Q. A class has 30 students with an average score of 75. If 5 new students join with an average score of 80, what is the new average? (2023)
A.
76
B.
77
C.
78
D.
79
Solution
Total score of 30 students = 30 * 75 = 2250. Total score of 5 new students = 5 * 80 = 400. New total = 2250 + 400 = 2650. New average = 2650 / 35 = 76.43.
Q. A class has 30 students with an average score of 75. If a new student joins and the average becomes 76, what is the score of the new student? (2023)
A.
80
B.
85
C.
90
D.
95
Solution
Total score of 30 students = 30 * 75 = 2250. New total = 31 * 76 = 2356. Score of new student = 2356 - 2250 = 106.
Q. A class has an average score of 75. If one student scored 90, what is the average score of the remaining students if there are 20 students in total?
A.
74
B.
75
C.
76
D.
77
Solution
The total score of the class is 75 * 20 = 1500. Removing the student who scored 90 gives a new total of 1500 - 90 = 1410. The average of the remaining 19 students is 1410 / 19 = 74.21, which rounds to 74.
Q. A group of students has an average age of 20 years. If a new student aged 22 joins the group, what will be the new average age if there were originally 15 students?
A.
20.5
B.
20.6
C.
20.7
D.
20.8
Solution
The total age of the original group is 20 * 15 = 300. Adding the new student gives 300 + 22 = 322. The new average age is 322 / 16 = 20.125, which rounds to 20.6.
Q. A group of students has an average height of 150 cm. If one student leaves the group and the average height becomes 148 cm, what is the height of the student who left?
A.
152 cm
B.
154 cm
C.
156 cm
D.
158 cm
Solution
Let the number of students be n. Total height = 150n. After one leaves, total height = 148(n - 1). Setting the equations gives 150n - 148(n - 1) = height of student.
Q. A group of students has an average height of 160 cm. If one student with a height of 170 cm leaves, what will be the new average height if the group size was 10?
A.
158 cm
B.
159 cm
C.
160 cm
D.
161 cm
Solution
Total height = 160 * 10 = 1600 cm. New total = 1600 - 170 = 1430 cm. New average = 1430 / 9 = 158.89 cm, approximately 159 cm.
Q. A student scores 80, 90, and 70 in three subjects. If he wants to achieve an average of 85 after scoring in a fourth subject, what score does he need?
A.
90
B.
95
C.
100
D.
85
Solution
The current total score is 80 + 90 + 70 = 240. To achieve an average of 85 over 4 subjects, the total score must be 4 * 85 = 340. Therefore, the score needed in the fourth subject is 340 - 240 = 100.
The concept of "Mean" is a fundamental topic in mathematics that plays a crucial role in various exams. Understanding the mean helps students analyze data effectively and solve problems efficiently. Practicing MCQs and objective questions on this topic not only enhances conceptual clarity but also boosts confidence, ensuring better performance in exams. With the right practice questions, students can tackle important questions with ease and improve their overall exam preparation.
What You Will Practise Here
Definition and types of Mean: Arithmetic Mean, Geometric Mean, and Harmonic Mean
Formulas for calculating the Mean
Applications of Mean in real-life scenarios
Mean in grouped and ungrouped data
Comparison of Mean with Median and Mode
Solving problems involving Mean in different contexts
Diagrams and visual representations related to Mean
Exam Relevance
The topic of Mean is frequently tested in various educational boards, including CBSE and State Boards, as well as in competitive exams like NEET and JEE. Students can expect questions that require them to calculate the mean from a set of data or interpret data using the mean. Common question patterns include direct calculation, application-based problems, and comparative analysis with other statistical measures.
Common Mistakes Students Make
Confusing the Mean with Median and Mode, leading to incorrect answers.
Misapplying the formula for Mean in grouped data scenarios.
Overlooking the significance of outliers in data sets when calculating the Mean.
Failing to interpret the context of the problem, which can affect the choice of the mean type.
FAQs
Question: What is the formula for calculating the Mean? Answer: The formula for calculating the Mean is the sum of all values divided by the number of values.
Question: How does the Mean differ from Median and Mode? Answer: The Mean is the average of all values, while Median is the middle value, and Mode is the most frequently occurring value in a data set.
Start solving practice MCQs on Mean today to strengthen your understanding and excel in your exams. Your success is just a question away!
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