Exercise: Average
Questions for: Average Calculation
A student took five quizzes in a course. Their scores were 75, 80, 85, 90, and 100.
What was the student's average score across these five quizzes?
A: 85
B: 86
C: 87.5
D: 88.75
Answer: B
1. Sum all the scores: 75 + 80 + 85 + 90 + 100 = 430.
2. Count the total number of quizzes: There are 5 quizzes.
3. Divide the total sum of scores by the number of quizzes to find the average: 430 / 5 = 86.
Why others are wrong:
A — This is the median score (the middle value when scores are ordered), not the average (mean).
C — This is the average of only the highest and lowest scores (75+100)/2 = 87.5, not all five scores.
D — This is the average calculated by summing only the four highest scores (80+85+90+100 = 355) and dividing by 4, incorrectly omitting the lowest score.
A training academy conducted a survey on employee satisfaction across two departments. Department X has 40 employees, and their average satisfaction rating (on a scale of 1-100) was 70. Department Y has 60 employees, and their average satisfaction rating was 80.
What is the combined average satisfaction rating for all employees surveyed across both departments?
A: 74.0
B: 75.0
C: 76.0
D: 77.0
Answer: C
1. Calculate the total satisfaction points for Department X: 40 employees * 70 points/employee = 2800 points.
2. Calculate the total satisfaction points for Department Y: 60 employees * 80 points/employee = 4800 points.
3. Sum the total satisfaction points from both departments: 2800 + 4800 = 7600 points.
4. Sum the total number of employees from both departments: 40 + 60 = 100 employees.
5. Divide the total satisfaction points by the total number of employees to find the combined average: 7600 / 100 = 76.0.
Why others are wrong:
A — This option results from incorrectly applying inverse weighting (weighting Department X's average by 60 and Department Y's by 40).
B — This is the simple arithmetic average of the two departmental average scores (70 + 80) / 2, ignoring the differing number of employees in each department.
D — This indicates a calculation error, such as miscalculating the total points or total employees.
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A class of 20 students achieved an average score of 75 on a recent mathematics examination. Another class, comprising 30 students, achieved an average score of 80 on the same examination.
What is the average score of all students from both classes combined?
A: 77
B: 77.5
C: 78
D: 79
Answer: C
Step 1: Calculate the total score for the first class.
Total score (Class 1) = Number of students × Average score = 20 × 75 = 1500
Step 2: Calculate the total score for the second class.
Total score (Class 2) = Number of students × Average score = 30 × 80 = 2400
Step 3: Calculate the combined total score for both classes.
Combined total score = Total score (Class 1) + Total score (Class 2) = 1500 + 2400 = 3900
Step 4: Calculate the total number of students in both classes.
Total students = Students (Class 1) + Students (Class 2) = 20 + 30 = 50
Step 5: Divide the combined total score by the total number of students to find the combined average.
Combined average score = Combined total score / Total students = 3900 / 50 = 78
Why others are wrong:
A — This likely results from incorrectly weighting the averages, for example, by swapping the number of students for each class in the calculation.
B — This is the simple average of the two average scores (75 + 80) / 2, which incorrectly ignores the different number of students in each class.
D — This indicates a calculation error in summing the total scores or dividing by the total number of students.
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A small company tracks its daily customer service inquiries. For the first 3 days of a week, the average number of inquiries was 40. For the remaining 4 days of the week, the average number of inquiries was 54.
What was the average number of inquiries per day for the entire 7-day week?
A: 47
B: 48
C: 56
D: 42
Answer: B
1. Calculate the total inquiries for the first 3 days: 3 days * 40 inquiries/day = 120 inquiries.
2. Calculate the total inquiries for the remaining 4 days: 4 days * 54 inquiries/day = 216 inquiries.
3. Calculate the total inquiries for the entire 7-day week: 120 + 216 = 336 inquiries.
4. Calculate the average inquiries per day for the week: Total inquiries / Total days = 336 / 7 = 48 inquiries/day.
Why others are wrong:
A — This option is the simple average of the two given averages (40 + 54) / 2, incorrectly ignoring the different number of days.
C — This option would result if the total inquiries (336) were incorrectly divided by 6 days instead of 7.
D — This option would result if the total inquiries (336) were incorrectly divided by 8 days instead of 7.
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A company comprises three departments. Department X has 20 employees, each producing an average of 15 units per day. Department Y has 30 employees, with an average daily production of 10 units per employee. Department Z has 50 employees, averaging 8 units per employee per day.
What is the overall average daily production per employee for the entire company?
A: 10
B: 11
C: 9.5
D: 9.8
Answer: A
Calculate total production for Department X: 20 employees * 15 units/employee = 300 units.
Calculate total production for Department Y: 30 employees * 10 units/employee = 300 units.
Calculate total production for Department Z: 50 employees * 8 units/employee = 400 units.
Sum the total productions: 300 + 300 + 400 = 1000 units.
Sum the total number of employees: 20 + 30 + 50 = 100 employees.
Divide the total production by the total employees: 1000 units / 100 employees = 10 units/employee.
Why others are wrong:
B — This option is the simple average of the departmental averages (15+10+8)/3 = 11, incorrectly ignoring the different number of employees in each department.
C — This option would result from an error such as miscalculating Department Z's total production (e.g., 50 employees * 7 units/employee = 350 units, leading to (300+300+350)/100 = 9.5).
D — This option would result from a different calculation error, such as miscalculating Department X's total production (e.g., 20 employees * 14 units/employee = 280 units, leading to (280+300+400)/100 = 9.8).
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