Question 1170870: Fifty Mass Communication students were surveyed about their preference on the three short films produced by students to be submitted as an entry in the local film festival. They ranked the three films and the result is shown in the table below. Which film is the most popular choice of this group of students?
Rankings
Kalinaw sa Mindanao 2 1 2 1 3
Ang Probasyon 3 2 1 3 1
Salome 1 3 3 2 2
Number of votes 8 7 7 15 13
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! To determine the most popular choice among the students, we need to analyze the rankings in a way that reflects overall preference. Here's how we can approach this:
**Understanding the Data**
The table shows how many students assigned each rank (1st, 2nd, or 3rd) to each film. To find the most popular film, we need to consider how many students ranked each film highly (especially as their 1st choice).
**Method: Point System (Borda Count)**
A common method for analyzing ranked preferences is the Borda Count. Here's how it works:
1. **Assign Points:**
* For each ranking, assign points:
* 3 points for a 1st-place ranking
* 2 points for a 2nd-place ranking
* 1 point for a 3rd-place ranking
2. **Calculate Total Points:**
* Multiply the number of votes for each ranking by the assigned points.
* Add up the points for each film.
3. **Determine the Most Popular:**
* The film with the highest total points is considered the most popular.
**Calculations**
**Kalinaw sa Mindanao:**
* 1st place: 2 points \* 8 votes = 16 points
* 2nd place: 1 point \* 7 votes = 7 points
* 2nd place: 1 point \* 7 votes = 7 points
* 1st place: 2 points \* 15 votes = 30 points
* 3rd place: 0 points \* 13 votes = 0 points
* Total points: 16 + 7 + 7 + 30 + 0 = 60 points
**Ang Probasyon:**
* 3rd place: 0 points \* 8 votes = 0 points
* 2nd place: 1 point \* 7 votes = 7 points
* 1st place: 2 points \* 7 votes = 14 points
* 3rd place: 0 points \* 15 votes = 0 points
* 1st place: 2 points \* 13 votes = 26 points
* Total points: 0 + 7 + 14 + 0 + 26 = 47 points
**Salome:**
* 1st place: 2 points \* 8 votes = 16 points
* 3rd place: 0 points \* 7 votes = 0 points
* 3rd place: 0 points \* 7 votes = 0 points
* 2nd place: 1 point \* 15 votes = 15 points
* 2nd place: 1 point \* 13 votes = 13 points
* Total points: 16 + 0 + 0 + 15 + 13 = 44 points
**Results**
* Kalinaw sa Mindanao: 60 points
* Ang Probasyon: 47 points
* Salome: 44 points
**Conclusion**
Kalinaw sa Mindanao has the highest total points (60). Therefore, **Kalinaw sa Mindanao** is the most popular choice of this group of students.
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