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Average Based Data Interpretation Quiz 1 (10 MCQs)

Q: What is the arithmetic mean in the context of average-based data interpretation?

The arithmetic mean, or average, is calculated by summing all the values in a data set and then dividing by the number of values. It provides a central value that represents the typical value in the data set.

Q: How can average monthly expenses be calculated?

To calculate average monthly expenses, sum up all the expenses for a given period and then divide by the number of months in that period. This gives you the average amount spent per month.

Q: What is the significance of the average score in cricket?

The average score in cricket is a measure of a batsman's performance, calculated by dividing the total runs scored by the number of times they have been dismissed. It helps in assessing the consistency and effectiveness of the batsman.

Q: How do you calculate the difference between the highest and lowest values in a data set?

To find the difference between the highest and lowest values in a data set, subtract the lowest value from the highest value. This difference is known as the range and provides insight into the spread of the data.

Q: What is the purpose of numerical computation in data interpretation?

Numerical computation in data interpretation involves performing calculations to derive meaningful insights from data. It helps in understanding trends, patterns, and relationships within the data set.

This set of multiple-choice questions evaluates skills in arithmetic mean, sum and divide, average calculation, and data interpretation. Concepts include annual expenses conversion, average monthly expenses, cricket scores, and numerical reasoning. Questions test the ability to compute averages, interpret data sets, and understand the impact of numerical manipulations.

Quiz Instructions

Select an option to see the correct answer instantly.

1. The Chins used records of their past expenditures to complete their budget sheet for the upcoming year. If their average monthly living expenses are $ 848, their fixed monthly expenses average $ 1,305, and their annual expenses are $ 3,816 what amount should they expect to spend monthly?

Correct Answer: Correct answer is: (C) $ 2,471.

Exam Relevance: GMAT, GRE, SAT, ACT

Difficulty: Moderate

Concept notes: To find the expected monthly spending, we need to sum the average monthly living expenses, the average fixed monthly expenses, and the average monthly portion of the annual expenses.

Common Mistakes: A common mistake is to overlook the need to convert the annual expenses into a monthly average before summing all the expenses.

Explanations: 1. The average monthly living expenses are $848. 2. The average fixed monthly expenses are $1,305. 3. The annual expenses are $3,816, which need to be converted to a monthly average: $3,816 / 12 = $318. 4. Sum the monthly expenses: $848 + $1,305 + $318 = $2,471. Thus, the Chins should expect to spend $2,471 monthly.

Option Analysis:

Option A: $318 is the monthly portion of the annual expenses, not the total monthly spending.
Option B: $497 is not a relevant sum of the given expenses.
Option C: $2,471 is the correct total monthly spending.
Option D: $5,969 is not a relevant sum of the given expenses.

2. The marks obtained by 5 students are 21, 27, 19, 26, 32. Later on 5 grace marks are added to each student. What are the average marks of the revised marks of the students?

Correct Answer: Correct answer is: (B) 30.

Exam Relevance: GMAT, GRE, SAT, ACT

Difficulty: Easy

Concept notes: The average of a set of numbers is the sum of the numbers divided by the count of the numbers. When a constant is added to each number in the set, the average also increases by that constant.

Common Mistakes: A common mistake is to recalculate the average from scratch after adding the grace marks, instead of simply adding the grace marks to the original average.

Explanations: 1. Calculate the original average of the marks: \[ \text{Original average} = \frac{21 + 27 + 19 + 26 + 32}{5} = \frac{125}{5} = 25 \] 2. Add the grace marks to the original average: \[ \text{Revised average} = 25 + 5 = 30 \]

Option Analysis:

Option A: 35. This is incorrect because the grace marks added to the original average should be 5, not 10.
Option B: 30. This is correct as the original average of 25 plus the 5 grace marks equals 30.
Option C: 25. This is incorrect because it does not account for the added grace marks.
Option D: 20. This is incorrect because it is less than the original average, which is not possible after adding grace marks.

3. Alfonso plays basketball on a team. He has played three games so far. In the first game, he scored 10 points. In the second game, he scored 16 points. In the third game, he scored 7 points. What is Alfonso's average points per game?

Correct Answer: Correct answer is: (C) 11 Points.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: The average points per game is calculated by summing the total points scored and dividing by the number of games played.

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

Explanations: To find Alfonso's average points per game, we first sum the points scored in each game: 10 (first game) + 16 (second game) + 7 (third game) = 33 points. Next, we divide the total points by the number of games played: 33 points / 3 games = 11 points per game. Thus, Alfonso's average points per game is 11 points.

Option Analysis:

Option A: 9 Points. This is incorrect because the sum of the points divided by the number of games is not 9.
Option B: 10 Points. This is incorrect because the sum of the points divided by the number of games is not 10.
Option C: 11 Points. This is correct because the sum of the points divided by the number of games is 11.
Option D: None of above. This is incorrect because 11 points is the correct average.

4. Virat Kohli scored 6,3,1,2,6,3 in a inning, and MS Dhoni scored 2,5,6,4,2,1 in a inning. Find the average score of both the players and tell who won the match?

Correct Answer: Correct answer is: (A) Virat Kohli.

Exam Relevance: GMAT, GRE, CAT, SAT

Difficulty: Easy

Concept notes: To find the average score of each player, sum their scores and divide by the number of innings.

Common Mistakes: A common mistake is to confuse the total score with the average score.

Explanations: First, calculate the total score for Virat Kohli: 6 + 3 + 1 + 2 + 6 + 3 = 21 Next, calculate the average score for Virat Kohli: 21 / 6 = 3.5 Now, calculate the total score for MS Dhoni: 2 + 5 + 6 + 4 + 2 + 1 = 20 Next, calculate the average score for MS Dhoni: 20 / 6 ≈ 3.33 Since 3.5 (Virat Kohli's average) is greater than 3.33 (MS Dhoni's average), Virat Kohli has the higher average score.

Option Analysis:

Option A: Correct. Virat Kohli has a higher average score.
Option B: Incorrect. MS Dhoni has a lower average score.

5. What is the difference between the average scores of Australia and England?

Correct Answer: Correct answer is: (A) 18.2.

Exam Relevance: CAT, GMAT, GRE, SAT

Difficulty: Moderate

Concept notes: The question requires calculating the difference between the average scores of two teams, Australia and England. This involves understanding how to compute and compare averages.

Common Mistakes: A common mistake could be misinterpreting the data or incorrectly calculating the average scores, leading to an incorrect difference.

Explanations: To find the difference between the average scores of Australia and England, we need to follow these steps: 1. Calculate the average score for Australia. 2. Calculate the average score for England. 3. Subtract the average score of England from the average score of Australia. Let's assume the scores for Australia are $ A_1, A_2, \ldots, A_n $ and the scores for England are $ E_1, E_2, \ldots, E_m $. The average score for Australia is: \[ \text{Average}_{\text{Australia}} = \frac{A_1 + A_2 + \ldots + A_n}{n} \] The average score for England is: \[ \text{Average}_{\text{England}} = \frac{E_1 + E_2 + \ldots + E_m}{m} \] The difference between the average scores is: \[ \text{Difference} = \text{Average}_{\text{Australia}} - \text{Average}_{\text{England}} \] Given that the correct answer is 18.2, we can infer that the calculated difference between the average scores of Australia and England is 18.2.

Option Analysis:

Option A: Correct. The difference between the average scores of Australia and England is 18.2.
Option B: Incorrect. The difference is not 18.6.
Option C: Incorrect. The difference is not 18.5.
Option D: Incorrect. The difference is not 18.4.

6. The average (arithmetic mean) of 4 numbers is greater than 11.5 and less than 14.5. Which of the following could NOT be the sum of these four numbers?

Correct Answer: Correct answer is: (C) 59.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The average of four numbers is the sum of the numbers divided by 4. The problem states that the average is greater than 11.5 and less than 14.5. This means the sum of the four numbers must be greater than $11.5 \times 4 = 46$ and less than $14.5 \times 4 = 58$.

Common Mistakes: A common mistake is to misinterpret the range for the sum of the numbers. Students might incorrectly calculate the range for the average and not multiply by 4 to find the range for the sum.

Explanations: The average of the four numbers is given to be greater than 11.5 and less than 14.5. To find the range for the sum of these four numbers, we multiply the average range by 4: \[ 11.5 \times 4 = 46 \] \[ 14.5 \times 4 = 58 \] Thus, the sum of the four numbers must be greater than 46 and less than 58. The only option that does not fall within this range is 59.

Option Analysis:

Option A: 47 is within the range (46 < 47 < 58).
Option B: 49 is within the range (46 < 49 < 58).
Option C: 59 is not within the range (59 > 58).
Option D: 55 is within the range (46 < 55 < 58).
Option E: 57 is within the range (46 < 57 < 58).

7. Compare the two data sets: Set A (2, 4, 6) and Set B (1, 3, 5). Which set has a higher average?

Correct Answer: Correct answer is: (A) Set A has a higher average.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: The average of a data set is calculated by summing all the values and dividing by the number of values.

Common Mistakes: A common mistake is to assume that the set with larger numbers will always have a higher average without performing the calculation.

Explanations: To find the average of Set A (2, 4, 6): 1. Sum the values: 2 + 4 + 6 = 12 2. Divide by the number of values: 12 / 3 = 4 To find the average of Set B (1, 3, 5): 1. Sum the values: 1 + 3 + 5 = 9 2. Divide by the number of values: 9 / 3 = 3 Since 4 (average of Set A) is greater than 3 (average of Set B), Set A has a higher average.

Option Analysis:

Option A: Correct. Set A has a higher average.
Option B: Incorrect. The averages are not the same.
Option C: Incorrect. Set B does not have a higher average.
Option D: Incorrect. Both sets have an average.

8. The Blue Star Taxi Company has locations in several cities. Today in New York City, the company transported 1,667 people. In Washington DC, it transported 2,318 people. In Austin, it transported 1,542. In Miami, it transported 1,823 people. How many people did Blue Star Taxi Company transport, on average, in these cities?

Correct Answer: Correct answer is: (C) 1,837.5.

Exam Relevance: GMAT, GRE, SAT, ACT

Difficulty: Moderate

Concept notes: To find the average number of people transported by the Blue Star Taxi Company across the cities, we need to sum the number of people transported in each city and then divide by the number of cities.

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

Explanations: To find the average number of people transported, we first sum the number of people transported in each city: 1,667 (New York City) + 2,318 (Washington DC) + 1,542 (Austin) + 1,823 (Miami) = 7,350. Next, we divide the total number of people transported by the number of cities, which is 4: 7,350 / 4 = 1,837.5. Thus, the average number of people transported by the Blue Star Taxi Company in these cities is 1,837.5.

Option Analysis:

Option A: Incorrect. The sum and division were likely miscalculated.
Option B: Incorrect. The sum and division were likely miscalculated.
Option C: Correct. The sum and division were correctly calculated.
Option D: Incorrect. The sum and division were likely miscalculated.
Option E: Incorrect. The sum and division were likely miscalculated.

9. A set of 6 numbers had an average of 48. One number was removed and now the average of the remaining numbers is 49. Which number was removed?

Correct Answer: Correct answer is: (C) 43.

Exam Relevance: GMAT, GRE, SAT, ACT

Difficulty: Moderate

Concept notes: The concept involves understanding how the removal of a number affects the average of a set of numbers.

Common Mistakes: A common mistake is to assume that the removed number is the same as the original average, which is not necessarily true.

Explanations: 1. The original average of 6 numbers is 48. Therefore, the sum of these 6 numbers is $6 \times 48 = 288$. 2. After removing one number, the average of the remaining 5 numbers is 49. Therefore, the sum of these 5 numbers is $5 \times 49 = 245$. 3. The number removed is the difference between the original sum and the new sum: $288 - 245 = 43$. Thus, the number removed is 43.

Option Analysis:

Option A: 48 is incorrect because the removed number is not necessarily the original average.
Option B: 44 is incorrect because it does not match the calculated difference.
Option C: 43 is correct as it matches the calculated difference.
Option D: 41 is incorrect because it does not match the calculated difference.

10. You are a chemist in a lab. You are currently testing several chemical solutions for various properties. You have 6 test tubes, which contain the following amounts of solution: 68 mL, 43 mL, 56 mL, 77 mL, 39 mL, and 83 mL. What is the average amount of solution in the test tubes?

Correct Answer: Correct answer is: (D) 61.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The average (mean) of a set of numbers is calculated by summing all the numbers and then dividing by the count of numbers.

Common Mistakes: A common mistake is to confuse the average with the median or mode, or to miscalculate the sum or the count of the numbers.

Explanations: To find the average amount of solution in the test tubes, we first sum the amounts of solution in each test tube: 68 + 43 + 56 + 77 + 39 + 83 = 366 mL. Next, we divide the total sum by the number of test tubes, which is 6: 366 ÷ 6 = 61 mL. Thus, the average amount of solution in the test tubes is 61 mL.

Option Analysis:

Option A: 39 is incorrect because it is the smallest amount in the set and not the average.
Option B: 46 is incorrect because it is less than the average of the set.
Option C: 56 is incorrect because it is one of the amounts in the set but not the average.
Option D: 61 is correct because it is the calculated average of the set.
Option E: 62 is incorrect because it is slightly higher than the calculated average.

Frequently Asked Questions

What is the arithmetic mean in the context of average-based data interpretation?

The arithmetic mean, or average, is calculated by summing all the values in a data set and then dividing by the number of values. It provides a central value that represents the typical value in the data set.

How can average monthly expenses be calculated?

To calculate average monthly expenses, sum up all the expenses for a given period and then divide by the number of months in that period. This gives you the average amount spent per month.

What is the significance of the average score in cricket?

The average score in cricket is a measure of a batsman's performance, calculated by dividing the total runs scored by the number of times they have been dismissed. It helps in assessing the consistency and effectiveness of the batsman.

How do you calculate the difference between the highest and lowest values in a data set?

To find the difference between the highest and lowest values in a data set, subtract the lowest value from the highest value. This difference is known as the range and provides insight into the spread of the data.

What is the purpose of numerical computation in data interpretation?

Numerical computation in data interpretation involves performing calculations to derive meaningful insights from data. It helps in understanding trends, patterns, and relationships within the data set.

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