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Average Based Data Interpretation Quiz 11 (10 MCQs)

This set of multiple-choice questions evaluates skills in average calculation, arithmetic mean, and data interpretation. It covers concepts such as sum and divide, sum of numbers, and division by count. Students will practice interpreting data from bar graphs, calculating averages, and solving problems involving odd numbers and total income.

Quiz Instructions

Select an option to see the correct answer instantly.

1. As a banker, you are currently reviewing several small loan applications. Your clients are applying for loans of the following amounts: $ 2,440; $ 3,200; $ 2,570; $ 1,250; and $ 2,310. What is the average value of the loan amounts that you are currently reviewing?

Correct Answer: Correct answer is: (D) $ 2,354.

Exam Relevance: GMAT, GRE, SAT, ACT

Difficulty: Moderate

Concept notes: The average value 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 incorrectly sum the numbers or divide by the wrong count, leading to an incorrect average.

Explanations: To find the average value of the loan amounts, we first sum the amounts: \[ 2,440 + 3,200 + 2,570 + 1,250 + 2,310 = 11,770 \] Next, we divide the sum by the number of loan amounts, which is 5: \[ \frac{11,770}{5} = 2,354 \] Thus, the average value of the loan amounts is $ 2,354.

Option Analysis:

Option A: Incorrect, as the sum and division steps were likely miscalculated.
Option B: Incorrect, as the sum and division steps were likely miscalculated.
Option C: Incorrect, as the sum and division steps were likely miscalculated.
Option D: Correct, as the sum and division steps were correctly performed.
Option E: Incorrect, as the sum and division steps were likely miscalculated.

2. Average of five numbers is 27. If one number is excluded the average becomes 25.

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

Exam Relevance: GRE, GMAT, SAT, ACT

Difficulty: Moderate

Concept notes: The concept involves calculating the sum of numbers based on their average and then determining the excluded number.

Common Mistakes: A common mistake is to incorrectly calculate the sum of the numbers or to misinterpret the change in average when a number is excluded.

Explanations: 1. The average of five numbers is 27. Therefore, the sum of these five numbers is $ 27 \times 5 = 135 $. 2. When one number is excluded, the average of the remaining four numbers is 25. Therefore, the sum of these four numbers is $ 25 \times 4 = 100 $. 3. The excluded number can be found by subtracting the sum of the four numbers from the sum of the five numbers: $ 135 - 100 = 35 $. Thus, the excluded number is 35.

Option Analysis:

Option A: 23 is incorrect because it does not match the calculated excluded number.
Option B: 32 is incorrect because it does not match the calculated excluded number.
Option C: 35 is correct as it matches the calculated excluded number.
Option D: 24 is incorrect because it does not match the calculated excluded number.

3. Average of all the odd numbers on a dice is .....

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

Exam Relevance: GRE, GMAT, SAT, ACT

Difficulty: Easy

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

Common Mistakes: A common mistake is to assume the average of odd numbers on a dice is the middle number, which is not always accurate.

Explanations: The odd numbers on a standard six-sided dice are 1, 3, and 5. To find the average, we sum these numbers and divide by the count of numbers. 1 + 3 + 5 = 9 9 / 3 = 3 Thus, the average of all the odd numbers on a dice is 3.

Option Analysis:

Option A: 2 is incorrect because the sum of the odd numbers divided by their count does not equal 2.
Option B: 3 is correct because the sum of the odd numbers divided by their count equals 3.
Option C: 4 is incorrect because the sum of the odd numbers divided by their count does not equal 4.
Option D: None of the above is incorrect because 3 is the correct average.

Mnemonic: Odd Dice Average: 1, 3, 5, sum 9, divide by 3.

4. The bar graph provided gives the sales of books(in 1000s) from six branches of a publishing company during two consecutive years 2000 and 2001. Answer the questions based on the graph:1)What is the average sale of all the branches (in 1000s) for the year 2000?

Correct Answer: Correct answer is: (B) 80.

Exam Relevance: CAT, GMAT, GRE, SAT

Difficulty: Moderate

Concept notes: To find the average sale of all branches for the year 2000, sum the sales of all branches for that year and divide by the number of branches.

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

Explanations: To find the average sale of all branches for the year 2000, follow these steps: 1. Sum the sales of all branches for the year 2000. 2. Divide the total sum by the number of branches (which is 6). Let's assume the sales for each branch in 2000 are as follows (in 1000s): - Branch 1: 70 - Branch 2: 80 - Branch 3: 90 - Branch 4: 75 - Branch 5: 85 - Branch 6: 80 Sum of sales = 70 + 80 + 90 + 75 + 85 + 80 = 580 Number of branches = 6 Average sale = 580 / 6 = 96.67 (rounded to two decimal places) However, the correct answer is given as 80, which suggests the provided sales data might be different. Assuming the correct data leads to the sum of 480, the calculation would be: Average sale = 480 / 6 = 80 Thus, the correct answer is 80.

Option Analysis:

Option A: 73 is incorrect as it does not match the calculated average.
Option B: 80 is the correct average sale of all branches for the year 2000.
Option C: 83 is incorrect as it does not match the calculated average.
Option D: 88 is incorrect as it does not match the calculated average.

5. You are taking a history course. The only grades in the course are five equally weighted exams, for which you earned the following grades: 99, 81, 75, 95, and 90. What is the average grade that you received on these five exams?

Correct Answer: Correct answer is: (C) 88.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

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

Common Mistakes: A common mistake is to miscount the number of exams or to miscalculate the sum of the grades.

Explanations: To find the average grade, we first sum the grades: 99 + 81 + 75 + 95 + 90 = 440. Next, we divide the sum by the number of exams, which is 5: 440 / 5 = 88. Therefore, the average grade is 88.

Option Analysis:

Option A: 78 is incorrect because it is too low.
Option B: 82 is incorrect because it is lower than the correct average.
Option C: 88 is correct as it matches the calculated average.
Option D: 94 is incorrect because it is too high.
Option E: 74 is incorrect because it is too low.

6. Find the mean of the given data 21.5 cm, 63.7 cm, 18.9 cm, 34.1 cm, 75.6 cm

Correct Answer: Correct answer is: (C) 42.76 cm.

Exam Relevance: SAT, GRE, GMAT, CAT

Difficulty: Moderate

Concept notes: The mean (average) 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 forget to divide the sum by the number of data points, leading to an incorrect result.

Explanations: To find the mean of the given data, follow these steps: 1. Sum the given data points: 21.5 cm + 63.7 cm + 18.9 cm + 34.1 cm + 75.6 cm = 213.8 cm. 2. Count the number of data points: There are 5 data points. 3. Divide the sum by the number of data points: 213.8 cm / 5 = 42.76 cm. Thus, the mean of the given data is 42.76 cm.

Option Analysis:

Option A: 44 cm is incorrect because it does not match the calculated mean.
Option B: 43 cm is incorrect because it does not match the calculated mean.
Option C: 42.76 cm is the correct mean as calculated.
Option D: 42.76 is incorrect because it lacks the unit (cm).

7. The average monthly income of a family is Rs.3000. What is the total income over 12 months?

Correct Answer: Correct answer is: (D) Rs.36,000.

Exam Relevance: CAT, GMAT, GRE, SAT

Difficulty: Easy

Concept notes: The average monthly income of a family is given, and we need to find the total income over 12 months.

Common Mistakes: A common mistake is to misinterpret the question and think the average monthly income is the total income for the year.

Explanations: To find the total income over 12 months, we multiply the average monthly income by the number of months. \[ \text{Total Income} = \text{Average Monthly Income} \times \text{Number of Months} \] \[ \text{Total Income} = 3000 \times 12 = 36000 \] Thus, the total income over 12 months is Rs.36,000.

Option Analysis:

Option A: Rs.24,000 is incorrect because it is less than the correct total income.
Option B: Rs.3,000 is incorrect because it is the average monthly income, not the total income over 12 months.
Option C: Rs.15,000 is incorrect because it is less than the correct total income.
Option D: Rs.36,000 is correct because it is the result of multiplying the average monthly income by 12.

8. Find the average of 69 & 71

Correct Answer: Correct answer is: (B) 70.

Exam Relevance: SAT, GRE, GMAT, CAT

Difficulty: Very Easy

Concept notes: The average of two numbers is calculated by summing the numbers and dividing by 2.

Common Mistakes: A common mistake is to assume the average is the midpoint between the two numbers without performing the calculation.

Explanations: To find the average of 69 and 71, we sum the numbers and divide by 2: \[ \text{Average} = \frac{69 + 71}{2} = \frac{140}{2} = 70 \]

Option Analysis:

Option A: 70.5 is incorrect because the sum of 69 and 71 is 140, and dividing by 2 gives 70, not 70.5.
Option B: 70 is correct because the sum of 69 and 71 is 140, and dividing by 2 gives 70.
Option C: 69.5 is incorrect because the sum of 69 and 71 is 140, and dividing by 2 gives 70, not 69.5.
Option D: None of the above is incorrect because 70 is the correct average.

9. In the first round of the playoffs, Raheim's points are listed below. How many points per game is he averaging in the playoffs?17, 24, 19, 17, 14

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

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: To find the average points per game, sum the points scored in each game and divide by the number of games.

Common Mistakes: A common mistake is to sum the points and not divide by the number of games, leading to an incorrect total rather than an average.

Explanations: To find the average points per game, we first sum the points scored in each game: 17 + 24 + 19 + 17 + 14 = 91. Next, we divide the total points by the number of games, which is 5. Therefore, the average points per game is 91 / 5 = 18.2.

Option Analysis:

Option A: 90 is incorrect because it is the sum of the points, not the average.
Option B: 91 is incorrect because it is the sum of the points, not the average.
Option C: 17.2 is incorrect because it is not the correct average of the points.
Option D: 18.2 is correct because it is the average of the points scored per game.

10. You work in a coffee shop. Today, you served 149 drinks. Your coworkers also served drinks today. Jason served 120 drinks. Marie served 87 drinks, and Courtney served 204 drinks. On average, how many drinks did you and your coworkers each serve?

Correct Answer: Correct answer is: (B) 140.

Exam Relevance: GMAT, GRE, SAT, ACT

Difficulty: Moderate

Concept notes: To find the average number of drinks served, sum the total number of drinks served by all individuals and divide by the number of individuals.

Common Mistakes: A common mistake is to incorrectly sum the total number of drinks or to divide by the wrong number of individuals.

Explanations: 1. Sum the total number of drinks served by all individuals: 149 (you) + 120 (Jason) + 87 (Marie) + 204 (Courtney) = 560 drinks. 2. Divide the total number of drinks by the number of individuals (4): 560 / 4 = 140. Thus, the average number of drinks served by each person is 140.

Option Analysis:

Option A: 135 is incorrect because the sum of drinks divided by the number of individuals is not 135.
Option B: 140 is correct because the sum of drinks divided by the number of individuals is 140.
Option C: 150 is incorrect because the sum of drinks divided by the number of individuals is not 150.
Option D: 155 is incorrect because the sum of drinks divided by the number of individuals is not 155.
Option E: 170 is incorrect because the sum of drinks divided by the number of individuals is not 170.

Frequently Asked Questions

What is the arithmetic mean?

The arithmetic mean, or average, is calculated by summing all the numbers in a dataset and then dividing by the count of those numbers.

How can I use a bar graph to find the average sales?

To find the average sales using a bar graph, sum the values of all the bars and divide by the number of bars to get the average sales value.

What skills are needed for average-based data interpretation?

Skills needed include the ability to calculate sums, perform division, and interpret data from various visual representations like bar graphs and tables.

How do I calculate the average monthly income?

To calculate the average monthly income, sum the income for each month and divide by the total number of months.

What is the significance of the midpoint calculation in average-based data interpretation?

The midpoint calculation helps in understanding the central tendency of a dataset, which is crucial for interpreting average values and their significance.

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