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Unit Vii Data Interpretation
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Average Based Data Interpretation – Quiz 15
Average Based Data Interpretation Quiz 15 (10 MCQs)
This set of multiple-choice questions evaluates the understanding of arithmetic mean calculation, including the use of Excel functions for average calculations. It covers concepts such as summing values, division by count, and data interpretation. Students will practice calculating averages for various scenarios, including test scores, total cost, and weighted averages.
Quiz Instructions
Select an option to see the correct answer instantly.
1.
How do you find the average of two numbers?
A) Add them up and multiply by 2.
B) Add them up and subtract by 2.
C) Add them up and divide by 2.
D) Add them up and add 2 more.
Show Answer
Correct Answer:
Correct answer is: (C) Add them up and divide by 2.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
The average of two numbers is calculated by summing the numbers and then dividing by the count of the numbers.
Common Mistakes:
A common mistake is to add the numbers and then multiply by 2, which would result in a value that is twice the sum of the numbers, not the average.
Explanations:
To find the average of two numbers, you first add the two numbers together. Then, you divide the sum by the number of values, which is 2 in this case. This gives you the average value.
Option Analysis:
Option A:
Incorrect. Adding the numbers and multiplying by 2 does not give the average. It gives a value that is twice the sum of the numbers.
Option B:
Incorrect. Adding the numbers and subtracting by 2 does not give the average. It results in a value that is the sum of the numbers minus 2.
Option C:
Correct. Adding the numbers and dividing by 2 gives the average of the two numbers.
Option D:
Incorrect. Adding the numbers and adding 2 more does not give the average. It results in a value that is the sum of the numbers plus 2.
2.
The weights of three children is 34.2 Kg, 36.8 Kg and 40.9 Kg. Find the average weight
A) 37.0 Kg.
B) 33.3 Kg.
C) 37.3 Kg.
D) 40.2 Kg.
Show Answer
Correct Answer:
Correct answer is: (C) 37.3 Kg.
Exam Relevance:
SAT, GRE, GMAT, CAT
Difficulty:
Moderate
Concept notes:
The average weight of a group of individuals is calculated by summing their weights and dividing by the number of individuals.
Common Mistakes:
A common mistake is to incorrectly sum the weights or divide by the wrong number of individuals.
Explanations:
To find the average weight, we first sum the weights of the three children:
34.2 Kg + 36.8 Kg + 40.9 Kg = 111.9 Kg.
Next, we divide the total weight by the number of children, which is 3:
111.9 Kg / 3 = 37.3 Kg.
Thus, the average weight is 37.3 Kg.
Option Analysis:
Option A:
37.0 Kg is incorrect because the sum of the weights divided by 3 does not equal 37.0 Kg.
Option B:
33.3 Kg is incorrect because the sum of the weights divided by 3 does not equal 33.3 Kg.
Option C:
37.3 Kg is correct because the sum of the weights divided by 3 equals 37.3 Kg.
Option D:
40.2 Kg is incorrect because the sum of the weights divided by 3 does not equal 40.2 Kg.
3.
The formula of average is .....
A) Difference of quantities divided by no. of quantities.
B) Product of quantities divided by no. of quantities.
C) Sum of quantities divided by no. of quantities.
D) None of the above.
Show Answer
Correct Answer:
Correct answer is: (C) Sum of quantities divided by no. of quantities.
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 confuse the formula for average with other operations, such as finding the difference or product of the quantities.
Explanations:
The average is a measure of central tendency that represents the typical value of a set of numbers. It is calculated by summing all the quantities and then dividing by the number of quantities. This method ensures that the average reflects the overall distribution of the values.
Option Analysis:
Option A:
This option is incorrect because the average is not calculated by dividing the difference of quantities by the number of quantities.
Option B:
This option is incorrect because the average is not calculated by dividing the product of quantities by the number of quantities.
Option C:
This option is correct because the average is calculated by dividing the sum of quantities by the number of quantities.
Option D:
This option is incorrect because the correct formula for average is provided in option C.
4.
You own a jewelry company. The number of pieces made by each of your five employees last week are as follows: 18,23,22,19, and 23. On average, how many pieces of jewelry did your employees make?
A) 19.
B) 21.
C) 27.
D) 32.
E) 38.
Show Answer
Correct Answer:
Correct answer is: (B) 21.
Exam Relevance:
GMAT, GRE, SAT, ACT
Difficulty:
Easy
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 numbers.
Explanations:
To find the average number of pieces of jewelry made by the employees, we first sum the number of pieces made by each employee: 18 + 23 + 22 + 19 + 23 = 105. Next, we divide the sum by the number of employees, which is 5: 105 ÷ 5 = 21. Therefore, the average number of pieces of jewelry made by the employees is 21.
Option Analysis:
Option A:
19 is incorrect because it does not match the calculated average.
Option B:
21 is correct as it matches the calculated average.
Option C:
27 is incorrect because it does not match the calculated average.
Option D:
32 is incorrect because it does not match the calculated average.
Option E:
38 is incorrect because it does not match the calculated average.
5.
The average age of a group of 12 students is 20 years. If 4 more students join the group, the average age increases by 1 year. The average age of the new students is .....
A) 24.
B) 26.
C) 28.
D) 22.
Show Answer
Correct Answer:
Correct answer is: (A) 24.
Exam Relevance:
GMAT, GRE, SAT, ACT
Difficulty:
Moderate
Concept notes:
The problem involves calculating the average age of a group of students before and after new students join. The key is to use the formula for the average and understand how the addition of new members affects the overall average.
Common Mistakes:
A common mistake is to assume that the average age of the new students is simply the new overall average age. However, the new students' average age must be calculated based on the change in the overall average.
Explanations:
1. Calculate the total age of the original 12 students:
\[
\text{Total age of original students} = 12 \times 20 = 240 \text{ years}
\]
2. After 4 more students join, the total number of students is 16. The new average age is 21 years:
\[
\text{Total age of all 16 students} = 16 \times 21 = 336 \text{ years}
\]
3. Calculate the total age of the 4 new students:
\[
\text{Total age of new students} = 336 - 240 = 96 \text{ years}
\]
4. Calculate the average age of the 4 new students:
\[
\text{Average age of new students} = \frac{96}{4} = 24 \text{ years}
\]
Option Analysis:
Option A:
Correct. The average age of the new students is 24 years.
Option B:
Incorrect. The average age of the new students is not 26 years.
Option C:
Incorrect. The average age of the new students is not 28 years.
Option D:
Incorrect. The average age of the new students is not 22 years.
6.
Carlos earned $ 23, $ 29, $ 25, $ 16, and $ 17 in tips at each of the tables he served at a restaurant. What is the mean of the tips he received?
A) 23.
B) 110.
C) 22.
D) 25.
Show Answer
Correct Answer:
Correct answer is: (C) 22.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The mean 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 confuse the mean with the median or mode, or to miscalculate the sum or the count of the numbers.
Explanations:
To find the mean of the tips Carlos received, we first sum the amounts: $23 + $29 + $25 + $16 + $17 = $110. Next, we divide the total sum by the number of tips, which is 5. Therefore, the mean is $110 / 5 = $22.
Option Analysis:
Option A:
23 is incorrect because it is not the mean of the given values.
Option B:
110 is incorrect because it is the sum of the values, not the mean.
Option C:
22 is correct because it is the mean of the given values.
Option D:
25 is incorrect because it is not the mean of the given values.
7.
The last four times that Jimmy filled up his tank of gas, the average price per gallon of gas was $ 3.05. If the average price stays drops to $ 2.50 the next two times that Jimmy fills up his tank, then what would the average price per gallon for all of the trips be?
A) $ 2.83.
B) $ 2.78.
C) $ 2.87.
D) $ 3.44.
Show Answer
Correct Answer:
Correct answer is: (C) $ 2.87.
Exam Relevance:
GMAT, GRE, SAT, ACT
Difficulty:
Moderate
Concept notes:
The question involves calculating the average price per gallon of gas over multiple trips. The key concept is to find the weighted average of the prices over all trips.
Common Mistakes:
A common mistake is to simply average the two given average prices, which does not account for the number of trips.
Explanations:
To find the average price per gallon for all six trips, we need to calculate the total cost of gas over all trips and divide by the total number of gallons.
1. Calculate the total cost for the first four trips:
\[
\text{Total cost for first four trips} = 4 \times 3.05 = 12.20
\]
2. Calculate the total cost for the next two trips:
\[
\text{Total cost for next two trips} = 2 \times 2.50 = 5.00
\]
3. Calculate the total cost for all six trips:
\[
\text{Total cost for all six trips} = 12.20 + 5.00 = 17.20
\]
4. Calculate the total number of gallons for all six trips:
\[
\text{Total number of gallons} = 4 + 2 = 6
\]
5. Calculate the average price per gallon for all six trips:
\[
\text{Average price per gallon} = \frac{17.20}{6} = 2.8667 \approx 2.87
\]
Thus, the average price per gallon for all six trips is $2.87.
Option Analysis:
Option A:
$2.83 is incorrect because it does not account for the weighted average correctly.
Option B:
$2.78 is incorrect because it does not account for the weighted average correctly.
Option C:
$2.87 is correct as it accurately reflects the weighted average price per gallon.
Option D:
$3.44 is incorrect because it is too high and does not account for the lower prices in the last two trips.
8.
Which formula will calculate the average of data in a given range?
A) AVEDATA.
B) AVERAGE.
C) AVERAGEIF.
D) AVERAGING.
Show Answer
Correct Answer:
Correct answer is: (B) AVERAGE.
Exam Relevance:
GMAT, GRE, Excel Certification
Difficulty:
Easy
Concept notes:
The AVERAGE function calculates the arithmetic mean of a range of numbers.
Common Mistakes:
A common mistake is to confuse AVERAGE with other similar functions like AVERAGEIF, which calculates the average of a range based on a specific condition.
Explanations:
The AVERAGE function is used to calculate the arithmetic mean of a range of numbers. It sums all the values in the range and then divides by the count of the numbers. This is the standard method for finding the average of a dataset.
Option Analysis:
Option A:
AVEDATA is not a valid Excel function.
Option B:
AVERAGE is the correct function to calculate the arithmetic mean of a range of numbers.
Option C:
AVERAGEIF is used to calculate the average of a range based on a specific condition, not just the average of a range.
Option D:
AVERAGING is not a valid Excel function.
9.
Hannah has scored the following number of points in the last five games: 2, 57, 38, 42, 6. What is her average over those games?
A) 29.
B) 38.
C) 50.
D) 145.
Show Answer
Correct Answer:
Correct answer is: (A) 29.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
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 confuse the average with the median or mode, or to miscalculate the sum or the count of the numbers.
Explanations:
To find the average, we first sum the points scored in the five games: 2 + 57 + 38 + 42 + 6 = 145. Next, we divide the sum by the number of games, which is 5. Therefore, the average is 145 / 5 = 29.
Option Analysis:
Option A:
Correct. The average is 29.
Option B:
Incorrect. 38 is one of the scores but not the average.
Option C:
Incorrect. 50 is not the average of the scores.
Option D:
Incorrect. 145 is the sum of the scores, not the average.
10.
Paulo got these markers in three tests: 72, 80 and 82. He had one more test to sit. He wanted an average of 80 for the four tests. What mark must he get in the fourth test?
A) 78.
B) 80.
C) 84.
D) 86.
Show Answer
Correct Answer:
Correct answer is: (D) 86.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
To find the required score for the fourth test, we need to calculate the total score needed to achieve an average of 80 over four tests.
Common Mistakes:
A common mistake is to assume that the average of the first three tests should be the same as the required average, leading to incorrect calculations.
Explanations:
1. Calculate the total score needed for an average of 80 over four tests:
\[
\text{Total score needed} = 80 \times 4 = 320
\]
2. Calculate the sum of the scores from the first three tests:
\[
\text{Sum of first three tests} = 72 + 80 + 82 = 234
\]
3. Determine the score needed on the fourth test:
\[
\text{Score needed on fourth test} = 320 - 234 = 86
\]
Option Analysis:
Option A:
78 is incorrect because it does not result in an average of 80.
Option B:
80 is incorrect because it does not result in an average of 80.
Option C:
84 is incorrect because it does not result in an average of 80.
Option D:
86 is correct because it results in an average of 80.
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Frequently Asked Questions
What is the arithmetic mean?
The arithmetic mean is the sum of a set of numbers divided by the count of those numbers, representing the average value.
How is the average age calculated?
The average age is calculated by summing the ages of all individuals and then dividing by the number of individuals.
What is the purpose of data interpretation in this context?
Data interpretation helps in understanding and analyzing numerical data to derive meaningful insights and conclusions.
How can the average function in Excel be used?
The average function in Excel calculates the arithmetic mean of a range of cells, simplifying the process of finding averages.
What is the difference between mean and weighted average?
The mean is the sum of all values divided by the number of values, while a weighted average takes into account the relative importance of each value.