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. A bag contains 3 red, 5 blue, and 2 green balls. What is the average number of balls per color?
A.
3
B.
5
C.
2
D.
4
Solution
Total balls = 3 + 5 + 2 = 10. Average = Total balls / Number of colors = 10 / 3 = 3.33.
Q. A class has 10 boys and 15 girls. If the average height of boys is 150 cm and that of girls is 145 cm, what is the average height of the class?
A.
147 cm
B.
148 cm
C.
149 cm
D.
150 cm
Solution
Total height of boys = 10 * 150 = 1500 cm. Total height of girls = 15 * 145 = 2175 cm. Total height = 1500 + 2175 = 3675 cm. Average height = 3675 / 25 = 147 cm.
Q. A class has 10 students with an average height of 150 cm. If 5 new students with an average height of 160 cm join, what is the new average height of the class?
A.
154
B.
155
C.
156
D.
157
Solution
Total height of 10 students = 10 * 150 = 1500 cm. Total height of 5 new students = 5 * 160 = 800 cm. New total height = 1500 + 800 = 2300 cm. New average = 2300 / 15 = 153.33 cm.
Q. A company has 3 departments with average salaries of $4000, $5000, and $6000. If the number of employees in each department is 10, 15, and 20 respectively, what is the overall average salary?
Q. A group of 4 friends has an average age of 25 years. If one friend leaves and the average age becomes 26 years, what is the age of the friend who left?
A.
24
B.
25
C.
26
D.
27
Solution
Total age of 4 friends = 4 * 25 = 100. New total age for 3 friends = 3 * 26 = 78. Age of friend who left = 100 - 78 = 22.
Q. A group of 8 friends has an average age of 25 years. If one friend leaves and the average age becomes 26 years, what is the age of the friend who left?
A.
24
B.
25
C.
26
D.
27
Solution
Total age of 8 friends = 8 * 25 = 200. New total age for 7 friends = 7 * 26 = 182. Age of friend who left = 200 - 182 = 18.
Q. A student scores 70, 80, and 90 in three subjects. If he wants to achieve an average of 85 after the fourth subject, what score does he need in the fourth subject?
A.
85
B.
90
C.
95
D.
100
Solution
Total score needed for average of 85 = 4 * 85 = 340. Current total = 70 + 80 + 90 = 240. Score needed in fourth subject = 340 - 240 = 100.
Q. In a class of 40 students, the average score in Mathematics is 75. If 10 new students join with an average score of 85, what will be the new average?
A.
78
B.
80
C.
82
D.
76
Solution
Total score of 40 students = 40 * 75 = 3000. Total score of 10 new students = 10 * 85 = 850. New average = (3000 + 850) / 50 = 77.
Q. In a group of 4 friends, the average age is 25 years. If one friend leaves and the average age becomes 26 years, what is the age of the friend who left?
A.
24
B.
25
C.
26
D.
27
Solution
Total age of 4 friends = 4 * 25 = 100 years. New total age for 3 friends = 3 * 26 = 78 years. Age of friend who left = 100 - 78 = 22 years.
