The mean is the sum of all the numbers in a set divided by how many numbers there are. In this case, the mean is 7, so it looks like this:
7=(a+b+c)/3, multiply by 3 to both sides to get
21=a+b+c Therefore I have to find three numbers which add together to equal 21. There are an infinitude of three numbers which add up to 21, such as {7,7,7} or {-22,1,42}, but the set I have chosen to go with is {6,7,8}.
The median is the middle number of an ordered set of numbers. If the set has an odd amount of numbers {1,2,3,4,5}, the median is, the middle number (3). If the set has an even amount of numbers {1,2,2,4}, then the median is the two central-most numbers added together and then divided by two (2+2)/2=2.
To make a set of four with a median of 12, I must have 2 centre-most numbers that, when added together and divided by 2, equal 12, so
12=(a+b)/2. Multiply by 2 to get
24= a+b. Therefore the two centre-most numbers must equal 24 when added together, while the other numbers don't matter. There is an infinitude of four-number sets who's median is 12, such as {pi,12,12,17} and {-100,-7,31,31.002}, but I chose the set of {1,11,13,20}, because
#(11+13)/2=12, the median.
I hope I helped!
