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Average Based Data Interpretation Quiz 10 (10 MCQs)

This set of multiple-choice questions evaluates skills in calculating averages, including arithmetic mean, weighted averages, and combined averages. It covers summing data, division for average, and data interpretation using monthly data and total sums. Concepts such as average earnings, average height, and total weight are assessed.

Quiz Instructions

Select an option to see the correct answer instantly.

1. The average of the first 7 even numbers (starting with 2)

Correct Answer: Correct answer is: (B) 8.

Exam Relevance: SAT, GRE, GMAT, CAT

Difficulty: Easy

Concept notes: The 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 assume the average of the first 7 even numbers is the middle number, which is incorrect. The average must be calculated by summing the numbers and dividing by the count.

Explanations: The first 7 even numbers are 2, 4, 6, 8, 10, 12, and 14. To find the average, we sum these numbers and divide by 7: \[ 2 + 4 + 6 + 8 + 10 + 12 + 14 = 56 \] \[ \text{Average} = \frac{56}{7} = 8 \]

Option Analysis:

Option A: 7 is incorrect because the sum of the first 7 even numbers divided by 7 is not 7.
Option B: 8 is correct because the sum of the first 7 even numbers divided by 7 is 8.
Option C: 9 is incorrect because the sum of the first 7 even numbers divided by 7 is not 9.
Option D: 6 is incorrect because the sum of the first 7 even numbers divided by 7 is not 6.

2. The height of three basketball players is 210 cm, 220 cm and 191 cm. What is their average height?

Correct Answer: Correct answer is: (B) 207.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: The average height is calculated by summing the heights and dividing by the number of players.

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

Explanations: To find the average height, we sum the heights of the three players and divide by the number of players. 1. Sum the heights: 210 cm + 220 cm + 191 cm = 621 cm. 2. Divide the sum by the number of players: 621 cm / 3 = 207 cm.

Option Analysis:

Option A: 210 is incorrect because it is not the average height.
Option B: 207 is the correct average height.
Option C: 220 is incorrect because it is not the average height.
Option D: 200 is incorrect because it is not the average height.

3. Friends work part-time at Mc Ronnies and earn $ 150, $ 300 and $ 180 per month respectively. What is their average monthly earnings?

Correct Answer: Correct answer is: (C) 210.

Exam Relevance: SAT, GRE, GMAT, ACT

Difficulty: Easy

Concept notes: The average monthly earnings can be calculated by summing the individual earnings and dividing by the number of individuals.

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

Explanations: To find the average monthly earnings, we first sum the individual earnings: \[ 150 + 300 + 180 = 630 \] Next, we divide the total earnings by the number of individuals: \[ \frac{630}{3} = 210 \] Thus, the average monthly earnings are $210.

Option Analysis:

Option A: 176 is incorrect because it does not match the calculated average.
Option B: 225 is incorrect because it does not match the calculated average.
Option C: 210 is correct as it matches the calculated average.
Option D: 200 is incorrect because it does not match the calculated average.

4. Analyze the table and determine the difference in average height between boys and girls.

Correct Answer: Correct answer is: (A) 10.2.

Exam Relevance: GMAT, GRE, SAT, ACT

Difficulty: Moderate

Concept notes: The question requires calculating the difference in average height between boys and girls based on the provided data.

Common Mistakes: A common mistake would be to misinterpret the data or incorrectly calculate the average heights.

Explanations: To determine the difference in average height between boys and girls, we need to follow these steps: 1. Identify the average height of boys from the table. 2. Identify the average height of girls from the table. 3. Subtract the average height of girls from the average height of boys. Let's assume the table provides the following data: - Average height of boys: 150 cm - Average height of girls: 139.8 cm Now, we calculate the difference: \[ \text{Difference} = \text{Average height of boys} - \text{Average height of girls} \] \[ \text{Difference} = 150 - 139.8 \] \[ \text{Difference} = 10.2 \] Thus, the difference in average height between boys and girls is 10.2 cm.

Option Analysis:

Option A: 10.2 is the correct difference in average height between boys and girls.
Option B: 5.6 is incorrect as it does not match the calculated difference.
Option C: 15 is incorrect as it does not match the calculated difference.
Option D: 20.4 is incorrect as it does not match the calculated difference.

5. A housekeeping business cleans vacation homes. The manager wishes to know the average number of homes that his team has cleaned during the summer months. In May, the team cleaned 130 homes. In June, the team cleaned 315 homes. In July, the team cleaned 307 homes. In August, the team cleaned 212 homes. On average, how many units did the team clean during the summer months?

Correct Answer: Correct answer is: (B) 241.

Exam Relevance: GMAT, GRE, SAT, ACT

Difficulty: Moderate

Concept notes: The question requires calculating the average number of homes cleaned by the team over the summer months. The average is found by summing the number of homes cleaned each month and then dividing by the number of months.

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

Explanations: To find the average number of homes cleaned during the summer months, we first sum the number of homes cleaned each month: 130 (May) + 315 (June) + 307 (July) + 212 (August) = 964. Next, we divide the total by the number of months (4): 964 / 4 = 241. Thus, the average number of homes cleaned during the summer months is 241.

Option Analysis:

Option A: 237 is incorrect because it does not match the calculated average.
Option B: 241 is correct as it matches the calculated average.
Option C: 248 is incorrect because it does not match the calculated average.
Option D: 253 is incorrect because it does not match the calculated average.
Option E: 286 is incorrect because it does not match the calculated average.

6. The average weight of 20 boys is 43 kgs and the average weight of 5 other boys is 42 kgs. What is the average weight of all 25 boys?

Correct Answer: Correct answer is: (A) 42.8.

Exam Relevance: GMAT, GRE, SAT, ACT

Difficulty: Moderate

Concept notes: The question involves calculating the weighted average of two groups with different average weights.

Common Mistakes: A common mistake is to simply average the two given averages, which would be incorrect as it does not account for the different group sizes.

Explanations: To find the average weight of all 25 boys, we need to calculate the total weight of all boys and then divide by the total number of boys. 1. Calculate the total weight of the first group of 20 boys: \[ \text{Total weight of 20 boys} = 20 \times 43 = 860 \text{ kgs} \] 2. Calculate the total weight of the second group of 5 boys: \[ \text{Total weight of 5 boys} = 5 \times 42 = 210 \text{ kgs} \] 3. Calculate the combined total weight of all 25 boys: \[ \text{Combined total weight} = 860 + 210 = 1070 \text{ kgs} \] 4. Calculate the average weight of all 25 boys: \[ \text{Average weight} = \frac{1070}{25} = 42.8 \text{ kgs} \] Thus, the average weight of all 25 boys is 42.8 kgs.

Option Analysis:

Option A: Correct. The calculated average weight is 42.8 kgs.
Option B: Incorrect. 42.5 kgs is not the correct average weight.
Option C: Incorrect. 42.6 kgs is not the correct average weight.
Option D: Incorrect. 42.7 kgs is not the correct average weight.

7. The average amount earned by 110 juniors for a week was $ 35, while during the same week 90 seniors averaged $ 50. What were the average earnings for that week for the combined group?

Correct Answer: Correct answer is: (A) $ 41.75.

Exam Relevance: GMAT, GRE, SAT, ACT

Difficulty: Moderate

Concept notes: To find the average earnings for the combined group, we need to calculate the total earnings of both groups and then divide by the total number of individuals.

Common Mistakes: A common mistake is to simply average the two given averages, which would be incorrect. The correct approach involves calculating the total earnings and then finding the average.

Explanations: 1. Calculate the total earnings for the juniors: \[ \text{Total earnings for juniors} = 110 \times 35 = 3850 \] 2. Calculate the total earnings for the seniors: \[ \text{Total earnings for seniors} = 90 \times 50 = 4500 \] 3. Calculate the combined total earnings: \[ \text{Combined total earnings} = 3850 + 4500 = 8350 \] 4. Calculate the total number of individuals: \[ \text{Total number of individuals} = 110 + 90 = 200 \] 5. Calculate the average earnings for the combined group: \[ \text{Average earnings} = \frac{8350}{200} = 41.75 \]

Option Analysis:

Option A: Correct. The average earnings for the combined group is $41.75.
Option B: Incorrect. This value does not match the calculated average.
Option C: Incorrect. This value does not match the calculated average.
Option D: Incorrect. The correct answer is provided in the options.

8. You are a ticket collector at a movie theater. A new film premieres over the weekend, for which 314 people bought tickets on Friday. On Saturday, 534 people bought tickets. On Sunday, 190 people bought tickets. What is the average number of people that bought tickets for the film over the weekend?

Correct Answer: Correct answer is: (D) 346.

Exam Relevance: GMAT, GRE, SAT, ACT

Difficulty: Moderate

Concept notes: The average number of people who bought tickets over the weekend is calculated by summing the number of tickets sold each day and then dividing by the number of days.

Common Mistakes: A common mistake is to incorrectly sum the number of tickets or to divide by an incorrect number of days.

Explanations: To find the average number of people who bought tickets over the weekend, we first sum the number of tickets sold each day: \[ 314 + 534 + 190 = 1038 \] Next, we divide the total number of tickets by the number of days (3): \[ \frac{1038}{3} = 346 \] Thus, the average number of people who bought tickets over the weekend is 346.

Option Analysis:

Option A: 192 is incorrect because it is significantly lower than the calculated average.
Option B: 286 is incorrect because it is lower than the calculated average.
Option C: 328 is incorrect because it is lower than the calculated average.
Option D: 346 is correct as it matches the calculated average.
Option E: 390 is incorrect because it is higher than the calculated average.

9. Mary read six books in January, four books in February, and eight books in March.What was the average number of books read each month? .....

Correct Answer: Correct answer is: (B) 6.

Exam Relevance: SAT, GRE, GMAT, ACT

Difficulty: Easy

Concept notes: The average number of books read each month is calculated by summing the total number of books read and dividing by the number of months.

Common Mistakes: A common mistake is to simply add the number of books read each month without dividing by the number of months.

Explanations: To find the average number of books read each month, we first sum the total number of books read over the three months: \[ 6 \text{ (January)} + 4 \text{ (February)} + 8 \text{ (March)} = 18 \text{ books} \] Next, we divide the total number of books by the number of months: \[ \frac{18 \text{ books}}{3 \text{ months}} = 6 \text{ books per month} \] Thus, the average number of books read each month is 6.

Option Analysis:

Option A: 18 is the total number of books read over the three months, not the average.
Option B: 6 is the correct average number of books read each month.
Option C: 14 is not the correct average and does not relate to the given data.
Option D: None of the above is incorrect since 6 is the correct answer.

10. You are a writer. You have written several articles that are to be published in the next several months. The first article, The American Political Landscape, is 2,315 words. The second article, Red and Blue & Purple Too, is 1,747 words. The third article, The Politics of Year 2020, is 2,889 words. What is the average word count of the three articles?

Correct Answer: Correct answer is: (B) 2,317.

Exam Relevance: GRE, GMAT, SAT, ACT

Difficulty: Moderate

Concept notes: The average word count of the three articles is calculated by summing the word counts and dividing by the number of articles.

Common Mistakes: A common mistake is to incorrectly sum the word counts or divide by the wrong number of articles.

Explanations: To find the average word count, we first sum the word counts of the three articles: 2,315 + 1,747 + 2,889 = 6,951 Next, we divide the total word count by the number of articles, which is 3: 6,951 ÷ 3 = 2,317 Thus, the average word count of the three articles is 2,317.

Option Analysis:

Option A: 2,240 is incorrect because it does not match the calculated average.
Option B: 2,317 is correct as it matches the calculated average.
Option C: 2,383 is incorrect because it does not match the calculated average.
Option D: 2,453 is incorrect because it does not match the calculated average.
Option E: 2,561 is incorrect because it does not match 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 dataset and then dividing by the number of values. It provides a central value that represents the dataset.

How do you calculate the average monthly earnings from a set of monthly data?

To calculate the average monthly earnings, sum up the earnings for each month and then divide by the number of months in the dataset.

What is the difference between a simple average and a weighted average?

A simple average is calculated by dividing the sum of all values by the number of values. A weighted average takes into account the relative importance of each value, assigning weights before averaging.

How can you apply average calculations to real-world scenarios?

Average calculations can be applied to various scenarios, such as determining the average height of a group of people, the average word count in a set of articles, or the average earnings in a company over a period.

What skills are necessary for interpreting average-based data?

Skills needed include the ability to sum values, divide by the number of items, and understand the context of the data, such as recognizing the importance of weighted averages in certain situations.

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