Create a set of numbers where:

the mode is equal to 10

the median is equal to 12

the average is 12

To create a set of number with the specified characteristics, we need to understand what those values would mean. First, we have the mode. The mode is the number which would appear often in the data set. For the set (1, 1, 3), the mode would be 1. The median is the value of the center position when the numbers are arranged in increasing order. For the same set, the median would be 1. The average would be a calculated central value of the data set. It is also known as the mean. It is calculated by adding all the data in the set then dividing it to the number of data in the set. For the same example, the average would be 1+1+3 / 3 = 5/3. 

Given:
mode = 10
median = 12
average = 12

The possible set would be:

(10,10,12,13,15)