HOW TO CALCULATE AN AVERAGE ?
An average is a single number that represents a set of numbers. It is the result of adding numerical values in a dataset and dividing their sum by the number of total values in that set.
The average is not just an arithmetic calculation; it is a very useful and widely used method to identify trends in large sets of data and to make logical judgments.
The average makes it easier to summarize a large set of numbers in a dataset with one value, for example, if the set of data contains 70, 80 and 90, so we will add these 3 values and divide them by 3, so the answer is (70 + 80 + 90 )/ 3 = 80.
Average Calculation Method
To calculate the average, we can simply use the average formula. The formula is as following:
Average = sum of values / total number of values
The first step is to add the numbers in the dataset that you are trying to find the average for. Then, count how many values there are and divide the sum by that count. The final answer is your average value. If you want to calculate an average quickly, you can use our Average Calculator to get the result instantly.
The Average value is not always a whole number, as it can be in decimals as well. An average only comes out as a whole number when the sum divides evenly by the count. For example:
Whole number average:
Data set: 10, 20, 30
Average = (10 + 20 + 30) ÷ 3 = 20
Decimal average :
Data set: 10, 20, 25
Average = (10 + 20 + 25) ÷ 3 = 18.33
Types of Average : Mean vs Median vs Mode
There are three main types of averages, mean, median and mode. Each average calculation form has different perspectives of representing the data.
To find each one of these, different methods are used. These forms are also known as measures of central tendency, which is widely utilised in statistics and decision making. They help us understand the data by giving us a single value that represents the central point of the dataset.
Mean
Mean is simply an average value, but it is specifically used as a proper term for arithmetic average in maths and statistics, that is because the word average is used casually as well, so the term mean is considered to be a proper mathematical word. To calculate the mean, you simply have to follow the same steps as finding an average. Add the numbers in the dataset, and divide the total by the number of values in that set.
Example :
Data set: 10, 20, 30
mean = (10 + 20 + 30) ÷ 3 = 20
Some symbols used to represent mean value are :
The formula for mean is written as : μ = ΣX / N
Median
The median on the other hand is a completely different average value, it is the middle value of the dataset when arranged in ascending or descending order. If the number of values in the set is odd, then the median is the central value, else if it is even, then the median is the average of two middle values. The median can be a whole number and a fraction as well. To calculate the median, first arrange the numbers in increasing or decreasing order, and then cross out the numbers one by one from both ends, you will either end up with a single number which would be the median or two numbers at the centre for which you would calculate the average and get your final answer. Some examples are:
Median as a whole number:
Numbers: 3, 5, 7, 9, 11
The middle value is 7, so the median is 7.
Median as a decimal:
Numbers: 2, 4, 7, 9
The two middle values are 4 and 7.
Median = (4 + 7) ÷ 2 = 5.5
Median formula
If the number of values is odd:
Median = middle value
If the number of values is even:
Median = two middle values \ 2
Mode
Mode is the most repeated value in the dataset. It is the value with the highest frequency. It is the only average calculation that can have no value, one value or more than one as well, depending on the repetition of numbers in the datset. For example:
Heights
Suppose the heights of 7 students are : 150 cm, 155 cm, 160 cm, 160 cm, 160 cm, 165 cm, 170 cm
Here, 160 cm appears three times, which is more frequent than any other height. Therefore, The mode is 160cm.
For mean every value contributes to the result, for median only the middle value matters when the data is arranged, and for mode only the frequency of each value matters. The mean average is also affected by one extreme value(outlier) in the dataset. Median and mode are not affected by outliers. For the results, mean is always a single value, mode can be none, just one value or more than one value in the dataset. Median is exactly one value as well.
Outliers are the values in the data that are unusually large or small relevant to the other values in that data. These values can affect the average calculation (mean) heavily, so the answer might not be very accurate. Median value is less affected by these outliers.
Suppose the monthly expenses of five people are:
$200, $220, $240, $250, and $1,000
Mean = ($200 + $220 + $240 + $250 + $1,000) ÷ 5 = $382
Here, $1,000 is an outlier, which significantly increases the mean.
All these forms of calculating average or measures of central tendency are interrelated. However, they are calculated differently using different methods.
Applications of Calculating An Average
Average calculation is used in real life applications very commonly, be it business management, education systems (institutions), sports, finance and everyday life.
In schools and other academic institutions teachers often use it to evaluate their students based on their marks. Similarly it is used in multiple businesses to calculate sales, revenue, and profit to understand their finances better.
One of the common applications of calculating an average is in sports, every type of sport calculates average of the different types of datasets like player statistics, average runs (cricket), and average time as well. Other than that, in day-to-day life people calculate their average expenses, monthly bills etc.
Averages are used in comparing datasets as well. These can include comparing the average income of people in two or more countries to draw a conclusion about their economic conditions.
Common Mistakes when Calculating an Average
It is very important to make sure that the average values you calculate are accurate. That could be achieved by avoiding some common mistakes.
Calculating an average is a simple but a very useful way of representing the numbers in sets. It gives a quick overview of large sets of data that can become hard to manage. It makes it easier to implement decisions and make accurate observations.