Understanding Weighted and Unweighted Averages is crucial for students preparing for school exams and competitive tests. These concepts are not only foundational in mathematics but also frequently appear in various objective questions and MCQs. By practicing these averages through targeted practice questions, students can enhance their problem-solving skills and improve their exam scores significantly.
What You Will Practise Here
Definitions and differences between weighted and unweighted averages
Formulas for calculating weighted and unweighted averages
Real-life applications of averages in different contexts
Step-by-step methods to solve average-related problems
Diagrams illustrating the concept of averages
Common scenarios where weighted averages are used
Practice questions with varying difficulty levels
Exam Relevance
The topic of Weighted and Unweighted Averages is highly relevant in various examinations, including CBSE, State Boards, NEET, and JEE. Students can expect to encounter questions that require them to calculate averages based on given data sets. Common question patterns include direct calculations, word problems, and application-based scenarios where students must choose the appropriate type of average to use.
Common Mistakes Students Make
Confusing the formulas for weighted and unweighted averages
Neglecting to account for the weights in weighted averages
Misinterpreting the context of a problem, leading to incorrect average calculations
Overlooking the importance of units when calculating averages
Failing to double-check their calculations, resulting in simple arithmetic errors
FAQs
Question: What is the difference between weighted and unweighted averages? Answer: Weighted averages consider the relative importance of each value, while unweighted averages treat all values equally.
Question: How do I calculate a weighted average? Answer: To calculate a weighted average, multiply each value by its weight, sum these products, and then divide by the total of the weights.
Question: Why are averages important in exams? Answer: Averages help summarize data, making it easier to analyze and interpret information, which is essential for solving various mathematical problems in exams.
Now is the time to enhance your understanding of Weighted and Unweighted Averages! Dive into our practice MCQs and test your knowledge to ensure you are well-prepared for your exams.
Q. The average of 5 numbers is 12. If one number is removed, the average of the remaining numbers becomes 10. What is the number that was removed?
A.
8
B.
10
C.
12
D.
14
Solution
Total of 5 numbers = 5 * 12 = 60. Total of 4 numbers = 4 * 10 = 40. Number removed = 60 - 40 = 20.
Q. The average of 5 numbers is 50. If the average of the first 3 numbers is 40, what is the average of the last 2 numbers?
A.
60
B.
70
C.
80
D.
90
Solution
Total of 5 numbers = 5 * 50 = 250. Total of first 3 numbers = 3 * 40 = 120. Total of last 2 numbers = 250 - 120 = 130. Average of last 2 numbers = 130 / 2 = 65.
Q. The average of three numbers is 30. If one number is removed, the average becomes 25. What is the removed number?
A.
35
B.
30
C.
25
D.
20
Solution
Let the three numbers be x, y, z. (x + y + z) / 3 = 30 => x + y + z = 90. After removing one number, (x + y) / 2 = 25 => x + y = 50. Therefore, removed number = 90 - 50 = 40.
