Mean is the average of a given set of numbers and it characterizes the central tendency of a set of numbers. There are two types of mean calculations; these are arithmetic mean and geometric mean. Mean is commonly called as average or average mean. This article on how to calculate mean will help you in calculating arithmetic as well as geometric mean. We mostly calculate mean if the calculations are complicated or to deal with a range of values.
Calculating arithmetic mean
Most of us are familiar with the calculation of arithmetic mean. Calculating arithmetic mean of a range of numbers is very simple. The example below will explain you the calculation of arithmetic mean.
Step 1: Suppose you have a set of numbers 5, 4, 8, 16, 23.
Step 2: If we add all these numbers, we get the sum as 56.
Step 3: Count the number of numbers you have in the group. In our example we have 5 numbers.
Step 4: Divide the sum by total number of numbers you have.
Step 5: Here, 56 divided by 5 gives us 11.2. Therefore the arithmetic mean is 11.2.
Calculating geometric mean
Geometric mean is calculated as the average of the logarithmic values of a given set of data which is converted to base 10 number. However, the actual definition of the geometric mean is the nth root of the product of n numbers. Therefore there are two methods of calculating the geometric mean of a given data set, using nth root of numbers and taking log of the given set of numbers.
Method 1: Calculating using the nth root method
Formula
Geometric mean = nth root of (X1) (X2)… (Xn)
Step 1: Suppose you want to calculate geometric mean of 2 and 32.
Step 2: Take the product of all the numbers you have in your data set. In this case if 2 multiplied by 32 we get 64.
Step 3: There are only two numbers in the data set, therefore we need to take square root of 64 which is 8. Hence, geometric mean of 2 and 32 is 8.
Method 2: Taking mean of the logs and converting into base 10 number.
For this method you either need the logarithmic tables or scientific calculators for calculating or finding the logarithmic value of the given set of numbers.
Step 1: Suppose you have a set of numbers as 6, 50, 9, 1200, the first step towards calculation is finding logarithmic values of each numbers.
Log 6= 0.77815
Log 50= 1.69897
Log 9= 0.95424
Log 1200= 3.07918
Step 2: When you have calculated the log of each number, add these logarithmic values
Sum = 0.77815 + 1.69897 + 0.95424 + 3.07918
Sum = 6.51054
Step 3: Calculate the mean of this obtained logarithm value. In this case there are 4 numbers in the given set so,
Mean = 6.51054
4
Mean = 1.62764
Step 4: Find the number whose logarithm is 1.62764, i.e. find antilog of 1.62764. Antilog of this number is 42.4. Therefore, geometric mean of the above data set is 42.4.
Geometric mean = 42.4
Calculating geometric mean of exponential values:
- You can use a simple trick to calculate the geometric mean for the numbers with exponents such as 23, 25, 28, 23, 21.
- Instead of finding the values of each numbers, just add their exponents which is 20 in this case.
- Divide it with the number of values in the data se. There are 5 numbers, so 20/5 is 4.
- The geometric mean is 2 4, which is 16.
Tips:
- If you are not able to find the log and antilog using the logarithmic tables then use scientific calculators for calculating these values.
- You can also use Excel sheets for calculation of mean, many functions are provided for calculating the mean on these Excel sheets.
- You can also use online calculators for calculating mean.
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