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
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.
- 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.
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.
☛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.
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.
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.
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.
How do you calculate the mean average of data? ›The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of values.
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 explain mean average? ›A mean in maths is the average of a data set, found by adding all numbers together and then dividing the sum of the numbers by the number of numbers. For example, with the data set: 8, 9, 5, 6, 7, the mean is 7, as 8 + 9 + 5 + 6 + 7 = 35, 35/5 = 7.
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.
Why do we calculate the mean average? ›The mean represents the average value in a dataset. The mean is important because it gives us an idea of where the center value is located in a dataset. The mean is also important because it carries a piece of information from every observation in a dataset.
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.
Why do we use mean average? ›The mean can be used to represent the typical value and therefore serves as a yardstick for all observations. For example, if we would like to know how many hours on average an employee spends at training in a year, we can find the mean training hours of a group of employees.
Which of the simplest methods is used to calculate average? ›- Select the data set that you want to find the average for. ...
- Calculate the sum of the data set. ...
- Count the numbers in your data set. ...
- Divide the sum of the data set by the total count of the numbers in the data set. ...
- Finding the average sales.
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 solve a simple average? ›The simple average of a set of observations is computed as the sum of the individual observations divided by the number of observations in the set.
How do you calculate average product with example? ›The Basic Calculation
Divide the total product by the input of labor to find the average product. For example, a factory that produces 100 widgets with 10 workers has an average product of 10. Average product is useful for defining production capabilities at a specific level of input.
The mean is the average or the most common value in a collection of numbers. In statistics, it is a measure of central tendency of a probability distribution along median and mode. It is also referred to as an expected value.
How do you explain mean results? ›The mean is the sum of all the data points divided by the number of the data points itself. To calculate mean, one must simply add all the values together. Then the individual must divide the resulting sum by the number of values itself. Consequently, the result that arrives is the mean or average score.
What is another word for average mean? ›adj.normal, typical. adj.numerical mean. nounnormal, typical amount. mean.
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? ›- Nominal data.
- Ordinal data.
- Discrete data.
- Continuous data.
Data typically comes in the form of graphs, numbers, figures, or statistics.
Why is mean average precision important? ›Mean Average Precision (mAP) is commonly used to analyze the performance of object detection and segmentation systems. Many object detection algorithms, such as Faster R-CNN, MobileNet SSD, and YOLO use mAP to evaluate the their models.
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 is the best method of measuring average? ›- Mean – what in everyday language would think of as the average of a set of figures.
- Median – the 'middle' value of a dataset.
- Mode – the most common value.
An average can be described as a summary of a group of numbers as a single number. There are different types of averages; the most common used in official statistics are mean and median.
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.
- median.
- typical.
- moderate.
- modest.
- middle.
- reasonable.
- middling.
- mean.
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 are the three most commonly used averages? ›Arithmetic mean, median and mode are the three most commonly used measures of central tendency.
Which is the best average method? ›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).
What is average and why is it important? ›“Average is an attempt to find one single figure to describe whole of figures”. “Averages are statistical constants which enable us to comprehend in a single effort the significance of the whole.” “An average is a single value within the range of the data that is used to represent all the values in the series.
Is average of average wrong? ›If you attempt to create an “average of averages”, the single data point will disproportionately affect the outcome. The average of 10,000 data items basically gets valued at the same rate as the average of the single data point. The “average of averages” would be 6, but the correct average of all values would be 10.
Does average mean most common? ›
Though we commonly use the word average in everyday life when discussing the number that's the most “typical” or that's “in the middle” of a group of values, more precise terms are used in math and statistics.