Complete The Two-Way Table To Understand Animal Grooming Statistics
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Let's dive into this grooming table, guys! We're going to break down the numbers to figure out the real story behind these pampered pets. We’ll complete the two-way table about animals at a groomer and answer the question by analyzing the data step by step. This involves understanding how to read the table, performing simple addition and subtraction, and then evaluating the given statements. So, grab your magnifying glasses (not really, but you know, metaphorically!) and let's get started!
Understanding Two-Way Tables
Before we jump into solving the problem, it’s super important to understand what a two-way table is and how it works. Think of a two-way table as a way to organize information into rows and columns. Each row and each column represents a different category, and where they intersect, you get some juicy data. These tables are fantastic for showing relationships between different categories, making it easier to spot trends and draw conclusions.
Two-way tables, also known as contingency tables, are used to display the frequency distribution of two categorical variables. The rows represent one variable, the columns represent another, and the cells at the intersections show the number of observations that fall into each combination of categories. For example, in our case, one variable is whether an animal is a cat or a dog, and the other variable is whether the animal has been bathed or not.
The beauty of these tables is that they help you visualize data in a structured way. Instead of just seeing a jumble of numbers, you get a clear picture of how different groups relate to each other. They are commonly used in surveys, experiments, and data analysis to summarize and present data in an accessible format.
When reading a two-way table, it’s crucial to pay attention to the row and column headers. These labels tell you what each category represents. The numbers inside the table then tell you how many items or individuals fall into each category combination. Additionally, many two-way tables include marginal totals, which show the sum of each row and each column. These totals are invaluable for getting a quick overview of the distribution of the data.
For instance, if we have a table showing the number of people who prefer coffee versus tea and whether they are morning people or night owls, the rows might represent the beverage preference (coffee or tea), and the columns might represent the chronotype (morning person or night owl). The numbers in the cells would then tell us how many people fall into each combination—e.g., how many people prefer coffee and are morning people. The marginal totals would tell us the total number of coffee drinkers, tea drinkers, morning people, and night owls.
In our grooming table example, the rows might represent the type of animal (cat or dog), and the columns might represent whether the animal has been bathed or not. By filling in the missing values and analyzing the totals, we can gain insights into the grooming preferences and patterns at the groomer. This understanding is crucial for accurately answering questions and drawing meaningful conclusions from the data.
Completing the Two-Way Table
Now, let’s roll up our sleeves and get to work on this table. To complete a two-way table, we need to use the information we already have to figure out the missing pieces. It’s like a puzzle, where each number fits in a specific spot. We’ll be using some simple addition and subtraction to fill in the blanks, so don't worry, it’s nothing too crazy!
First off, let's break down the basic principles of completing a two-way table. The fundamental concept is that the totals in the rows and columns must add up correctly. For example, if you know the total number of dogs and the number of bathed dogs, you can subtract the latter from the former to find the number of unbathed dogs. Similarly, if you know the total number of animals and the total number of cats, you can find the number of dogs.
Let’s consider a hypothetical scenario. Suppose we know the following:
- Total animals at the groomer: 28
- Total cats: 8
- Bathed cats: 5
- Bathed dogs: 2
We can represent this information in a partially completed table:
| Bathed | Unbathed | Total | |
|---|---|---|---|
| Cats | 5 | 8 | |
| Dogs | 2 | ||
| Total | 28 |
Our mission is to fill in the missing values using the information provided. Let’s start with the number of unbathed cats. We know there are 8 cats in total, and 5 of them have been bathed. To find the number of unbathed cats, we subtract the number of bathed cats from the total number of cats:
Unbathed cats = Total cats - Bathed cats
Unbathed cats = 8 - 5 = 3
So, we can fill in the table:
| Bathed | Unbathed | Total | |
|---|---|---|---|
| Cats | 5 | 3 | 8 |
| Dogs | 2 | ||
| Total | 28 |
Next, let’s find the total number of dogs. We know the total number of animals is 28, and the total number of cats is 8. To find the total number of dogs, we subtract the number of cats from the total number of animals:
Total dogs = Total animals - Total cats
Total dogs = 28 - 8 = 20
Now we can add this to our table:
| Bathed | Unbathed | Total | |
|---|---|---|---|
| Cats | 5 | 3 | 8 |
| Dogs | 2 | 20 | |
| Total | 28 |
To find the number of unbathed dogs, we can subtract the number of bathed dogs from the total number of dogs:
Unbathed dogs = Total dogs - Bathed dogs
Unbathed dogs = 20 - 2 = 18
Adding this to the table gives us:
| Bathed | Unbathed | Total | |
|---|---|---|---|
| Cats | 5 | 3 | 8 |
| Dogs | 2 | 18 | 20 |
| Total | 28 |
Now, let's find the total number of bathed animals. We add the number of bathed cats and bathed dogs:
Total bathed animals = Bathed cats + Bathed dogs
Total bathed animals = 5 + 2 = 7
And the total number of unbathed animals:
Total unbathed animals = Unbathed cats + Unbathed dogs
Total unbathed animals = 3 + 18 = 21
Finally, we fill in the totals:
| Bathed | Unbathed | Total | |
|---|---|---|---|
| Cats | 5 | 3 | 8 |
| Dogs | 2 | 18 | 20 |
| Total | 7 | 21 | 28 |
With the table complete, we can easily see the distribution of animals at the groomer. This systematic approach helps ensure we don't miss any information and that our calculations are accurate.
Evaluating the Statements
Alright, with our table all filled in and looking snazzy, it’s time to put on our detective hats and evaluate those statements. We need to figure out which one is the truth, the whole truth, and nothing but the truth. This involves carefully reading each statement and comparing it to the information we’ve compiled in our completed two-way table. Let’s break down each statement one by one.
Statement A: 28 animals are at the groomer.
This one seems straightforward, right? To check this statement, we look at the total number of animals in our table. If the total matches the statement, then we’ve got a potential winner. In our completed table, the total number of animals is indeed 28. So, this statement looks promising! But hold your horses, we need to check the other statements too, just to be sure. It’s like a multiple-choice test where you don’t pick the first right answer you see; you read all the options before making a decision.
Statement B: 3 unbathed dogs are at the groomer.
For this statement, we need to zero in on the number of unbathed dogs. Our table gives us this information directly. We look at the intersection of the “Unbathed” column and the “Dogs” row. According to our completed table, there are 18 unbathed dogs, not 3. So, this statement is definitely not true. We can cross this one off our list with confidence. It’s essential to be precise when reading the table; a slight misreading can lead to the wrong conclusion.
Statement C: 8 cats are at the groomer.
This statement is about the total number of cats. We find this information in the “Total” column and the “Cats” row. Our table shows that there are 8 cats in total. This statement aligns with the data in our table, making it another potential contender. We’re building a list of possible correct answers, and so far, statements A and C are in the running. But let’s not get ahead of ourselves; we still have one more statement to analyze.
Statement D: 7 bathed animals are at the groomer.
This statement focuses on the total number of bathed animals. We can find this number in the “Bathed” column and the “Total” row. Our table tells us that there are 7 bathed animals. This statement also matches the information in our table, adding it to our list of possible correct answers. Now we have three statements—A, C, and D—that seem to be true based on our table. But remember, in a multiple-choice question, there’s usually only one correct answer. This means we need to revisit our analysis and make sure we haven’t missed anything.
Determining the Correct Answer
Okay, so we’ve evaluated all the statements, and it looks like we have multiple possibilities. Statements A, C, and D all seem to align with the information in our completed two-way table. But here’s the catch: we need to find the single statement that is definitively true, according to the context of the problem. This is where a little bit of critical thinking comes into play.
Let’s recap the statements and our findings:
- Statement A: 28 animals are at the groomer. This is true according to the total in our table.
- Statement B: 3 unbathed dogs are at the groomer. We ruled this out because there are 18 unbathed dogs.
- Statement C: 8 cats are at the groomer. This also matches the total number of cats in our table.
- Statement D: 7 bathed animals are at the groomer. This aligns with the total number of bathed animals.
Now, let’s think about what the question is really asking. It’s asking us to identify a statement that is true based on the completed table. The statements A, C, and D are all factually correct based on our calculations. However, there’s a subtle nuance we need to consider.
Statement A says, “28 animals are at the groomer.” This is a general statement about the total number of animals. Statement C says, “8 cats are at the groomer,” and statement D says, “7 bathed animals are at the groomer.” These are also true, but they are specific details within the larger context of the table.
The key here is that the question is likely looking for the most comprehensive and overarching true statement. While it’s true that there are 8 cats and 7 bathed animals, the most inclusive statement is that there are 28 animals at the groomer. This statement encompasses all the animals, both cats and dogs, bathed and unbathed.
So, when we consider the overall picture, Statement A stands out as the best answer. It’s like looking at a family photo and saying, “There are ten people in the photo.” It’s true that there might be four kids and six adults, but the most general true statement is that there are ten people.
Therefore, after careful evaluation and consideration, we can confidently conclude that the correct answer is A. 28 animals are at the groomer.
Conclusion
Woohoo! We did it! We successfully navigated the two-way table, crunched the numbers, evaluated the statements, and found the correct answer. Completing two-way tables and interpreting data can seem a bit tricky at first, but with a systematic approach and a little bit of practice, you’ll be a pro in no time. The main takeaways here are understanding how to fill in the table using basic math, carefully reading each statement, and thinking critically about which statement best answers the question.
Remember, data analysis is a valuable skill in many areas of life, from school and work to making informed decisions in your personal life. So keep practicing, keep asking questions, and keep exploring the world of data. You’ve got this!
#seo-title Complete the Two-Way Table to Understand Animal Grooming Statistics #repair-input-keyword Which statement accurately describes the number of animals at the groomer, based on the completed two-way table?
