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Unit Vii Data Interpretation
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Average Based Data Interpretation – Quiz 17
Average Based Data Interpretation Quiz 17 (10 MCQs)
This set of multiple-choice questions evaluates skills in calculating averages, including arithmetic mean, sum of values, and division by the number of items. It covers concepts such as summing heights, expenditures, and grades, and interpreting data to find central tendencies. Students will practice summing numbers, dividing by the total count, and understanding the impact of constant increases on the mean.
Quiz Instructions
Select an option to see the correct answer instantly.
1.
The average of 5 quantities is 6. The average of 3 of those 5 quantities is 8. What is the average of the remaining two quantities?
Show Answer
Correct Answer:
Correct answer is: (C) 3.
Exam Relevance:
GMAT, GRE, SAT, ACT
Difficulty:
Moderate
Concept notes:
The question involves calculating the average of remaining quantities based on given averages and totals.
Common Mistakes:
A common mistake is to assume the average of the remaining quantities can be directly calculated from the given averages without considering the total sums.
Explanations:
1. The average of 5 quantities is 6. Therefore, the total sum of these 5 quantities is \(5 \times 6 = 30\).
2. The average of 3 of those 5 quantities is 8. Therefore, the total sum of these 3 quantities is \(3 \times 8 = 24\).
3. The sum of the remaining 2 quantities is \(30 - 24 = 6\).
4. The average of the remaining 2 quantities is \(\frac{6}{2} = 3\).
Thus, the average of the remaining two quantities is 3.
Option Analysis:
Option A:
5 is incorrect because the sum of the remaining two quantities is 6, and their average is \(\frac{6}{2} = 3\).
Option B:
2 is incorrect because the sum of the remaining two quantities is 6, and their average is \(\frac{6}{2} = 3\).
Option C:
3 is correct because the sum of the remaining two quantities is 6, and their average is \(\frac{6}{2} = 3\).
Option D:
1 is incorrect because the sum of the remaining two quantities is 6, and their average is \(\frac{6}{2} = 3\).
2.
You are a mathematics professor. You are currently teaching five courses at a university. After giving the final exams to each of your courses, you find that the average grade in each course is as follows: 72, 81, 75, 63, and 80. What is the total average of the average grades from the five courses you are teaching at the university?
A) 45.7.
B) 56.2.
C) 74.2.
D) 76.8.
E) 81.5.
Show Answer
Correct Answer:
Correct answer is: (C) 74.2.
Exam Relevance:
GRE, GMAT, SAT, ACT
Difficulty:
Moderate
Concept notes:
The question requires calculating the average of the average grades from five courses. This involves summing the individual averages and then dividing by the number of courses.
Common Mistakes:
A common mistake is to incorrectly sum the grades or divide by an incorrect number of courses.
Explanations:
To find the total average of the average grades from the five courses, we need to sum the individual averages and then divide by the number of courses. The individual averages are 72, 81, 75, 63, and 80.
Step 1: Sum the individual averages.
\[ 72 + 81 + 75 + 63 + 80 = 371 \]
Step 2: Divide the sum by the number of courses.
\[ \frac{371}{5} = 74.2 \]
Thus, the total average of the average grades from the five courses is 74.2.
Option Analysis:
Option A:
45.7 is incorrect because it is significantly lower than the correct average.
Option B:
56.2 is incorrect because it is lower than the correct average.
Option C:
74.2 is the correct average calculated by summing the individual averages and dividing by the number of courses.
Option D:
76.8 is incorrect because it is slightly higher than the correct average.
Option E:
81.5 is incorrect because it is significantly higher than the correct average.
3.
There are an average of 20 kids in each class. There are 36 classes in the school. Using the average find about how many kids are in the school.
A) 720.
B) 750.
C) 613.
D) 553.
E) 837.
Show Answer
Correct Answer:
Correct answer is: (A) 720.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
The concept of average is used to find the total number of kids in the school by multiplying the average number of kids per class by the total number of classes.
Common Mistakes:
A common mistake is to misinterpret the average as a fixed number and not use it to calculate the total.
Explanations:
To find the total number of kids in the school, we use the formula:
\[ \text{Total number of kids} = \text{Average number of kids per class} \times \text{Number of classes} \]
Given:
\[ \text{Average number of kids per class} = 20 \]
\[ \text{Number of classes} = 36 \]
\[ \text{Total number of kids} = 20 \times 36 = 720 \]
Option Analysis:
Option A:
720 is the correct answer as calculated above.
Option B:
750 is incorrect because it does not match the calculation.
Option C:
613 is incorrect because it does not match the calculation.
Option D:
553 is incorrect because it does not match the calculation.
Option E:
837 is incorrect because it does not match the calculation.
4.
Find the average of 73 & 66
A) 71.
B) 62.5.
C) 69.5.
D) None of above.
Show Answer
Correct Answer:
Correct answer is: (C) 69.5.
Exam Relevance:
SAT, GRE, GMAT, CAT
Difficulty:
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 simply take the midpoint between the two numbers without performing the actual calculation.
Explanations:
To find the average of 73 and 66, we first sum the numbers: 73 + 66 = 139. Then, we divide the sum by 2: 139 / 2 = 69.5. Therefore, the average of 73 and 66 is 69.5.
Option Analysis:
Option A:
71 is incorrect because it does not match the calculated average.
Option B:
62.5 is incorrect because it does not match the calculated average.
Option C:
69.5 is correct as it matches the calculated average.
Option D:
None of the above is incorrect because 69.5 is one of the options.
5.
What does "mean" mean?
A) Average.
B) Middle.
C) Repeats the most.
D) Variation.
Show Answer
Correct Answer:
Correct answer is: (A) Average.
Exam Relevance:
SAT, GRE, GMAT, ACT
Difficulty:
Easy
Concept notes:
The term "mean" in statistics refers to the average value of a set of numbers.
Common Mistakes:
A common misunderstanding is confusing "mean" with other measures of central tendency, such as median (middle value) or mode (most frequent value).
Explanations:
In the context of average-based data interpretation, "mean" is the sum of all values divided by the number of values. This is the most common interpretation of "average" in statistical analysis.
Option Analysis:
Option A:
Correct. The mean is the arithmetic average of a set of numbers.
Option B:
Incorrect. The middle value is the median, not the mean.
Option C:
Incorrect. The value that repeats the most is the mode, not the mean.
Option D:
Incorrect. Variation refers to the spread of data, not the average.
6.
You are a biologist working on an experiment. You are testing several compounds that are meant to assist in the growth of tomato plants. Compound A results in a 148 cm plant. Compound B results in a 231 cm plant. Compound C results in a 125 cm plant. Compound D results in a 235 cm plant. Compound E results in a 196 cm plant. On average, what is the height of the plants that these compounds resulted in?
A) 187.
B) 189.
C) 191.
D) 195.
E) 202.
Show Answer
Correct Answer:
Correct answer is: (A) 187.
Exam Relevance:
GRE, GMAT, SAT, ACT
Difficulty:
Moderate
Concept notes:
To find the average height of the plants, sum the heights of the plants and divide by the number of compounds.
Common Mistakes:
A common mistake is to miscount the number of compounds or to make an arithmetic error in summing the heights.
Explanations:
To find the average height of the plants, we first sum the heights of the plants:
148 cm + 231 cm + 125 cm + 235 cm + 196 cm = 935 cm.
Next, we divide the total height by the number of compounds, which is 5:
935 cm / 5 = 187 cm.
Thus, the average height of the plants is 187 cm.
Option Analysis:
Option A:
187 cm is the correct average height.
Option B:
189 cm is incorrect.
Option C:
191 cm is incorrect.
Option D:
195 cm is incorrect.
Option E:
202 cm is incorrect.
7.
If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is:
A) 30.
B) 40.
C) 37.
D) NOTA.
Show Answer
Correct Answer:
Correct answer is: (B) 40.
Exam Relevance:
GRE, GMAT, SAT, ACT
Difficulty:
Easy
Concept notes:
The arithmetic mean of a set of numbers is the sum of the numbers divided by the count of the numbers. If each number in the set is increased by a constant value, the mean of the new set of numbers will also increase by that constant value.
Common Mistakes:
A common mistake is to think that the mean will change in a more complex way, such as by a percentage or by a different constant value.
Explanations:
The original mean of the seventy-five numbers is 35. If each number is increased by 5, the new mean will also increase by 5. Therefore, the new mean is:
\[ 35 + 5 = 40 \]
Option Analysis:
Option A:
30 is incorrect because the mean increases by 5, not decreases.
Option B:
40 is correct because the mean increases by 5.
Option C:
37 is incorrect because the mean increases by 5, not by 2.
Option D:
NOTA is incorrect because 40 is the correct answer.
8.
Amy's current grades for her assignments in math class are 85, 90, 95, and 80. What grade does she have to earn on her next assignment to attain an average of 90?
A) 88.
B) 90.
C) 95.
D) 100.
Show Answer
Correct Answer:
Correct answer is: (D) 100.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
To find the required grade for Amy to achieve an average of 90, we need to use the concept of averages. The average of a set of numbers is the sum of the numbers divided by the count of the numbers.
Common Mistakes:
A common mistake is to assume that the required grade can be found by simply averaging the current grades and the desired average. However, the correct approach involves calculating the total sum needed to achieve the desired average and then finding the missing grade.
Explanations:
To find the required grade, follow these steps:
1. Calculate the total sum of the current grades: 85 + 90 + 95 + 80 = 350.
2. Determine the total sum needed to achieve an average of 90 over 5 assignments: 90 * 5 = 450.
3. Find the required grade for the next assignment: 450 - 350 = 100.
Thus, Amy needs to earn a grade of 100 on her next assignment to attain an average of 90.
Option Analysis:
Option A:
88 is incorrect because it does not result in an average of 90.
Option B:
90 is incorrect because it does not result in an average of 90.
Option C:
95 is incorrect because it does not result in an average of 90.
Option D:
100 is correct because it results in an average of 90.
9.
The recent electric bills for the Rafael family were as follows: August $ 187.55; September $ 197.34; October $ 200.44; and November $ 256.88. Find the average monthly expenditures.
A) $ 842.21.
B) $ 210.55.
C) $ 195.11.
D) $ 168.44.
Show Answer
Correct Answer:
Correct answer is: (B) $ 210.55.
Exam Relevance:
GMAT, GRE, SAT, ACT
Difficulty:
Moderate
Concept notes:
The average monthly expenditure is calculated by summing the monthly expenditures and dividing by the number of months.
Common Mistakes:
A common mistake is to miscount the number of months or to incorrectly sum the expenditures.
Explanations:
To find the average monthly expenditure, we first sum the expenditures for each month:
\[ 187.55 + 197.34 + 200.44 + 256.88 = 842.21 \]
Next, we divide the total sum by the number of months (4):
\[ \frac{842.21}{4} = 210.55 \]
Thus, the average monthly expenditure is $ 210.55.
Option Analysis:
Option A:
This option represents the total sum of the expenditures, not the average.
Option B:
This option correctly represents the average monthly expenditure.
Option C:
This option is incorrect as it does not match the calculated average.
Option D:
This option is incorrect as it does not match the calculated average.
Mnemonic:
Sum and divide, average guide.
10.
The 5th grade class was in charge of the dinosaur exhibit at the school science fair. Jason brought21 dinosaur models, Lisa brought 13 dinosaur models, Sara brought 6 dinosaur models, and Jimbrought 24 dinosaur models.What is the average number of dinosaur models that each student brought to the fair? .....
A) 24.
B) 16.
C) 6.
D) 4.
Show Answer
Correct Answer:
Correct answer is: (B) 16.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The average is calculated by summing all the values and then dividing by the number of values.
Common Mistakes:
A common mistake is to simply guess the average without performing the calculation, or to miscount the number of values.
Explanations:
To find the average number of dinosaur models each student brought, we first sum the number of models brought by each student:
\[ 21 + 13 + 6 + 24 = 64 \]
Next, we divide the total number of models by the number of students, which is 4:
\[ \frac{64}{4} = 16 \]
Thus, the average number of dinosaur models each student brought is 16.
Option Analysis:
Option A:
24 is incorrect because it is not the result of the average calculation.
Option B:
16 is correct as it is the result of the average calculation.
Option C:
6 is incorrect because it is not the result of the average calculation.
Option D:
4 is incorrect because it is not the result of the average calculation.
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Frequently Asked Questions
What is the arithmetic mean in the context of data interpretation?
The arithmetic mean, or average, is a measure of central tendency that represents the sum of all values divided by the total number of values. It provides a single value that summarizes the dataset.
How do you calculate the average monthly expenditure?
To calculate the average monthly expenditure, sum up the total expenditures for each month and then divide by the number of months. This gives you the average expenditure per month.
What skills are required to solve average-based data interpretation problems?
To solve average-based data interpretation problems, you need skills in addition, division, and understanding how to calculate the sum of values and divide by the number of values to find the average.
How can the concept of average be applied in real-life scenarios?
The concept of average can be applied in various real-life scenarios, such as calculating the average height of a group of people, determining the average grade in a class, or finding the average monthly expenditure for budgeting purposes.
What is the significance of the number of values in calculating the average?
The number of values is crucial in calculating the average because it determines the divisor in the calculation. Dividing the sum of values by the number of values gives the average, which represents the central tendency of the dataset.