Gather a set of data for finding the mean. It is best to use the mean when all of the numbers in a dataset are symmetrical and there are no outliers. For instance, if the numbers in your set of data are 100, 150 and 300, it would be practical to use the mean for finding an average. However, if the numbers in your set of data are 100, 150 and 9,875, you would not want to use the mean to find your average, because 9,875 is an outlier and will skew the average. It is better to use the median in these instances.
Add together all of the numbers in your set of data to get the sum.
Count the number of numbers in your data set.
Divide the sum of the data by the number of numbers in your data set to get your mean.
Gather a set of data for finding the median. It is best to use the median when there are outliers in your dataset. For example, if you have a set of data containing the numbers 300, 600, 91,000, 500, 408 and 320, you should use the median to determine your average because 91,000 is an outlier and skew your representation of the dataset's true central tendency. The median is often used, for example, when determining average incomes because there are often incomes in a dataset that offset other incomes because they are extremely low or extremely high.
Arrange your data in order from lowest value to highest value. For example, the set of data in step one should be arranged as 300, 320, 408, 500, 600 and 91,000.
Pinpoint the middle number to get your median. If there is an uneven amount of numbers in the dataset, then add the two middle numbers together. In this case, the two middle numbers are 408 and 500 which equal 908.
Divide the sum of the two middle numbers by two to get the median. In this case, 908 divided by two equals a median of 454.
Gather a set of data for finding the mode. It is best to use the mode for finding an average when a set of data often repeats numbers. For example, if your set of data contains the numbers 20, 21, 22, 22, 23, 23, 29, 28, 27, 27, 27 and 27, then the mode is the best method for finding the average. The mode is often used in voting situations or when determining the popularity of something.
Count the number that occurs the most often in the data set to get your mode. In this case, 27 occurs the most, so it is the mode.
Count the data again to determine if any other numbers in the set of data also occur the same amount of times. In this case, no other number reoccurs four times, so 27 remains the mode. If there was another number in the data set that reoccured four times, there would be two modes.