Understanding the Vegetable Preference Survey

This problem asks us to analyze data from a survey of 75 students regarding their preferences for different vegetables: cabbage, cauliflower, carrot, and capsicum. We are given the number of students who like specific vegetables or combinations.

Analyzing the Given Data

Here is a breakdown of the information provided:

• Total students surveyed: 75
• Students who like only cabbage: 12
• Students who like only cauliflower: 15
• Students who like only carrot: 21
• Students who like both carrot and cabbage: 12
• Students who like only capsicum: 13
• Students who like both capsicum and cauliflower: 2

Let's check if the sum of these categories equals the total number of students:

\(12 + 15 + 21 + 12 + 13 + 2 = 75\)

Yes, the sum matches the total number of students. This implies that every student falls into one of these specified categories, and there are no students who like other combinations not listed, or no students who like none of these vegetables.

Calculating Total Students Who Like Carrot

To find the total number of students who like carrot, we need to include all categories where liking carrot is mentioned. Based on the given data, these are:

• Students who like only carrot
• Students who like both carrot and cabbage

Total students who like carrot = (Students who like only carrot) + (Students who like both carrot and cabbage)

Total students who like carrot = \(21 + 12 = 33\)

Calculating Total Students Who Like Cauliflower

Similarly, to find the total number of students who like cauliflower, we need to include all categories where liking cauliflower is mentioned. Based on the given data, these are:

• Students who like only cauliflower
• Students who like both capsicum and cauliflower

Total students who like cauliflower = (Students who like only cauliflower) + (Students who like both capsicum and cauliflower)

Total students who like cauliflower = \(15 + 2 = 17\)

Finding the Difference Between Liking Carrot and Cauliflower

The question asks for the difference between the number of people who like carrot and the number of people who like cauliflower.

Difference = (Total students who like carrot) - (Total students who like cauliflower)

Difference = \(33 - 17 = 16\)

The difference between the people who like carrot and cauliflower is 16.

Thus, the difference is 16.

Revision Table: Vegetable Preference Data

Additional Information: Understanding Survey Data

Survey data often provides information about preferences or characteristics of a group. When analyzing such data, it is important to carefully identify what each category represents. Categories like "only X" refer exclusively to liking X and nothing else mentioned in the survey context. Categories like "both X and Y" refer to liking both X and Y. To find the total number of people who like a specific item, say 'Carrot', you must sum up the numbers from all categories that include 'Carrot', whether it's 'only Carrot', 'both Carrot and Cabbage', 'Carrot and Cauliflower', etc., based on the categories provided in the problem. In this specific problem, the categories provided perfectly cover the total number of students, simplifying the calculation as we don't need to worry about students liking combinations not explicitly listed or liking none of the vegetables.