# How Do You Find a Missing Number When You Already Know the Mean?

To find a missing number in a data set given the mean of the data set, count the total number of data points in the data set, including the missing number, and multiply the mean by this total number. Next, add together the known numbers in the data set. Finally, take the difference of the two numbers just calculated. The difference is the missing number.

The mean, or average, of a data set is calculated by summing all of the numbers in the data set and dividing that sum by the number of data points in the set. If the mean of a data set is known, then that mean contains information on the missing number. Multiplying the mean by the number of data points gives the “true” sum of all the data points, including the missing number.

The sum of the known data points is less than this true sum, because the sum of the known points does not include the value of the missing number. The difference between the sum of the known data points and the true sum is exactly the value of the missing number. However, if multiple data points are missing, this method does not work.