Create a set of 5 positive numbers repeats allowed that have

Create a set of 5 positive numbers (repeats allowed) that have a median 10 and mean 7.

What thought process did you use to create your numbers?

Solution

Start with the median, which is the middle value in the ordered set of numbers, this will be 10. ?,?,10,?,? The question marks are numbers that we need to find now. Since the average must be 14 we know that (?+?+10+?+?)/5 = 14. If we multiply both sides by 5 we find that: ?+?+10+?+? = 70. Subtract the 10 from both sides and now ?+?+?+? = 60. We can replace the question marks by variables (call them a,b,c,d) a+b+c+d = 60, and we know that a and b must be less than or equal to 10, while c and d must be greater than or equal to 10, but not all equal to 10 a+b+c+d = 60 Lets start by making c and d both 25 a+b+25+25 = 60 means that a+b = 10. Any of the combinations (1,9),(2,8),(3,7),(4,6),(5,5) will satisfy this so lets just call them both 5. We then get the set 5,5,10,25,25. The median of which is 10 and the mean of which is (5+5+10+25+25)/5 = 70/5 = 14.