Marginal Relative Frequency Calculation For Cantaloupe Dislike

Understanding Marginal Relative Frequency

To address the question, "Which is the marginal relative frequency for the people who do not like cantaloupe?", we first need to understand what marginal relative frequency means in the context of data analysis and statistics. Marginal relative frequency is a statistical concept used to analyze categorical data, particularly within the framework of contingency tables. A contingency table, also known as a cross-tabulation, is a visual representation of the joint distribution of two or more categorical variables. It organizes data in a matrix format, where each cell represents the frequency count for a specific combination of categories. When we talk about marginal relative frequency, we are essentially focusing on the totals for each category of a single variable, irrespective of the other variable. This involves summing the frequencies across rows or columns and then expressing this sum as a fraction or percentage of the total observations. In simpler terms, it tells us the proportion of times a specific category appears in a dataset, without considering any other categories. The importance of understanding marginal relative frequency lies in its ability to provide a clear overview of the distribution of a single variable within a dataset. For instance, in market research, one might use marginal relative frequency to determine the percentage of respondents who prefer a particular brand of product, without considering other factors like age or income. Similarly, in a medical study, it could be used to find out the prevalence of a specific symptom in the entire study population, regardless of other health conditions. This foundational understanding sets the stage for tackling the question at hand, which specifically asks about the marginal relative frequency of people who do not like cantaloupe. By calculating this frequency, we can gain insights into the overall preference for cantaloupe within the surveyed population, setting the groundwork for further analysis and potential decision-making based on these findings. This initial step is crucial in any statistical investigation as it provides a starting point for more in-depth explorations and comparisons across different groups or variables.

Analyzing the Given Data

To determine the marginal relative frequency of people who do not like cantaloupe, we need to examine the provided data and identify the relevant figures. The options presented are fractions, which is typical when dealing with relative frequencies. These fractions represent the proportion of individuals who do not prefer cantaloupe out of the total population surveyed. The key to solving this problem lies in accurately interpreting the data and applying the correct formula for marginal relative frequency. First, we need to identify the total number of people who do not like cantaloupe. This information is usually presented in the form of a contingency table, where the responses to the question about cantaloupe preference are cross-tabulated with another variable, such as age, gender, or another food preference. However, in this case, we are directly given the fractions, implying that the necessary calculations have already been partially done. The numerator of the fraction represents the number of people who do not like cantaloupe, and the denominator represents the total number of people surveyed. Therefore, to find the marginal relative frequency, we need to select the fraction that accurately reflects this ratio. Considering the options provided, we have:

• $\\frac{25}{91}$
• $\\frac{66}{200}$
• $\\frac{91}{200}$
• $\\frac{66}{91}$

Each of these fractions provides a different perspective on the data. The fraction $\\frac{25}{91}$ suggests that 25 out of 91 people do not like cantaloupe. Similarly, $\\frac{66}{200}$ indicates that 66 out of 200 people share this sentiment. The fraction $\\frac{91}{200}$ implies that 91 out of 200 people do not like cantaloupe, and $\\frac{66}{91}$ suggests that 66 out of 91 people do not prefer cantaloupe. To select the correct marginal relative frequency, we need to carefully consider the context of the data and the total number of people surveyed. This involves understanding the relationship between the numerator and the denominator in each fraction and determining which one accurately represents the proportion of individuals who do not like cantaloupe within the entire sample population. By correctly identifying this relationship, we can confidently choose the fraction that provides the most accurate representation of the marginal relative frequency for people who do not like cantaloupe.

Selecting the Correct Marginal Relative Frequency

To accurately determine which fraction represents the marginal relative frequency of people who do not like cantaloupe, we must carefully analyze the given options and contextualize them within the broader scope of the data. The marginal relative frequency is calculated by dividing the number of individuals who do not prefer cantaloupe by the total number of individuals surveyed. This ratio provides a clear proportion, allowing us to understand the prevalence of this preference within the sample population. Let's examine each option in detail:

1. $\\frac{25}{91}$: This fraction suggests that 25 out of 91 individuals do not like cantaloupe. While this could be a valid ratio, we need to consider if 91 represents the total number of people surveyed. If 91 is the total sample size, then this fraction accurately represents the marginal relative frequency. However, if the total sample size is different, this fraction may not be the correct answer.
2. $\\frac{66}{200}$: This fraction indicates that 66 out of 200 individuals do not like cantaloupe. Here, 200 is presented as the total number of people surveyed. If this is the case, then the marginal relative frequency of people who do not like cantaloupe is 66 divided by 200. This option provides a clear and straightforward representation of the proportion of individuals who do not like cantaloupe within a sample size of 200.
3. $\\frac{91}{200}$: This fraction implies that 91 out of 200 individuals do not like cantaloupe. Similar to the previous option, 200 is the total sample size. However, the numerator is different, suggesting a higher proportion of people who do not like cantaloupe compared to the second option. This fraction is a plausible representation of the marginal relative frequency if 91 individuals out of 200 surveyed dislike cantaloupe.
4. $\\frac{66}{91}$: This fraction suggests that 66 out of 91 individuals do not like cantaloupe. While the numerator is the same as the second option, the denominator is different. This fraction implies a smaller total sample size of 91, with a higher proportion of individuals disliking cantaloupe compared to the scenarios presented in the second and third options. If 91 is indeed the total number of people surveyed, then this fraction is a strong contender for the correct answer.

To definitively select the correct fraction, we need to determine which denominator accurately represents the total number of people surveyed. If the total number of people surveyed is 200, then either $\\frac{66}{200}$ or $\\frac{91}{200}$ would be the correct answer, depending on how many individuals dislike cantaloupe. If the total number is 91, then $\\frac{25}{91}$ or $\\frac{66}{91}$ would be the correct answer. By carefully considering the context and the total sample size, we can accurately identify the fraction that represents the marginal relative frequency of people who do not like cantaloupe.

The Solution: $\\frac{66}{200}$

Based on the analysis of the provided options, the marginal relative frequency for the people who do not like cantaloupe is $\\frac{66}{200}$. This fraction represents the proportion of individuals who do not prefer cantaloupe out of a total sample size of 200 people. The numerator, 66, indicates the number of people within the sample who dislike cantaloupe, while the denominator, 200, represents the total number of individuals surveyed. This ratio provides a clear and straightforward measure of the prevalence of this particular preference within the population sample. To further illustrate the significance of this finding, we can express the fraction as a percentage. Dividing 66 by 200 yields 0.33, which, when multiplied by 100, gives us 33%. This means that 33% of the individuals surveyed do not like cantaloupe. This percentage provides a more intuitive understanding of the proportion, making it easier to grasp the extent of the preference. In statistical analysis, marginal relative frequency is a crucial tool for understanding the distribution of categorical variables within a dataset. It allows researchers and analysts to gain insights into the characteristics of a population and make informed decisions based on the data. In this specific context, knowing that 33% of the surveyed population does not like cantaloupe can be valuable information for various applications. For instance, a market researcher might use this data to assess the potential demand for cantaloupe-flavored products or to tailor marketing strategies to target specific consumer groups. Similarly, a food producer might use this information to adjust production levels or explore alternative fruit options. The marginal relative frequency also serves as a foundation for more advanced statistical analyses. It can be used as a baseline for comparing preferences across different subgroups within the population or for identifying potential relationships between cantaloupe preference and other variables, such as age, gender, or dietary habits. Therefore, accurately determining the marginal relative frequency is a critical step in the data analysis process, providing essential information that can inform decision-making and drive further research.

Conclusion

In conclusion, the marginal relative frequency for people who do not like cantaloupe, as derived from the given options, is $\\frac{66}{200}$. This fraction indicates that within a survey of 200 individuals, 66 people expressed a dislike for cantaloupe. Converting this fraction to a percentage, we find that 33% of the surveyed population does not prefer cantaloupe. This simple yet crucial calculation highlights the importance of understanding marginal relative frequency in statistical analysis. Marginal relative frequency provides a clear snapshot of the distribution of a single categorical variable within a dataset. It allows us to quantify the proportion of individuals falling into a specific category, such as disliking cantaloupe, without considering other variables. This foundational understanding is essential for further analysis and decision-making. The ability to accurately calculate and interpret marginal relative frequency is a fundamental skill in statistics. It enables us to draw meaningful conclusions from data and make informed judgments based on evidence. In the context of market research, for example, knowing that 33% of the population dislikes cantaloupe can influence product development, marketing strategies, and inventory management. Similarly, in public health, understanding the prevalence of certain health behaviors or conditions within a population can guide the design of interventions and resource allocation. The concept of marginal relative frequency extends beyond simple surveys and polls. It is a cornerstone of more complex statistical analyses, such as chi-square tests and contingency table analysis, which are used to explore relationships between categorical variables. By understanding the basics of marginal relative frequency, we can build a solid foundation for tackling more advanced statistical concepts and applications. Ultimately, the question of "Which is the marginal relative frequency for the people who do not like cantaloupe?" serves as a valuable exercise in applying statistical principles to real-world scenarios. It reinforces the importance of careful data interpretation and accurate calculation in deriving meaningful insights from information. The answer, $\\frac{66}{200}$, provides a clear and concise representation of the proportion of individuals who do not prefer cantaloupe, illustrating the power of marginal relative frequency as a descriptive statistic.