The Table Displays The Scores Of Students On A Recent Exam. Find The Mean Of The Scores To The Nearest Tenth.$[ \begin{tabular}{|c|c|} \hline \text{Score} & \text{Number Of Students} \ \hline 75 & 7 \ \hline 80 & 7 \ \hline 85 & 5 \ \hline 90
Introduction
In mathematics, the mean is a fundamental concept used to calculate the average value of a set of numbers. It is an essential tool in statistics and data analysis, providing a way to summarize and understand large datasets. In this article, we will explore how to find the mean of a set of scores, using a table that displays the scores of students on a recent exam.
Understanding the Table
The table below displays the scores of students on a recent exam, along with the number of students who achieved each score.
| Score | Number of Students |
|---|---|
| 75 | 7 |
| 80 | 7 |
| 85 | 5 |
| 90 | 3 |
Calculating the Mean
To find the mean of the scores, we need to multiply each score by the number of students who achieved it, and then add up the results. This is known as the weighted sum.
First, let's multiply each score by the number of students who achieved it:
- 75 x 7 = 525
- 80 x 7 = 560
- 85 x 5 = 425
- 90 x 3 = 270
Next, let's add up the results:
525 + 560 + 425 + 270 = 1780
Finding the Mean
Now that we have the weighted sum, we can find the mean by dividing the result by the total number of students. To do this, we need to add up the number of students who achieved each score:
7 + 7 + 5 + 3 = 22
Now, we can divide the weighted sum by the total number of students:
1780 ÷ 22 = 80.909...
Rounding to the Nearest Tenth
Since we are asked to find the mean to the nearest tenth, we need to round the result to one decimal place. To do this, we can look at the hundredths place, which is 0.9 in this case. Since 0.9 is less than 5, we round down to 80.9.
Conclusion
In this article, we have explored how to find the mean of a set of scores, using a table that displays the scores of students on a recent exam. We have calculated the weighted sum, added up the results, and then divided by the total number of students to find the mean. Finally, we have rounded the result to the nearest tenth, as requested.
Tips and Variations
- If the table had more scores or a different distribution of scores, the calculation would be more complex.
- If the table had a different number of students for each score, the weighted sum would be different.
- If the scores were not integers, the calculation would be more complex, and we would need to use a calculator or computer program to find the mean.
Real-World Applications
The concept of mean is used in many real-world applications, such as:
- Finance: The mean is used to calculate the average return on investment for a portfolio of stocks or bonds.
- Business: The mean is used to calculate the average sales or revenue for a company.
- Science: The mean is used to calculate the average value of a set of measurements, such as the average temperature or the average height of a population.
Common Mistakes
- Rounding errors: When rounding the result to the nearest tenth, it is easy to make mistakes. Make sure to look at the hundredths place and round accordingly.
- Calculation errors: When calculating the weighted sum, it is easy to make mistakes. Make sure to double-check your calculations.
- Not using the correct formula: Make sure to use the correct formula for finding the mean, which is the weighted sum divided by the total number of students.
Conclusion
Introduction
In our previous article, we explored how to find the mean of a set of scores, using a table that displays the scores of students on a recent exam. In this article, we will answer some common questions related to finding the mean, and provide additional tips and variations.
Q&A
Q: What is the mean, and why is it important?
A: The mean is a fundamental concept in mathematics that represents the average value of a set of numbers. It is an essential tool in statistics and data analysis, providing a way to summarize and understand large datasets. The mean is important because it helps us to understand the central tendency of a dataset, and to make informed decisions based on that data.
Q: How do I calculate the mean?
A: To calculate the mean, you need to multiply each score by the number of students who achieved it, and then add up the results. This is known as the weighted sum. Next, you need to divide the weighted sum by the total number of students.
Q: What if the table has more scores or a different distribution of scores?
A: If the table has more scores or a different distribution of scores, the calculation would be more complex. You would need to multiply each score by the number of students who achieved it, and then add up the results. However, the basic steps remain the same.
Q: What if the scores are not integers?
A: If the scores are not integers, the calculation would be more complex, and you would need to use a calculator or computer program to find the mean.
Q: How do I round the result to the nearest tenth?
A: To round the result to the nearest tenth, you need to look at the hundredths place. If the hundredths place is 5 or greater, you round up. If the hundredths place is less than 5, you round down.
Q: What are some common mistakes to avoid when finding the mean?
A: Some common mistakes to avoid when finding the mean include:
- Rounding errors: Make sure to look at the hundredths place and round accordingly.
- Calculation errors: Make sure to double-check your calculations.
- Not using the correct formula: Make sure to use the correct formula for finding the mean, which is the weighted sum divided by the total number of students.
Q: What are some real-world applications of the mean?
A: The concept of mean is used in many real-world applications, such as:
- Finance: The mean is used to calculate the average return on investment for a portfolio of stocks or bonds.
- Business: The mean is used to calculate the average sales or revenue for a company.
- Science: The mean is used to calculate the average value of a set of measurements, such as the average temperature or the average height of a population.
Q: How do I use the mean in real-world applications?
A: To use the mean in real-world applications, you need to understand the context and the data. You need to calculate the mean, and then use it to make informed decisions. For example, if you are a business owner, you can use the mean to calculate the average sales or revenue for your company, and then use that information to make decisions about pricing or marketing.
Conclusion
In conclusion, finding the mean of a set of scores is a simple yet powerful concept that can be used in many real-world applications. By following the steps outlined in this article, you can find the mean of a set of scores and understand the underlying mathematics. Remember to avoid common mistakes, and to use the mean in context to make informed decisions.
Additional Resources
- For more information on the mean, see our previous article on finding the mean of a set of scores.
- For more information on real-world applications of the mean, see our article on using the mean in finance, business, and science.
- For more information on common mistakes to avoid when finding the mean, see our article on common mistakes to avoid when finding the mean.