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Unit Vii Data Interpretation
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Average Based Data Interpretation – Quiz 13
Average Based Data Interpretation Quiz 13 (10 MCQs)
This set of multiple-choice questions evaluates skills in average calculation, data correction, and sum adjustment. It covers arithmetic mean, average sales, temperature calculation, and weekly data interpretation. Students will practice summing data, dividing by count, and interpreting subsets to find overall averages.
Quiz Instructions
Select an option to see the correct answer instantly.
1.
A scientist records the growth of a plant over 5 weeks, measuring heights of 12 cm, 15 cm, 13 cm, 14 cm, and 11 cm. What is the average weekly growth?
A) 13 cm.
B) 12.5 cm.
C) 13.5 cm.
D) 14 cm.
Show Answer
Correct Answer:
Correct answer is: (A) 13 cm.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
The average weekly growth is calculated by summing the weekly heights and dividing by the number of weeks.
Common Mistakes:
A common mistake is to miscount the number of weeks or to incorrectly sum the heights.
Explanations:
To find the average weekly growth, we sum the heights: 12 cm + 15 cm + 13 cm + 14 cm + 11 cm = 65 cm. Then, we divide the total by the number of weeks, which is 5. So, the average is 65 cm / 5 = 13 cm.
Option Analysis:
Option A:
Correct. The average weekly growth is 13 cm.
Option B:
Incorrect. 12.5 cm is not the correct average.
Option C:
Incorrect. 13.5 cm is not the correct average.
Option D:
Incorrect. 14 cm is not the correct average.
2.
Jen has $ 10, Connie has $ 15, and Elsa has $ 2. What is the average amount of money each person has?
A) 9.
B) 13.5.
C) 27.
D) None of above.
Show Answer
Correct Answer:
Correct answer is: (A) 9.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
The average amount of money is calculated by summing the total amount of money and dividing by the number of people.
Common Mistakes:
A common mistake is to incorrectly sum the amounts or divide by the wrong number of people.
Explanations:
To find the average amount of money each person has, we first sum the total amount of money:
\[ 10 + 15 + 2 = 27 \]
Next, we divide the total amount by the number of people, which is 3:
\[ \frac{27}{3} = 9 \]
Thus, the average amount of money each person has is 9.
Option Analysis:
Option A:
Correct. The average amount of money is 9.
Option B:
Incorrect. This is the sum of Jen's and Connie's money divided by 2, not the average of all three.
Option C:
Incorrect. This is the total sum of all the money, not the average.
Option D:
Incorrect. The correct answer is provided in Option A.
3.
The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
A) 12.4.
B) 14.
C) 16.
D) 18.6.
Show Answer
Correct Answer:
Correct answer is: (C) 16.
Exam Relevance:
GMAT, GRE, SAT, ACT
Difficulty:
Moderate
Concept notes:
The question involves calculating the correct average after identifying an error in the initial data set. The concept of average and the impact of a single incorrect data point on the overall average is crucial.
Common Mistakes:
A common mistake is to assume that the error in one number does not significantly affect the overall average, leading to incorrect recalculations.
Explanations:
1. The initial average of 10 numbers is 15, so the sum of these numbers is \(15 \times 10 = 150\).
2. One number, 36, was wrongly read as 26. The difference between the correct and incorrect number is \(36 - 26 = 10\).
3. To find the correct sum, add this difference to the initial sum: \(150 + 10 = 160\).
4. The correct average is then calculated by dividing the new sum by the number of values: \(\frac{160}{10} = 16\).
Option Analysis:
Option A:
12.4 is incorrect because it does not account for the correction in the sum.
Option B:
14 is incorrect because it does not reflect the adjustment needed due to the error.
Option C:
16 is correct as it reflects the recalculated average after correcting the error.
Option D:
18.6 is incorrect because it overestimates the impact of the error on the average.
4.
Over three days the average temperature was 82 degrees. After the fourth day, the average temp for the four days went up to 84 degrees. What was the temperature on the fourth day?
A) -14 degrees.
B) 82 degrees.
C) 90 degrees.
D) 84 degrees.
Show Answer
Correct Answer:
Correct answer is: (C) 90 degrees.
Exam Relevance:
SAT, GRE, GMAT, ACT
Difficulty:
Moderate
Concept notes:
The question involves calculating the temperature on the fourth day based on the average temperatures over three and four days.
Common Mistakes:
A common mistake is to assume the temperature on the fourth day is the same as the average temperature over the four days, which is not necessarily true.
Explanations:
To find the temperature on the fourth day, we need to use the information about the average temperatures over three and four days.
1. Calculate the total temperature for the first three days:
\[
\text{Average temperature for three days} = 82 \text{ degrees}
\]
\[
\text{Total temperature for three days} = 82 \times 3 = 246 \text{ degrees}
\]
2. Calculate the total temperature for the four days:
\[
\text{Average temperature for four days} = 84 \text{ degrees}
\]
\[
\text{Total temperature for four days} = 84 \times 4 = 336 \text{ degrees}
\]
3. Determine the temperature on the fourth day:
\[
\text{Temperature on the fourth day} = \text{Total temperature for four days} - \text{Total temperature for three days}
\]
\[
\text{Temperature on the fourth day} = 336 - 246 = 90 \text{ degrees}
\]
Thus, the temperature on the fourth day is 90 degrees.
Option Analysis:
Option A:
-14 degrees is incorrect because it is not a reasonable temperature given the context.
Option B:
82 degrees is incorrect because it is the average temperature for the first three days, not the temperature on the fourth day.
Option C:
90 degrees is correct as calculated above.
Option D:
84 degrees is incorrect because it is the average temperature for the four days, not the temperature on the fourth day.
5.
As a professional video gamer, you practice often. On Monday, you played 48 matches. On Tuesday, you played 54 matches. On Wednesday, you played 67 matches. On Thursday, you played 35 matches. What is the average number of matches you played over the four days of practice?
A) 58.
B) 67.
C) 51.
D) 45.
E) 32.
Show Answer
Correct Answer:
Correct answer is: (C) 51.
Exam Relevance:
GMAT, GRE, SAT, ACT
Difficulty:
Moderate
Concept notes:
The average number of matches played over the four days is calculated by summing the number of matches played each day and then dividing by the number of days.
Common Mistakes:
A common mistake is to incorrectly sum the matches or divide by the wrong number of days.
Explanations:
To find the average number of matches played over the four days, we first sum the matches played each day:
\[ 48 + 54 + 67 + 35 = 204 \]
Next, we divide the total number of matches by the number of days (4):
\[ \frac{204}{4} = 51 \]
Thus, the average number of matches played over the four days is 51.
Option Analysis:
Option A:
58 is incorrect because the sum of matches divided by 4 does not equal 58.
Option B:
67 is incorrect because it is the number of matches played on one day, not the average.
Option C:
51 is correct as calculated above.
Option D:
45 is incorrect because the sum of matches divided by 4 does not equal 45.
Option E:
32 is incorrect because the sum of matches divided by 4 does not equal 32.
6.
The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
A) 46.
B) 32.
C) 68.
D) 51.
Show Answer
Correct Answer:
Correct answer is: (A) 46.
Exam Relevance:
GRE, GMAT, CAT, SAT
Difficulty:
Moderate
Concept notes:
The question involves calculating the average of a set of numbers and using the given averages to find a specific number within the set.
Common Mistakes:
A common mistake is to incorrectly sum the averages of the subsets and assume it gives the total sum of the entire set.
Explanations:
1. The average of 13 numbers is 60. Therefore, the total sum of these 13 numbers is \( 13 \times 60 = 780 \).
2. The average of the first 7 numbers is 57. Therefore, the sum of the first 7 numbers is \( 7 \times 57 = 399 \).
3. The average of the last 7 numbers is 61. Therefore, the sum of the last 7 numbers is \( 7 \times 61 = 427 \).
4. The sum of the first 7 and the last 7 numbers includes the 8th number twice. Therefore, the sum of the first 7 and the last 7 numbers is \( 399 + 427 = 826 \).
5. The 8th number is included twice in the sum of 826, but only once in the total sum of 780. Therefore, the 8th number is \( 826 - 780 = 46 \).
Option Analysis:
Option A:
46 is the correct answer as calculated above.
Option B:
32 is incorrect as it does not match the calculated value.
Option C:
68 is incorrect as it does not match the calculated value.
Option D:
51 is incorrect as it does not match the calculated value.
7.
A biologist records the number of leaves on a plant over four weeks: 15, 18, 20, and 17. What is the average number of leaves per week?
A) 17 leaves.
B) 17.5 leaves.
C) 18 leaves.
D) 16.5 leaves.
Show Answer
Correct Answer:
Correct answer is: (B) 17.5 leaves.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
The average number of leaves per week is calculated by summing the number of leaves over the four weeks and then dividing by the number of weeks.
Common Mistakes:
A common mistake is to incorrectly sum the numbers or divide by the wrong number of weeks.
Explanations:
To find the average number of leaves per week, we first sum the number of leaves over the four weeks: 15 + 18 + 20 + 17 = 70. Next, we divide the total number of leaves by the number of weeks: 70 / 4 = 17.5. Therefore, the average number of leaves per week is 17.5.
Option Analysis:
Option A:
17 leaves is incorrect because the sum of the leaves divided by the number of weeks is 17.5, not 17.
Option B:
17.5 leaves is correct because the sum of the leaves divided by the number of weeks is 17.5.
Option C:
18 leaves is incorrect because the sum of the leaves divided by the number of weeks is 17.5, not 18.
Option D:
16.5 leaves is incorrect because the sum of the leaves divided by the number of weeks is 17.5, not 16.5.
8.
The average of 5 numbers is 10. The average of the first three numbers is 6. What is the average of the last two numbers?
A) 20.
B) 16.
C) 8.
D) 12.
Show Answer
Correct Answer:
Correct answer is: (B) 16.
Exam Relevance:
GMAT, GRE, SAT, ACT
Difficulty:
Moderate
Concept notes:
The question involves calculating the average of a subset of numbers based on the overall average and the average of another subset.
Common Mistakes:
A common mistake is to assume that the average of the last two numbers can be directly derived from the overall average without considering the contribution of the first three numbers.
Explanations:
1. The average of 5 numbers is 10, so the sum of these 5 numbers is \(5 \times 10 = 50\).
2. The average of the first three numbers is 6, so the sum of these three numbers is \(3 \times 6 = 18\).
3. The sum of the last two numbers is \(50 - 18 = 32\).
4. The average of the last two numbers is \(\frac{32}{2} = 16\).
Thus, the average of the last two numbers is 16.
Option Analysis:
Option A:
20. This is incorrect because the sum of the last two numbers is 32, and their average is 16.
Option B:
16. This is correct as calculated above.
Option C:
8. This is incorrect because the sum of the last two numbers is 32, and their average is 16.
Option D:
12. This is incorrect because the sum of the last two numbers is 32, and their average is 16.
9.
Average of 1.1, 2.2 and 3.3 is .....
A) 4.4.
B) 2.2.
C) 2.1.
D) 1.5.
Show Answer
Correct Answer:
Correct answer is: (B) 2.2.
Exam Relevance:
SAT, GRE, GMAT, ACT
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 the numbers.
Common Mistakes:
A common mistake is to incorrectly sum the numbers or divide by the wrong count.
Explanations:
To find the average of 1.1, 2.2, and 3.3, we first sum the numbers:
1.1 + 2.2 + 3.3 = 6.6
Next, we divide the sum by the count of the numbers, which is 3:
6.6 ÷ 3 = 2.2
Thus, the average is 2.2.
Option Analysis:
Option A:
4.4 is incorrect because it is the sum of the numbers, not the average.
Option B:
2.2 is correct as it is the calculated average.
Option C:
2.1 is incorrect because it is not the correct average.
Option D:
1.5 is incorrect because it is not the correct average.
10.
A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
A) 3991.
B) 4991.
C) 5991.
D) 6991.
Show Answer
Correct Answer:
Correct answer is: (B) 4991.
Exam Relevance:
CAT, GMAT, GRE, Bank PO
Difficulty:
Moderate
Concept notes:
The question involves calculating the required sale amount for the sixth month to achieve a specific average sale over six months.
Common Mistakes:
A common mistake is to incorrectly calculate the total required sales without properly accounting for the average requirement.
Explanations:
To find the required sale for the sixth month, we first calculate the total sales needed to achieve an average of Rs. 6500 over six months. The formula for the average is:
\[ \text{Average} = \frac{\text{Total Sales}}{\text{Number of Months}} \]
Given the average sale is Rs. 6500 over 6 months, the total sales required is:
\[ 6500 \times 6 = 39000 \]
The total sales for the first five months are:
\[ 6435 + 6927 + 6855 + 7230 + 6562 = 34009 \]
To find the required sale for the sixth month, we subtract the total sales of the first five months from the total required sales:
\[ 39000 - 34009 = 4991 \]
Thus, the required sale for the sixth month is Rs. 4991.
Option Analysis:
Option A:
3991 is incorrect because it does not meet the requirement to achieve an average sale of Rs. 6500 over six months.
Option B:
4991 is correct as it is the amount needed to achieve the required average sale.
Option C:
5991 is incorrect because it exceeds the amount needed to achieve the required average sale.
Option D:
6991 is incorrect because it exceeds the amount needed to achieve the required average sale.
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Frequently Asked Questions
What is the arithmetic mean in the context of 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 sales over a period?
To calculate the average sales, sum the total sales for the period and divide by the number of weeks or months in that period. This gives you the average sales per week or month.
What is the importance of data correction in average calculations?
Data correction is crucial because incorrect data can skew the average. Ensuring data accuracy helps in obtaining a true representation of the dataset, leading to more reliable average calculations.
How do overlapping elements affect the calculation of an average?
Overlapping elements can affect the average if they are counted multiple times. To avoid this, ensure that each element is counted only once in the sum and the count of elements used to calculate the average.
What is the significance of sum adjustment in average calculations?
Sum adjustment is necessary when there are errors or changes in the dataset. Adjusting the sum ensures that the average reflects the most current and accurate data, providing a more precise average value.