Question

A kindergarten class was surveyed to determine the children's favorite cartoon characters among Mickey Mouse, Bugs Bunny, and Scooby Doo. The students ranked the characters in order of preference; the results are shown in the preference schedule below.

Answer 1

b) We have to find how many votes are required for a majority.

We are assured to have a majority when we have votes as half the voters plus one.

In this case, as we have 36 voters, this quantity is 36/2+1 = 18+1 = 19.

Then, a majority is made by 19 students.

This doesn't mean that 19 votes are needed to win the survey, but it means that if one character has 19 votes for the first place, it is the winner for sure.

c) We can consider for a plurality voting only the character that was chosen in the first place.

Then, for Mickey Mouse we have 5 + 6 = 11 students that chose him as first.

For Bugs Bunny, we have 6 + 6 = 12 students that chose him as first.

Finally, Scooby Doo was chosen first by 5 + 8 = 13 students.

With this criteria, we have that Scooby Doo is the prefered character.

Answer:

b) 19.

c) Scooby Doo.