Matchmaking

1. For each of the lists above, rank the items in order of how much you like them, with a ‘1’ being the one you like most and a ‘6’ the one you like least.  You must rank them all, and ties aren’t allowed!  You may want to do it on this template (PRINT ME).

2. Now, find someone to compare your choices with.

   • In the table on the right (PRINT ME), write down your ranks and their ranks for the same items. 

   • Then in the other columns work out the difference between your ranks (d), and finally square the difference (d2).

   • Finally, add up the totals in the last column (d2).

3. Once you have this total, do the following:

   •  Multiply it by 6,

   •  Divide the answer by 210,

   •  Subtract the answer from 1.

4. What was your score?  What does this mean?

5. Now repeat steps 2 to 4 with other other people in the class.  How well matched are you with other people?

Further Questions and Challenges

1. Plot both people’s scores on a graph like the one shown on the right.

   • What would a perfect match look like?

   • What would a perfect mismatch look like? 

   • What would a score close to zero look like?

2. What would the score be for a perfect match?

3. What about a perfect mismatch?

4. What total would give a negative score?

5. What would a score of ‘0’ mean?

6. How would you achieve a score of 0?

7. What would the divisor be (i.e. not 210) if there were 5 items rather than 6? 

8. What would the divisor be (i.e. not 210) if there were a different number of items rather than 6 ?

9. What is the connection between the divisor and the number of items? 

1. • Hint 1: think about cube numbers

   • Hint 2: look at the formula on the right!