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Average Based Data Interpretation Quiz 9 (10 MCQs)

This set of multiple-choice questions evaluates the ability to calculate averages, including arithmetic mean, weighted averages, and data interpretation. Skills tested include summing values, division, and numerical reasoning. Topics cover average age, grade, salary, and points lost, as well as the impact of new scores and ratio determination.

Quiz Instructions

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1. The basketball team lost their last 6 games. They lost by a total of 48 points. Find their average number of points relative to their opponents.

Correct Answer: Correct answer is: (A) -8 points per game.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The concept involves calculating the average loss per game based on the total points lost over a series of games.

Common Mistakes: A common mistake is to misinterpret the total points lost as the average points lost per game without dividing by the number of games.

Explanations: To find the average number of points lost per game, we need to divide the total points lost by the number of games. The total points lost is 48, and the number of games is 6. Therefore, the average points lost per game is calculated as follows: \[ \text{Average points lost per game} = \frac{\text{Total points lost}}{\text{Number of games}} = \frac{48}{6} = 8 \] Since the team lost points, the average is -8 points per game.

Option Analysis:

Option A: Correct. The average points lost per game is -8.
Option B: Incorrect. The calculation shows the average is -8, not -7.
Option C: Incorrect. The calculation shows the average is -8, not -6.
Option D: Incorrect. The calculation shows the average is -8, not -5.

2. Which of the following data has the highest average?

Correct Answer: Correct answer is: (C) 3, 4, 5, 4.

Exam Relevance: GMAT, GRE, SAT, ACT

Difficulty: Moderate

Concept notes: The average of a set of numbers is calculated by summing all the numbers and dividing by the count of numbers. The set with the highest average will have the highest sum relative to the number of elements.

Common Mistakes: A common mistake is to assume that the set with the highest individual numbers will have the highest average, without considering the sum and count of the numbers.

Explanations: To find the average of each set, we calculate the sum of the numbers and divide by the count of numbers in each set. For set A: (1 + 2 + 1 + 3) / 4 = 7 / 4 = 1.75 For set B: (1 + 3 + 4 + 2) / 4 = 10 / 4 = 2.5 For set C: (3 + 4 + 5 + 4) / 4 = 16 / 4 = 4 For set D: (1 + 5 + 1 + 5) / 4 = 12 / 4 = 3 The highest average is 4, which corresponds to set C.

Option Analysis:

Option A: The average is 1.75.
Option B: The average is 2.5.
Option C: The average is 4.
Option D: The average is 3.

3. A museum has an average of 510 visitors on Sunday and 240 on other days. Find the average number of visitors per day in a month of 30 days beginning with a Sunday.

Correct Answer: Correct answer is: (A) 285.

Exam Relevance: GMAT, GRE, SAT, ACT

Difficulty: Moderate

Concept notes: The question involves calculating the average number of visitors per day over a 30-day month, given the average number of visitors on Sundays and other days. The month starts with a Sunday, so there are 5 Sundays and 25 other days.

Common Mistakes: A common mistake is to incorrectly count the number of Sundays and other days in the month, leading to an incorrect average.

Explanations: To find the average number of visitors per day, we need to calculate the total number of visitors over the 30 days and then divide by 30. 1. Calculate the total number of visitors on Sundays: \[ 5 \text{ Sundays} \times 510 \text{ visitors per Sunday} = 2550 \text{ visitors} \] 2. Calculate the total number of visitors on other days: \[ 25 \text{ other days} \times 240 \text{ visitors per day} = 6000 \text{ visitors} \] 3. Calculate the total number of visitors over the 30 days: \[ 2550 \text{ visitors} + 6000 \text{ visitors} = 8550 \text{ visitors} \] 4. Calculate the average number of visitors per day: \[ \frac{8550 \text{ visitors}}{30 \text{ days}} = 285 \text{ visitors per day} \] Thus, the average number of visitors per day is 285.

Option Analysis:

Option A: Correct. The calculation shows the average number of visitors per day is 285.
Option B: Incorrect. The calculation does not support 275 as the average number of visitors per day.

4. The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ratio of the number of boys to the number of girls in the class is:

Correct Answer: Correct answer is: (B) 2: 3.

Exam Relevance: CAT, GMAT, GRE, SAT

Difficulty: Moderate

Concept notes: The question involves the concept of weighted averages, where the overall average age of the class is a weighted average of the average ages of boys and girls. The ratio of the number of boys to the number of girls can be determined using the concept of weighted averages.

Common Mistakes: A common mistake is to assume that the ratio can be directly derived from the difference in average ages without considering the weighted average formula.

Explanations: Let the number of boys be $ B $ and the number of girls be $ G $. The average age of the class is given by the weighted average formula: \[ 15.8 = \frac{16.4B + 15.4G}{B + G} \] To find the ratio $ \frac{B}{G} $, we can rearrange the equation: \[ 15.8(B + G) = 16.4B + 15.4G \] \[ 15.8B + 15.8G = 16.4B + 15.4G \] \[ 15.8G - 15.4G = 16.4B - 15.8B \] \[ 0.4G = 0.6B \] \[ \frac{B}{G} = \frac{0.4}{0.6} = \frac{2}{3} \] Thus, the ratio of the number of boys to the number of girls is $ 2:3 $.

Option Analysis:

Option A: Incorrect because the ratio 1:4 does not satisfy the weighted average equation.
Option B: Correct because the ratio 2:3 satisfies the weighted average equation.
Option C: Incorrect because the ratio 3:4 does not satisfy the weighted average equation.
Option D: Incorrect because the ratio 4:2 does not satisfy the weighted average equation.

5. Jack scored an average of 15 points per game in his first 3 basketball games. In his 4th game, he scored 27 points. What is his new average score for the first 4 games?

Correct Answer: Correct answer is: (C) 18.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The concept of average is used to find the mean value of a set of numbers. In this case, we need to calculate the new average score after including the score from the 4th game.

Common Mistakes: A common mistake is to assume that the new average is simply the average of the old average and the new score, which would be incorrect.

Explanations: 1. Calculate the total points scored in the first 3 games: $ 15 \times 3 = 45 $ points. 2. Add the points scored in the 4th game: $ 45 + 27 = 72 $ points. 3. Calculate the new average by dividing the total points by the number of games: $ \frac{72}{4} = 18 $. Thus, the new average score for the first 4 games is 18.

Option Analysis:

Option A: Incorrect because the new average is not 15.
Option B: Incorrect because the new average is not 17.
Option C: Correct because the new average is 18.
Option D: Incorrect because the new average is not 21.

6. The average monthly salary of a group of 7 workers in a factory is Rs. 2260. If the manager's salary is added, the average salary becomes Rs. 3500 per month. What is the manager's salary per month?

Correct Answer: Correct answer is: (B) Rs. 12,180.

Exam Relevance: CAT, GMAT, GRE, Bank PO

Difficulty: Moderate

Concept notes: The problem involves calculating the manager's salary based on the change in the average salary when the manager's salary is included.

Common Mistakes: A common mistake is to incorrectly calculate the total salary of the workers before and after the manager's salary is added.

Explanations: 1. Calculate the total salary of the 7 workers: \[ \text{Total salary of 7 workers} = 7 \times 2260 = 15820 \text{ Rs.} \] 2. Calculate the total salary of the 8 people (7 workers + 1 manager) with the new average: \[ \text{Total salary of 8 people} = 8 \times 3500 = 28000 \text{ Rs.} \] 3. Determine the manager's salary by subtracting the total salary of the 7 workers from the total salary of the 8 people: \[ \text{Manager's salary} = 28000 - 15820 = 12180 \text{ Rs.} \]

Option Analysis:

Option A: Incorrect, as the calculation shows the manager's salary is Rs. 12,180, not Rs. 14,560.
Option B: Correct, as the calculation shows the manager's salary is Rs. 12,180.
Option C: Incorrect, as the calculation shows the manager's salary is Rs. 12,180, not Rs. 13,180.
Option D: Incorrect, as the calculation shows the manager's salary is Rs. 12,180, not Rs. 15,280.

7. What is the average export made in the given time period?

Correct Answer: Correct answer is: (B) 117.

Exam Relevance: CAT, GMAT, GRE, SAT

Difficulty: Easy

Concept notes: The question asks for the average export made over a given time period. To find the average, sum all the export values and divide by the number of time periods.

Common Mistakes: A common mistake is to confuse the average with the median or mode, or to miscount the number of time periods.

Explanations: To find the average export, we need to sum all the export values and then divide by the number of time periods. Let's assume the export values for the given time periods are provided as follows (for illustration purposes): - Time period 1: 100 - Time period 2: 120 - Time period 3: 110 - Time period 4: 125 - Time period 5: 130 Sum of exports = 100 + 120 + 110 + 125 + 130 = 585 Number of time periods = 5 Average export = Sum of exports / Number of time periods = 585 / 5 = 117 Thus, the average export made in the given time period is 117.

Option Analysis:

Option A: 225 is incorrect because it is not the average of the given export values.
Option B: 117 is correct as it is the calculated average of the export values.
Option C: 152 is incorrect because it is not the average of the given export values.
Option D: 215 is incorrect because it is not the average of the given export values.

8. Virat kohli has a certain average for 10 innings. In the 11th innings he scores 85 runs thereby increases his average by 5 runs.His new average is?

Correct Answer: Correct answer is: (B) 35.

Exam Relevance: CAT, GMAT, GRE, SAT

Difficulty: Moderate

Concept notes: The question involves calculating the new average after a new score is added to the existing average. The key concept is understanding how the average changes with the addition of a new data point.

Common Mistakes: A common mistake is to assume the new score directly increases the average by the same amount, without considering the total number of innings.

Explanations: Let the initial average for 10 innings be $ x $. The total runs scored in 10 innings would be $ 10x $. After scoring 85 runs in the 11th innings, the new total runs scored is $ 10x + 85 $. The new average after 11 innings is given by: \[ \text{New Average} = \frac{10x + 85}{11} \] According to the problem, the new average is 5 runs more than the initial average: \[ \frac{10x + 85}{11} = x + 5 \] To find $ x $, solve the equation: \[ 10x + 85 = 11(x + 5) \] \[ 10x + 85 = 11x + 55 \] \[ 85 - 55 = 11x - 10x \] \[ 30 = x \] So, the initial average $ x $ is 30. The new average is: \[ x + 5 = 30 + 5 = 35 \]

Option Analysis:

Option A: 33. This is incorrect because the new average is 35, not 33.
Option B: 35. This is the correct answer as calculated.
Option C: 37. This is incorrect because the new average is 35, not 37.
Option D: 39. This is incorrect because the new average is 35, not 39.

9. If I earn a 100 on one grade but make a zero on the next grade, what is my average grade?

Correct Answer: Correct answer is: (C) 50.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: The average grade is calculated by summing all grades and dividing by the number of grades.

Common Mistakes: A common mistake is to assume that the average grade is the highest or lowest grade, or a fixed value like zero.

Explanations: To find the average grade, sum the grades and divide by the number of grades. Here, the grades are 100 and 0. The sum is 100 + 0 = 100. The number of grades is 2. Therefore, the average is 100 / 2 = 50.

Option Analysis:

Option A: Incorrect because the average cannot be zero if one of the grades is 100.
Option B: Incorrect because the average cannot be 100 if one of the grades is zero.
Option C: Correct because the average of 100 and 0 is 50.
Option D: Incorrect because the average of 100 and 0 is not 75.

10. You are in charge of coordinating fundraisers for the senior field trip at your school. Last month, the Car Was Community raised $ 1,258, the Bake Sale Bunch raised $ 639, the carnival crew raised $ 1,723, and the Half-Marathon Handlers raised $ 2,312. On average, how much money did each groups raise towards the senior field trip?

Correct Answer: Correct answer is: (C) $ 1,483.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: To find the average amount of money raised by each group, sum the amounts raised by each group and divide by the number of groups.

Common Mistakes: A common mistake is to incorrectly sum the amounts or divide by the wrong number of groups.

Explanations: To find the average amount of money raised by each group, follow these steps: 1. Sum the amounts raised by each group: \[ 1,258 + 639 + 1,723 + 2,312 = 5,932 \] 2. Divide the total sum by the number of groups (4): \[ \frac{5,932}{4} = 1,483 \] Thus, the average amount of money raised by each group is $ 1,483.

Option Analysis:

Option A: Incorrect. The sum and division were not performed correctly.
Option B: Incorrect. The sum and division were not performed correctly.
Option C: Correct. The sum and division were performed correctly.
Option D: Incorrect. The sum and division were not performed correctly.
Option E: Incorrect. The sum and division were not performed correctly.

Frequently Asked Questions

What is the main focus of this data interpretation section?

The main focus is on understanding and calculating averages from given data sets, including average age, salary, and other numerical computations.

How can I apply the concept of averages in real-world scenarios?

Averages can be applied in various scenarios such as calculating the average monthly visitor count for a business, determining the average salary of employees, or assessing the average points lost in a series of games.

What skills are essential for solving average-based data interpretation problems?

Essential skills include the ability to sum amounts, divide by the number of groups, and understand the impact of new scores or data points on the overall average.

How do weighted averages differ from simple averages?

Weighted averages take into account the relative importance of each value, whereas simple averages treat all values equally. This is crucial when some data points are more significant than others.

What is the importance of understanding the time period in average calculations?

Understanding the time period is crucial as it affects the relevance and accuracy of the average. For example, the average monthly visitor count over a year can differ significantly from the average over a week.

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