The concept of "Average" is a fundamental topic in mathematics that plays a crucial role in various exams. Understanding averages not only helps in solving mathematical problems but also enhances analytical skills. Practicing MCQs and objective questions on averages is essential for students aiming to excel in their exams. By focusing on important questions and practice questions, students can significantly improve their performance in both school and competitive exams.
What You Will Practise Here
Definition and types of averages: Mean, Median, and Mode
Formulas for calculating averages
Applications of averages in real-life scenarios
Solving problems involving weighted averages
Understanding the impact of outliers on averages
Comparison of averages in different data sets
Practice with Average MCQ questions and objective questions with answers
Exam Relevance
The topic of averages is frequently tested in various examinations such as CBSE, State Boards, NEET, and JEE. Students can expect questions that require them to calculate the mean, median, or mode of given data sets. Common question patterns include direct calculations, word problems, and scenarios that require the application of averages in practical contexts. Mastering this topic is vital for achieving high scores in both school assessments and competitive exams.
Common Mistakes Students Make
Confusing mean with median and mode
Overlooking the effect of outliers on the average
Misapplying formulas in weighted average problems
Failing to read the question carefully, leading to incorrect interpretations
Neglecting to check calculations for accuracy
FAQs
Question: What is the difference between mean, median, and mode? Answer: Mean is the average of all numbers, median is the middle value when numbers are arranged in order, and mode is the number that appears most frequently.
Question: How do outliers affect the average? Answer: Outliers can skew the mean significantly, making it higher or lower than the typical values in the data set.
Question: Why is it important to practice Average MCQ questions? Answer: Practicing MCQs helps reinforce understanding, improves problem-solving speed, and prepares students for the types of questions they will encounter in exams.
Start your journey towards mastering averages today! Solve practice MCQs and test your understanding to ensure you are well-prepared for your upcoming exams.
Q. In a class of 30 students, the average age is 15 years. If 5 new students aged 16 years join, what will be the new average age?
A.
15.5
B.
15.8
C.
16
D.
16.2
Solution
Total age of 30 students = 30 * 15 = 450. Total age of 5 new students = 5 * 16 = 80. New total age = 450 + 80 = 530. New average = 530 / 35 = 15.14.
Q. In a class of 40 students, the average height is 150 cm. If 10 new students with an average height of 160 cm join, what is the new average height?
A.
152
B.
154
C.
156
D.
158
Solution
Total height of 40 students = 40 * 150 = 6000 cm. Total height of 10 new students = 10 * 160 = 1600 cm. New total height = 6000 + 1600 = 7600 cm. New average = 7600 / 50 = 152 cm.
Q. In a class of 40 students, the average height is 150 cm. If 10 new students with an average height of 160 cm join, what will be the new average height?
A.
152
B.
154
C.
156
D.
158
Solution
The total height of the original students is 40 * 150 = 6000 cm. The total height of the new students is 10 * 160 = 1600 cm. The new total height is 6000 + 1600 = 7600 cm. The new average height is 7600 / 50 = 152 cm.
Q. In a group of 10 people, the average age is 30 years. If two new members join the group and the average age becomes 32 years, what is the average age of the new members?
A.
34
B.
36
C.
38
D.
40
Solution
Total age of 10 people = 10 * 30 = 300. New total age = 12 * 32 = 384. Age of new members = 384 - 300 = 84. Average age of new members = 84 / 2 = 42.
Q. In a group of 5 friends, the average age is 24 years. If the age of one friend is 30 years, what is the average age of the remaining friends?
A.
22
B.
23
C.
24
D.
25
Solution
The total age of the 5 friends is 5 * 24 = 120. The total age of the remaining 4 friends is 120 - 30 = 90. The average age of the remaining friends is 90 / 4 = 22.5.
Q. In a group of 5 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 5 friends = 5 * 25 = 125. Total age of 4 friends = 4 * 26 = 104. Age of friend who left = 125 - 104 = 21.
Q. In a group of 6 friends, the average age is 22 years. If one friend leaves and the average age becomes 23 years, what is the age of the friend who left?
A.
20
B.
22
C.
24
D.
26
Solution
Total age of 6 friends = 6 * 22 = 132. Total age of 5 friends = 5 * 23 = 115. Age of friend who left = 132 - 115 = 17.
Q. In a race, the average speed of a runner is 10 km/h. If he runs for 2 hours and then increases his speed to 15 km/h for the next 3 hours, what is his average speed for the entire race?
A.
12
B.
13
C.
14
D.
15
Solution
Total distance = (10 * 2) + (15 * 3) = 20 + 45 = 65 km. Total time = 2 + 3 = 5 hours. Average speed = 65 / 5 = 13 km/h.
Q. The average age of a group of 10 people is 30 years. If two new members join the group, increasing the average age to 32 years, what is the average age of the new members?
A.
36
B.
38
C.
40
D.
42
Solution
Total age of 10 people = 10 * 30 = 300. New total age = 12 * 32 = 384. Age of new members = 384 - 300 = 84. Average age of new members = 84 / 2 = 42.
Q. The average age of a group of 5 people is 30 years. If a new person joins the group, making the average age 32 years, what is the age of the new person?
A.
35
B.
40
C.
45
D.
50
Solution
Total age of 5 people = 5 * 30 = 150. New total age = 6 * 32 = 192. Age of new person = 192 - 150 = 42.
Q. The average of 10 numbers is 50. If one number is increased by 10, what will be the new average?
A.
50
B.
51
C.
52
D.
53
Solution
The total of the 10 numbers is 10 * 50 = 500. If one number is increased by 10, the new total becomes 500 + 10 = 510. The new average is 510 / 10 = 51.
Q. The average of 10 numbers is 50. If one number is replaced by 70, what will be the new average?
A.
50
B.
52
C.
54
D.
56
Solution
The sum of the 10 numbers is 10 * 50 = 500. Replacing one number with 70 gives a new sum of 500 - x + 70. The new average is (500 - x + 70) / 10. Since x is 50, the new average is (500 - 50 + 70) / 10 = 52.
Q. The average of 5 numbers is 40. If the largest number is 60, what is the average of the other four numbers?
A.
35
B.
40
C.
45
D.
50
Solution
The total of the 5 numbers is 5 * 40 = 200. The sum of the other four numbers is 200 - 60 = 140. The average of the other four numbers is 140 / 4 = 35.
