Average - Calculation of Average, Meaning, Examples (2023)

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 the average.

1.What is the Meaning of Average?
2.Calculation of Average
3.Can Median Considered Be As Average?
4.Uses of Average
5.FAQs on Average

What is the Meaning of 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. Hence, the average formula is:

Average = Sum of the Observations/Number of Observations

(Video) What is Average? definition and meaning

Average - Calculation of Average, Meaning, Examples (1)

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

(Video) Return on Average Equity (ROAE) - Meaning, Formula, Example, Calculation

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.

Average - Calculation of Average, Meaning, Examples (2)

  • 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.

Average - Calculation of Average, Meaning, Examples (3)

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.

(Video) Average | meaning of Average

  • 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.

☛Related Topics

Listed below are a few topics that are related to average.

  • Mean, Median and Mode
  • Weighted Average
  • Measures of Central Tendency
  • Arithmetic Mean
  • Geometric Average Formula

FAQs on Average

How to Calculate Average?

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.

(Video) Difference Between Average and Mean | What is mean | Average meaning | Concept of average

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

(Video) What Does AVERAGE Means || Meanings And Definitions With Example in ENGLISH

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.

What is the Average Formula?

If the set of 'n' number of observations is given then the average can be easily calculated by using a general average formula that is, average = {Sum of Observations} ÷ {Total number of Observations}.

FAQs

What is the meaning of average with examples? ›

Average is the central value of a given set of values. For example, the average of 3 and 5 is equal to (3+5)/2 = 8/2 = 4. Hence, 4 is the central value for 3 and 5.

What does find the average mean mean? ›

Published on October 9, 2020 by Pritha Bhandari. Revised on May 22, 2022. The mean (aka the arithmetic mean, different from the geometric mean) of a dataset is the sum of all values divided by the total number of values. It's the most commonly used measure of central tendency and is often referred to as the “average.”

What are the 3 ways to calculate average? ›

There are three main types of average: mean, median and mode. Each of these techniques works slightly differently and often results in slightly different typical values. The mean is the most commonly used average. To get the mean value, you add up all the values and divide this total by the number of values.

How do you calculate the mean average in math? ›

The mean is the average number in a set of numbers, which gives us an idea about the overall trends within the data. It is calculated by adding all of the numbers together, then dividing by the total number of numbers.

How do you calculate average example? ›

Average This is the arithmetic mean, and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.

What is the example of average data? ›

Mean: The "average" number; found by adding all data points and dividing by the number of data points. Example: The mean of 4, 1, and 7 is ( 4 + 1 + 7 ) / 3 = 12 / 3 = 4 (4+1+7)/3 = 12/3 = 4 (4+1+7)/3=12/3=4left parenthesis, 4, plus, 1, plus, 7, right parenthesis, slash, 3, equals, 12, slash, 3, equals, 4.

Is it correct to calculate average of averages? ›

When you derive the average of a sample sample of numbers, the resulting number is just another number. So if you truly want just the average of averages, you just take all of the averages and add them together and divide by how many averages you have. No difference in the process.

How do you convert average to mean? ›

The mean is calculated by adding all the scores together, then dividing by the number of scores you added.

What does the average mean in statistics? ›

The average is the statistical summary, in one value, of a group of numbers. There are three main types of averages: the mean (the sum or product of the values of a group of numbers divided by how many numbers there are in the group); the median (the middle value of a group of numbers);

Can you average an average? ›

There is a common question that crops up in analytics, which is can you average your averages. The short answer is no, but a longer explanation is probably needed. Whether you have grouped your data by month, or region, or some other facet – each average you see is based on a different number of data points.

Why do we calculate average? ›

Finding an average gives us an idea as to an overall behaviour or trend – Mrs Mansell's average spend on shopping gives us an idea as to whether she usually spends a lot or a little money and Keiran's average spelling score gives us an idea as to how good he usually is at spelling.

What is a simple average method? ›

It is a method for inventory valuation or delivery cost calculation, where even if accepting inventory goods with different unit cost, the average unit cost is calculated by multiplying the total of these unit costs simply by the number of receiving.

What is the average of mean score? ›

A mean scale score is the average performance of a group of students on an assessment. Specifically, a mean scale score is calculated by adding all individual student scores and dividing by the number of total scores. It can also be referred to as an average.

How can we find the mean or average of 3 and 4? ›

How to Find the Mean. The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.

Does average and mean mean the same thing? ›

Average can be defined as the sum of all the numbers divided by the total number of values. A mean is defined as the mathematical average of the set of two or more data values. Average is usually defined as mean or arithmetic mean.

How do you solve average problems? ›

Average can be calculated simply by dividing the sum of all values in a set by the total number of values.

How do you find the average of 4? ›

The average is simply the sum of the numbers in a given problem, divided by the number of numbers added together. For example, if four number are added together their sum is divided by four to find the average or arithmetic mean.

How do you write an average equation? ›

The general average formula is mathematically expressed as Average = {Sum of Observations} ÷ {Total number of Observations}.

What are the 4 types of averages? ›

We consider there to be four types of average: mean, mode, median and range. Actually, range is a measure of spread or distribution but the others are our most common “measures of central tendency”.

What are the 4 types of data examples? ›

What are Types of Data in Statistics?
  • Nominal data.
  • Ordinal data.
  • Discrete data.
  • Continuous data.

What are the 3 examples of data? ›

Data typically comes in the form of graphs, numbers, figures, or statistics.

How do I average two averages? ›

Answer and Explanation: If we are given two averages and we need to find their average, then we can sum up the two averages and divide the sum by 2 according to the definition of the averages.

How do you combine multiple averages? ›

Add the means of each group—each weighted by the number of individuals or data points, Divide the sum from Step 1 by the sum total of all individuals (or data points).

How do you find the overall mean of two means? ›

Simply sum the means of all your samples and divide by the number of means.

How do you calculate average mean percentage score? ›

Divide the sum of the percentages by the sum of the total products produced from each category. So, 615 divided by 900 is equal to 0.68. Multiply this decimal by 100 to get the average percentage. So, 0.68 times 100 equals 68, or 68%.

Is the sum of averages an average? ›

No, in general the average of sub-averages is not the average of the original set of numbers.

Can you add an average to an average? ›

false. Adding or 'averaging' averages is not valid. But now here were the two groups 1, 2, 3 was the first group. The Second group was 90, 95, 100, 105, 110.

Can you average a mean? ›

An Average can be defined as the sum of all numbers divided by the total number of values. A mean can be defined as an average of the set of values in a sample of data. In other words, an average is also called the arithmetic mean. Describing the average is called a mean.

Why is the mean average called the mean? ›

What is Mean? Mean is the central point of the set of values. It is the average of values present in the data set. The central value which is called the average in mathematics is called the mean in statistics.

Which is the best method of calculating average value? ›

The most widely used method of calculating an average is the 'mean'. When the term 'average' is used in a mathematical sense, it usually refers to the mean, especially when no other information is given. Add the numbers together and divide by the number of numbers. (The sum of values divided by the number of values).

Which of the simplest methods is used to calculate average? ›

How to find the average
  1. Select the data set that you want to find the average for. ...
  2. Calculate the sum of the data set. ...
  3. Count the numbers in your data set. ...
  4. Divide the sum of the data set by the total count of the numbers in the data set. ...
  5. Finding the average sales.
Jul 14, 2021

How do you use average in a sentence? ›

Use “average” in a sentence

The average person must drink at least a liter of water every day. I sleep six hours a day on average. What's the average temperature here? Your work is below average.

How is average used? ›

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.

Does average mean good? ›

Something that is average is neither very good nor very bad, usually when you had hoped it would be better. I was only average academically. Most children are not geniuses or stars. They just do averagely well.

What is the average of averages called? ›

This phenomenon has a name: the fact that the average of averages is not the average is an instance of Simpson's Paradox. Here is an example, consider the following list of numbers: 3. 4.

What are the three most commonly used averages? ›

Arithmetic mean, median and mode are the three most commonly used measures of central tendency.

What is another word for average mean? ›

adj.normal, typical. adj.numerical mean. nounnormal, typical amount. mean.

Does average always mean mean? ›

Average, also called the arithmetic mean, is the sum of all the values divided by the number of values. Whereas, mean is the average in the given data. In statistics, the mean is equal to the total number of observations divided by the number of observations.

What does the average value tell you? ›

In very simplistic terms, it indicates the average distance of all the values or scores from the mean of the distribution. The more each value differs from the mean, the larger the standard deviation will be.

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