? 

No, the median is not considered as average. The average is the mean value of the data and is different from the median value of the data. Median is the middle value of a set of data arranged in increasing order. The median or middle value is also known as a central tendency. To find the measure of central tendency, we have to write the data points in increasing or decreasing order. Further, the calculation of the median depends on the number of data points. Let us look at the following two cases for the calculation of the median value.

  • Case 1: n is Odd. Here for the odd number of data points, there is only one middle data point. And the median of the data is the (n + 1)/2 observation.

Median for Odd Data

  • Case 2: n is Even. Here for the even number of data points, there are two middle data points. And the median is the average of n/2 and (n/2 + 1) observation.

Median for Even Data

For special cases of data having equally spaced data points, the average is equal to the median. Let us consider the numbers: 5, 10, 15, 20, and 25. The average of this data is equal to the sum(5 + 10 + 15 + 20 + 25) divided by 5.  Hence the average of the data is 75/5 = 15. And the median is the middlemost value and it is equal to 15. The average and the median for this data is equal to 15.

Uses of Average

Average is useful in many ways in the real world. The average is useful to represent a single value for a large amount of data. A few examples of average are listed below.

  • If a student is reading a particular subject with n number of chapters in x hours. Then, the average time can be calculated for other similar subjects and chapters. This will help the student in time analysis.
  • If a child is participating in a particular sport, then the average is helpful for his\her coach to keep track of the changes in speed or energy.
  • Average can be used to plan daily schedules for children to ensure sufficient time is provided for all activities. 
  • The price of the shares of a company keeps changing every day. Here the average price of the share is quoted for reference.
  • The time duration for travel between two places keeps varying for each day. Here the average time duration is used to help understand the time it takes to travel between two places.

Important Topics

Given below is the list of topics that are closely connected to average. These topics will also give you a glimpse of how such concepts are covered in Cuemath.


FAQs on Average

How Average Is Calculated?

The average is calculated by taking the sum of the values, divided by the number of values. The average is a single value, which is a summary of all the data points. Let us find the average of the data points 2, 5, 11, 17, 24. Average = (2 + 5 + 11 + 17 + 24)/5 = 59/5 = 10.8

What Are The 3 Types of Averages?

The 3 types of averages are the mean, median, and mode. All these three kinds of mean give a different estimate of the summary of the given data. The mean is the sum of the data points divided by the number of data points. The median is obtained by arranging the data in ascending order and taking the middlemost value. The mode of the data is the most frequently occurring data point. In a good number of instances, the mean is also referred to as average. For equally spaced data points such as 2, 4, 6, 8, 10, the mean is equal to the median. And for data points such as 5, 5, 5, 5, 5, 5, the mean, median, and mode have equal values.

What Is the Difference Between Average and Mode?

The average is the mean of the data and is different from the mode. The average is the sum of the data divided by the number of data points. The mode of the data is equal to the most frequently occurring data point. In some instances when all the data point values are equal, the average is equal to the mode. The average is the mean of the data and mode is the most frequently occurring data point.

Why Are Averages Misleading?

In certain instances, the average can be misleading. The average is only a summary value and it does not give any idea of the individual values. The range of the data, and the outliers, cannot be understood from the average value. The average is only the mean of the data and it does not inform the lowest and the highest value of the data. Let us understand this with a simple example. The average time of travel is 30 minutes between two places, and if the actual time of travel is 45minutes, he would be late by 15 minutes. In this kind of situation, the average values can be misleading.

What Is the Average Used For?

The average is used to represent one single value for a given set of quantities. Further, it is always difficult to represent all the observations, and hence the average of the observations is taken to represent all the observations. Also in instances of changing values, the average of the values is taken to represent all the values. A few examples of average include, the average temperature of a place, the average marks of a student, and the average price of a stock.

Can the Average Value be Zero?

The average value can be zero. For quantities having some positive values and some negative values, the sum of the values can equalize to zero. Let us consider an example of a set of values, 40, 90, -180, 20, 60, -30. The sum of these quantities is equal to zero. Hence the average value also is equal to zero

How Do you Find the Average of 4 Observations?

Let us consider the four observations 5, 10, 15, 20. The formula for the average of observations is equal to the sum of the observations divided by the number of observations. Hence the sum of these 4 observations is 50, and its average is 50/4. Therefore the average of 4 observations is 12.5 

What Is the Average of 2 Observations?

Let us consider 2 observations 5 and 10. The average of these observations is equal to some of the observations divided by the number of observations. Hence the sum of 2 observations is 15 and its average is 15/2 or 7.5

How To Find a Weighted Average?

To find the weighted average, first, each of the individual quantities has to be assigned some weights. The weights can be whole numbers or decimals. The weights indicate the level of importance of each of the quantities. The formulae for weighted average is equal to the summation of the product of the respective weights and quantities divided by the number of quantities.

Weighted Average = Summation of the product of weights and quantities / Number of quantities

Why Do We Need a Weighted Average?

We need a weighted average because each of the quantities has its individual importance. Based on the importance different quantities are assigned different weights. The weighted average helps to rightly justify the contribution of each individual quantities, to the overall average. 


Solved Examples 

Example 1: William has 3 boxes of cookies that have 3, 7, and 11 cookies each. What is the average cookie count per box?

Solution:

To find the average cookie count per box we need to divide the sum of the cookies by the total number of boxes. For the three boxes, the sum of the cookies is 3 + 7 + 11 = 21. The average cookies per box is the total number of cookies divided by the number of boxes. Hence the average = 21/3 = 7. Therefore the average cookie count per box is 7

Example 2: Rizo scored 70, 60, 80, and 50 marks in Math, English, Science, and Social Studies. What is the average mark he scored in the four subjects?

Solution:

To find the average we need to find the sum of the marks and divide it by the number of subjects. Here we have four subjects, Maths, Science, Social Studies, and English. Summing up all the scores we have 70 + 60 + 80 + 50 = 260. The average mark is equal to the sum of the scores divided by the number of subjects. Hence the average mark is 260/4 = 65. Therefore, the average marks scored in all the subjects is 65

Practice Questions 

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

 

 
 
 
 
  
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