Samuel Had The Following Scores On His Weekly English Quizzes: 76, 65, 88, 90, 74, And 98 Points. What Was His Average Weekly Score On The Six Weekly English Quizzes (to The Nearest Hundredth)?A. 80.67 B. 81.83 C. 80.83 D. 81.67
Understanding the Problem
In this problem, we are given a set of scores that Samuel achieved on his weekly English quizzes. The task is to calculate his average weekly score on the six quizzes, rounded to the nearest hundredth. To solve this problem, we need to understand the concept of averages and how to calculate them.
What is an Average?
An average is a measure of the central tendency of a set of numbers. It is calculated by adding up all the numbers in the set and then dividing by the total number of values. In this case, we have six scores, and we want to find the average of these scores.
Calculating the Average
To calculate the average, we need to add up all the scores and then divide by the total number of scores. The scores are: 76, 65, 88, 90, 74, and 98.
# Calculating the Sum of Scores
Step 1: Add up the scores
76 + 65 = 141
141 + 88 = 229
229 + 90 = 319
319 + 74 = 393
393 + 98 = 491
Step 2: Count the number of scores
There are 6 scores in total.
Step 3: Calculate the average
Average = Sum of scores / Number of scores
Average = 491 / 6
Average = 81.83333333333333
Rounding to the Nearest Hundredth
The average score is 81.83333333333333. To round this to the nearest hundredth, we look at the digit in the thousandths place, which is 3. Since 3 is less than 5, we round down to 81.83.
Conclusion
In conclusion, Samuel's average weekly score on the six weekly English quizzes is 81.83.
Answer
The correct answer is B. 81.83.
Discussion
This problem requires a basic understanding of averages and how to calculate them. It also requires attention to detail, as we need to round the average to the nearest hundredth. In real-life scenarios, calculating averages is an essential skill, and it is used in a wide range of applications, from business to science.
Real-World Applications
Calculating averages is a crucial skill in many real-world applications. For example, in business, averages are used to calculate employee performance, customer satisfaction, and product quality. In science, averages are used to calculate statistical measures, such as mean and standard deviation.
Tips and Tricks
When calculating averages, it is essential to pay attention to the details. Make sure to add up all the scores correctly and count the number of scores accurately. Also, when rounding to the nearest hundredth, make sure to look at the digit in the thousandths place and round accordingly.
Practice Problems
Try solving the following problems to practice your skills:
- What is the average of the following scores: 85, 92, 78, 95, 88, and 76?
- What is the average of the following scores: 90, 85, 92, 88, 95, and 78?
Conclusion
Q: What is an average?
A: An average is a measure of the central tendency of a set of numbers. It is calculated by adding up all the numbers in the set and then dividing by the total number of values.
Q: How do I calculate an average?
A: To calculate an average, you need to add up all the numbers in the set and then divide by the total number of values. For example, if you have the following scores: 76, 65, 88, 90, 74, and 98, you would add them up and then divide by 6.
Q: What is the formula for calculating an average?
A: The formula for calculating an average is:
Average = (Sum of scores) / (Number of scores)
Q: How do I round an average to the nearest hundredth?
A: To round an average to the nearest hundredth, you need to look at the digit in the thousandths place. If it is 5 or greater, you round up. If it is less than 5, you round down.
Q: What is the difference between a mean and an average?
A: A mean and an average are the same thing. The term "mean" is often used in statistical contexts, while the term "average" is more commonly used in everyday language.
Q: Can I calculate an average with negative numbers?
A: Yes, you can calculate an average with negative numbers. The process is the same as with positive numbers. For example, if you have the following scores: -5, 10, -2, 15, -8, and 20, you would add them up and then divide by 6.
Q: Can I calculate an average with decimals?
A: Yes, you can calculate an average with decimals. The process is the same as with whole numbers. For example, if you have the following scores: 3.5, 2.8, 4.2, 3.1, 2.5, and 4.9, you would add them up and then divide by 6.
Q: What is the importance of calculating averages?
A: Calculating averages is an essential skill in many real-world applications, such as business, science, and finance. It helps you to understand the central tendency of a set of numbers and make informed decisions.
Q: How do I calculate an average with a large dataset?
A: To calculate an average with a large dataset, you can use a calculator or a computer program to add up the numbers and divide by the total number of values. Alternatively, you can use a formula or a statistical software package to calculate the average.
Q: Can I calculate an average with missing values?
A: Yes, you can calculate an average with missing values. However, you need to decide how to handle the missing values. One common approach is to ignore the missing values and calculate the average based on the available data.
Q: What is the difference between a weighted average and an unweighted average?
A: A weighted average is an average that takes into account the relative importance of each value. An unweighted average is an average that gives equal weight to each value. For example, if you have the following scores: 10, 20, 30, and 40, and you want to calculate a weighted average with weights 1, 2, 3, and 4, you would multiply each score by its weight and then add them up and divide by the total weight.
Conclusion
In conclusion, calculating averages is an essential skill that requires attention to detail and a basic understanding of the concept of averages. By following the steps outlined in this article, you can calculate averages with ease and apply this skill to real-world applications.