In Exercises 23 and 24, construct the relative frequency distr...

Question

In Exercises 23 and 24, construct the relative frequency distributions and answer the given questions.

Oscar Winners Construct one table (similar to Table 2-5) that includes relative frequencies based on the frequency distributions from Exercises 5 and 6, and then compare the ages of Oscar-winning actresses and actors. Are there notable differences?

Table displaying the ages of Best Actress winners with corresponding frequencies for each age range. Table displaying the ages of Oscar-winning actors with corresponding frequency counts for each age range.

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says to construct a relative frequency distribution for the ages of gold medal winning male and female athletes, and then compare the ages of gold medal winning male and female athletes. Are there noticeable differences in their ages? And below the pro text, we're given two tables. The first table is dealing with the male athletes, and it has two columns. The first column is the age of when the gold medal was won, and we have the categories of 20 to 24, 25 to 29, 30 to 34, and 35 to 39. And in the second column, we have the frequency, which has the values of 397, and 1. The second table deals with the female athletes, and We have the same two columns. In the first column, it is the age of when the gold medal was won, and we have the same categories of 20 to 24, 25 to 29, 30 to 34, and 35 to 39. And in the last column, we have the frequency, and it has the values of 6, 11, 3, and 0. We're also given four possible choices as our answers. For choice A, we have female athletes show a wider age distribution than males, with more winners in the 30 to 34 age group. For choice B, we have male athletes win gold medals, mostly in their early 20s, whereas females tend to win in their early 30s. For choice C, we have female athletes tend to win gold medals at younger ages, while male athletes have a broader distribution across ages. And for choice D, the frequency distribution suggests that both male and female athletes win gold medals at similar ages, with no noticeable differences. So the first thing we need to do is to calculate our relative frequency. And recall that our relative frequency. is going to be equal to. The class frequency, which is what's given in the table. Divided by The sum Of all class frequencies. Will have divided by the sum of all the frequencies. And so we're gonna have to do this for both the male and female athletes, and this is actually best done in a table. And so on the screen here, we have two tables. The first table is dealing with the female athletes, and so we'll look at it first. And so, this table has 4 columns. It has the first column our class interval, second column is going to be your frequency. The third column is going to be for our calculation, and the final column is going to be our relative frequency. And so, for the 20 to 24 age range, we had a frequency of 6, and so we'll take 6 and divide it by 20, which is the total number of female, um. At the frequencies that we had. And when we do that calculation, the relative frequency is going to be 0.30. If we look at the next class, that's going to be the 25 to 29 age range, and this had a frequency of 11, so we'll have 11 divided by 20, and this gives us a relative frequency of 0.55. For the next age range, we have 30 to 34, and that had a frequency of 3. So we have 3 divided by 20, which is equal to 0.15. And then for our final class, we have 35 to 39 age range. It had a frequency of 0, so we'll have 0 divided by 20, that makes our relative frequency 0. We'll do the same thing for the uh male athletes, and so for the sorry, for the 20 to 24 age range. We had a frequency of 3, and if we solve all of our frequencies for the male athletes, we again get 20, so we'll take 3 and divide it by 20, and that will give us a relative frequency of 0.15. For the next interval, we have the 25 to 29 age range, that had a frequency of 9, so we'll have 9 divided by 20, and this gives us a relative frequency of 0.45. And for the next class interval, we have the 30 to 34 range, and that had a frequency of 7, so a 7 divided by 20, which gives us a relative frequency of 0.35. And then finally, for our last class interval, we'll have 35 to 39 age range, and here we had a frequency of 1, and so we'll have 1 divided by 20, which gives us a relative frequency of 0.05. So, this is the relative frequency distribution that the question was asking for. Now, we also need to compare the ages of gold medal winning male and female athletes. So, if we look at the female athletes first, we see that the class interval from 25 to 29 age range, had the highest relative frequency of 0.55 or 55%. So more than half of the gold medals, one were by people in this age range. And if we look at the age range going from 20 to 29, Which would be our first two classes combined, that accounts for 85% of all the gold medals won by females. However, if we look at the male distribution, We see that none of the age ranges actually break 0.5% or the 50% mark. This means that the gold medals are more broadly distributed across the different age groups. So, the main difference between the two groups is that female athletes tend to win gold medals at younger ages, whereas male athletes win gold medals across a broader age distribution. So, with that conclusion, if we look at our answer choices, we see that the correct answer choice corresponds to answer choice C. Which says that female athletes tend to win gold medals at younger ages, while male athletes have a broader distribution across ages. So, I hope that this explanation has been useful, and I'll see you in the next video.

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