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. A bag contains 5 red balls and 3 blue balls. If the average weight of the red balls is 200 grams and the blue balls is 150 grams, what is the average weight of all the balls?
A.
175
B.
180
C.
185
D.
190
Solution
Total weight of red balls = 5 * 200 = 1000 grams. Total weight of blue balls = 3 * 150 = 450 grams. Total weight = 1000 + 450 = 1450 grams. Average weight = 1450 / 8 = 181.25.
Q. A class has 20 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?
A.
152
B.
154
C.
156
D.
158
Solution
Total height of 20 students = 20 * 150 = 3000. Total height of 5 new students = 5 * 160 = 800. New total = 3000 + 800 = 3800. New average = 3800 / 25 = 152.
Q. A class has 20 students with an average height of 150 cm. If one student leaves and the average height becomes 148 cm, what is the height of the student who left?
A.
160 cm
B.
150 cm
C.
140 cm
D.
130 cm
Solution
Total height of 20 students = 20 * 150 = 3000 cm. Total height of 19 students = 19 * 148 = 2812 cm. Height of the student who left = 3000 - 2812 = 188 cm.
Q. A class has 30 students. If the average score of the class is 75 and one student scored 90, what will be the new average if that student is removed?
A.
74
B.
75
C.
76
D.
77
Solution
Total score = 30 * 75 = 2250. New total = 2250 - 90 = 2160. New average = 2160 / 29 = 74.48, approximately 74.
Q. A class has 30 students. If the average score of the class is 75 and one student scored 90, what is the average score of the remaining students?
A.
72
B.
74
C.
76
D.
78
Solution
Total score of 30 students = 30 * 75 = 2250. Total score of remaining 29 students = 2250 - 90 = 2160. Average of remaining = 2160 / 29 = 74.48, approximately 74.
Q. A class of 30 students has an average score of 75. If a new student joins and the average becomes 76, what is the score of the new student?
A.
80
B.
85
C.
90
D.
95
Solution
The total score of 30 students is 30 * 75 = 2250. After the new student joins, the total score becomes 31 * 76 = 2356. Therefore, the new student's score is 2356 - 2250 = 106.
Q. A company has 100 employees with an average salary of $5000. If 10 employees leave with an average salary of $6000, what is the new average salary?
A.
$4900
B.
$4950
C.
$5000
D.
$5050
Solution
Total salary of 100 employees = 100 * 5000 = $500000. Total salary of 10 employees leaving = 10 * 6000 = $60000. New total salary = 500000 - 60000 = $440000. New average = 440000 / 90 = $4888.89, which rounds to $4900.
Q. A family has 4 members with an average age of 25 years. If the youngest member is 10 years old, what will be the average age if the youngest member turns 20?
A.
26
B.
27
C.
28
D.
29
Solution
Total age of family = 4 * 25 = 100. New total age after youngest turns 20 = 100 - 10 + 20 = 110. New average = 110 / 4 = 27.5, approximately 27.
Q. A family has 4 members with an average age of 30 years. If a new member joins the family, making the average age 32 years, what is the age of the new member?
A.
32
B.
34
C.
36
D.
38
Solution
Total age of 4 members = 4 * 30 = 120. Total age of 5 members = 5 * 32 = 160. Age of new member = 160 - 120 = 40.
Q. A family has 4 members with an average age of 30 years. If a new member joins with an age of 40 years, what will be the new average age?
A.
30
B.
32
C.
34
D.
36
Solution
The total age of the family is 4 * 30 = 120 years. Adding a new member aged 40 gives a new total age of 120 + 40 = 160 years. The new average age is 160 / 5 = 32.
Q. A group of 6 people has an average weight of 70 kg. If one person weighing 80 kg leaves, what is the new average weight?
A.
68
B.
69
C.
70
D.
71
Solution
The total weight of the group is 6 * 70 = 420 kg. After the 80 kg person leaves, the total weight becomes 420 - 80 = 340 kg. The new average is 340 / 5 = 68 kg.
Q. A group of friends has an average age of 25 years. If one friend aged 30 leaves the group, what will be the new average age if the group had 5 members?
A.
24
B.
25
C.
26
D.
27
Solution
Total age = 25 * 5 = 125. New total age = 125 - 30 = 95. New average = 95 / 4 = 23.75.
Q. A group of friends has an average age of 25 years. If one friend leaves the group, the average age becomes 26 years. How old was the friend who left?
A.
24
B.
25
C.
26
D.
27
Solution
Let the number of friends be n. Total age = 25n. New total age = 26(n - 1). Therefore, 25n - 26(n - 1) = age of friend who left. Solving gives age = 27.
Q. A group of friends has an average age of 30 years. If a new friend aged 40 joins, what will be the new average age if there were originally 5 friends?
A.
31
B.
32
C.
33
D.
34
Solution
Total age = 5 * 30 = 150. New total = 150 + 40 = 190. New average = 190 / 6 = 31.67.
Q. A group of friends has an average age of 30 years. If one friend leaves who is 40 years old, what will be the new average age if the group has 5 members?
A.
28
B.
29
C.
30
D.
31
Solution
Total age of 5 friends = 5 * 30 = 150. New total = 150 - 40 = 110. New average = 110 / 4 = 27.5.
Q. A man earns Rs. 5000 in the first month, Rs. 6000 in the second month, and Rs. 7000 in the third month. What is his average monthly income over these three months?
A.
5500
B.
6000
C.
6500
D.
7000
Solution
Total income = 5000 + 6000 + 7000 = 18000. Average income = 18000 / 3 = 6000.
Q. A man has an average expenditure of $200 per month. If he spends $250 in the first month, what will be his average expenditure for the first two months?
A.
200
B.
225
C.
210
D.
220
Solution
Total expenditure for two months = 250 + 200 = 450. Average = 450 / 2 = 225.
