Five students each rated some chocolate bars. Their ratings are shown on the diagram. Part a) Which rating was the mode? Part b) Each person rated the same number of chocolate bars. How many different types of chocolate bars were rated by each person?
So first of all, we need to start off by looking at the mode for part a. So what is the mode? Well, the mode is the most common or the one with the highest frequency. In our case, it’s the rating with the highest frequency or value with the highest frequency. But with the mode, the great thing about it is that it doesn’t always have to be a value. It can also be a category or an item. So before we actually find the mode, what I want to talk about is a couple of the common misconceptions or common errors that students make.
First of all, they might say, well, five. Five is the answer because five is the most. So that means it’s the most common. But that’s not the case because when we’re looking at the mode, we’re looking at the number or rating in our case that appears the most. So it has the highest frequency.
So the first thing we want to do is see what is the frequency of each of our ratings. Well, we can see that the frequency of rating one is two. So that means that the rating of one appeared twice. Rating two appeared three times. Rating three appeared five times. Rating four appeared once. And rating five appeared four times. So we can see that the rating that appeared the most number of times was rating three.
Well, here, we can also point out another common mistake. A common mistake in this question would be to write five. And this time, the reason for writing five would be because that’s the number of times the three appears. Or it’s the frequency. However, what we’re looking for is the rating that the mode is and, therefore, the rating with the highest frequency. So it’s not five that we want. It’s three because that’s the rating that has a frequency of five. So therefore, we’ve answered part a. And the rating that the mode is is three.
Okay. So now, let’s move on to part b. Well, for part b, we want to find out how many different types of chocolate bars were rated by each person. So the first thing we want to do is work out the total number of ratings. Well, the total number of ratings is gonna be equal to the sum of the frequencies, remembering that sum means add. So we’re gonna add altogether our frequencies. So we’re gonna add two, three, five, one, and four. So we’ve got two add three, which is five, add five is 10, add one is 11, add another four is 15. So therefore, the total number of ratings is 15. Okay, great.
So now, what we do? Well, we check back into the question to look for information to help us. But we can see that there were five students doing the ratings. And we’re told in part b that each person rated the same number of chocolate bars. So to find out how many chocolate bars they rated each, we’re gonna do a division because we’re gonna do 15 divided by five, because that’s the total number of ratings, divided by the total number of people or total number of students.
So as we said, the number of ratings by each person is gonna be equal to 15, because that was the total ratings, divided by five, because that was the number of students or the number of people. And this is equal to three.
So therefore, we can say that three types of chocolate bar were rated by each person.