IBGE Census 2010: Time To Complete 82 Questionnaires
Hey guys! Let's dive into a fascinating math problem related to the 2010 IBGE Demographic Census. This is a real-world scenario that helps us understand how math is used in everyday situations, particularly in large-scale surveys and data collection. We're going to break down the question step by step, making sure you understand the logic and calculations involved. So, buckle up and let’s get started!
Understanding the Problem
The core of the problem is figuring out how much time it took to complete 82 questionnaires during the 2010 IBGE Census, given that each questionnaire took an average of 15 minutes to complete. It sounds simple, right? But it’s a great example of how we use multiplication and unit conversion in practical situations. The key here is to multiply the number of questionnaires by the time taken for each, and then convert the result into hours and minutes. This kind of calculation is essential not just in surveys but also in project management, time tracking, and many other fields. Think about it – if you’re planning a project and know how long each task takes, you can use this same method to estimate the total time needed. This problem is more than just a math question; it’s a lesson in practical time management and calculation skills!
Breaking Down the Given Information
First, let's highlight the important information we have:
- Number of questionnaires: 82
- Time per questionnaire: 15 minutes
These two pieces of information are our building blocks. We know how many questionnaires there are, and we know how much time each one takes. Our mission is to combine these to find the total time. Think of it like this: if you know you have 82 tasks, and each task takes 15 minutes, you just need to add up 15 minutes 82 times. But instead of adding, we can use multiplication, which is a much faster way to get to the answer. So, we're essentially converting a repetitive addition problem into a simple multiplication one. This is a fundamental concept in math that simplifies many calculations and makes our lives easier. Understanding this principle is crucial for tackling more complex problems later on.
The Calculation: Minutes First
To find the total time in minutes, we simply multiply the number of questionnaires by the time it takes to complete each one. The calculation looks like this: 82 questionnaires * 15 minutes/questionnaire = Total minutes. Let's do the math:
82
* 15
----
410
+82
----
1230
So, 82 multiplied by 15 equals 1230. This means it took a total of 1230 minutes to complete all 82 questionnaires. But 1230 minutes doesn't really give us a clear picture, does it? It's a big number, and it's hard to visualize. That's why we need to convert it into hours and minutes. This conversion is a crucial step because it makes the answer more relatable and understandable. Instead of just having a large number, we can now express the time in a format that we use every day – hours and minutes. This is a common practice in many real-world scenarios, like scheduling meetings, planning travel time, or even cooking!
Converting Minutes to Hours and Minutes
Now that we know the total time in minutes is 1230, we need to convert this into hours and minutes. Remember, there are 60 minutes in an hour. So, to convert minutes to hours, we divide the total minutes by 60. This is a basic but vital conversion factor to remember. You'll use it all the time when dealing with time-related calculations. Think of it as a fundamental unit conversion, similar to converting inches to feet or centimeters to meters. Knowing these conversions makes handling different units of measurement much easier.
Let's perform the division:
1230 ÷ 60 = ?
To do this, we can use long division:
20
60|1230
-120
----
30
From the division, we get a quotient of 20 and a remainder of 30. This means that 1230 minutes is equal to 20 hours and 30 minutes. The quotient (20) represents the whole hours, and the remainder (30) represents the remaining minutes. This is a classic example of how division helps us break down a quantity into larger and smaller units, making it easier to interpret and use.
The Final Answer and Why It Matters
So, after all the calculations, we've arrived at our answer: it took 20 hours and 30 minutes to complete 82 questionnaires. Isn't it amazing how a simple multiplication and division problem can give us such a clear picture of the time investment in a large survey? This kind of calculation is super practical. Imagine being a project manager – you could use this to estimate how long a team would take to complete a certain number of tasks. Or, if you're planning a road trip, you can calculate your travel time based on the distance and speed. This is why understanding basic math concepts is so important; they empower us to make informed decisions and manage our time effectively.
Real-World Application and Significance
Understanding the time and effort involved in conducting a census, like the IBGE Demographic Census in 2010, gives us a new appreciation for the scale and complexity of such operations. The census is a massive undertaking, providing crucial data that governments and organizations use for planning and policy-making. Knowing that each interviewer spent an average of 15 minutes per questionnaire and that thousands of interviewers worked on this project helps us grasp the sheer magnitude of the effort. This information influences resource allocation, policy development, and even the distribution of funds for various social programs.
Implications for Data Collection and Analysis
Moreover, this calculation highlights the importance of efficiency in data collection. Fifteen minutes per questionnaire might seem short, but when multiplied by thousands of questionnaires, it adds up to a significant amount of time. This emphasizes the need for well-designed questionnaires and efficient data collection processes. If the questionnaire were longer or more complex, the time per interview would increase, impacting the overall cost and timeline of the census. Therefore, organizations continually seek ways to streamline data collection while maintaining accuracy and reliability. The lessons learned from the IBGE Census and similar projects inform best practices in survey design and data analysis worldwide.
Reflecting on the Broader Impact of Census Data
Finally, it's worth reflecting on why the census data matters in the first place. The information gathered during the census is used to determine everything from congressional representation to funding for schools and hospitals. It provides a snapshot of the population, including demographics, housing, and economic characteristics, which is essential for effective governance and societal planning. By understanding the time and effort involved in collecting this data, we can better appreciate the value of the census and the importance of participating in it. So next time you hear about a census or survey, remember the calculations and planning that go into it, and recognize the significance of the data it provides. You guys nailed it! Understanding the calculation behind this real-world problem not only sharpens your math skills but also gives you a peek into how data collection and analysis work in large-scale projects. Keep practicing, and you'll be solving even more complex problems in no time!