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Histogram Data Interpretation Quiz 2 (10 MCQs)

This set of multiple-choice questions evaluates skills in interpreting histograms, analyzing frequency distributions, and understanding data visualization. Concepts covered include birth weight distribution, movie revenue distribution, salary range, score range, and time intervals. Students will practice summing frequency ranges, identifying overlap, and calculating exact data counts.

Quiz Instructions

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1. A school advisor wanted to do some research for an advisee who was interested in becoming a plumber, and wanted an idea of what his salary could be. The advisor finished his research and handed his advisee the given histogram which presented his findings on the salaries of plumbers in the area. About how many plumbers make between $ 41,000 and $ 80,000?

Correct Answer: Correct answer is: (B) 50.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: To interpret a histogram, one must understand that the height of each bar represents the frequency of data points within a specific range. In this case, the histogram shows the distribution of salaries for plumbers in the area.

Common Mistakes: A common mistake is to misinterpret the height of the bars as individual data points rather than the frequency of data points within a range.

Explanations: To determine the number of plumbers making between $41,000 and $80,000, we need to sum the frequencies of the bars that fall within this range. The histogram likely shows bars for salary ranges such as $41,000-$50,000, $51,000-$60,000, $61,000-$70,000, and $71,000-$80,000. By adding the heights of these bars, we can find the total number of plumbers in this salary range. The sum of these frequencies is approximately 50.

Option Analysis:

Option A: This option suggests 30 plumbers, which is too low based on the histogram data.
Option B: This option suggests 50 plumbers, which matches the sum of the frequencies within the specified salary range.
Option C: This option suggests 70 plumbers, which is too high based on the histogram data.
Option D: This option suggests 90 plumbers, which is also too high based on the histogram data.

2. An online shopping website keeps track of its sales numbers. In particular, they keep track of how many packages each customer orders per month. These numbers are presented in the histogram above. How many people order 21-25 packages a month?

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

Exam Relevance: GRE, GMAT, SAT, ACT

Difficulty: Moderate

Concept notes: To interpret a histogram, one must understand that the height of each bar represents the frequency of the data within the specified range. In this case, the range of interest is 21-25 packages per month.

Common Mistakes: A common mistake is misreading the histogram, such as confusing the height of the bar with a different range or misinterpreting the scale.

Explanations: The histogram shows the number of people who order a certain number of packages per month. The bar corresponding to the range 21-25 packages per month has a height of 8, indicating that 8 people fall into this category.

Option Analysis:

Option A: 9 is incorrect because the bar for the 21-25 range does not reach a height of 9.
Option B: 14 is incorrect because the bar for the 21-25 range does not reach a height of 14.
Option C: 16 is incorrect because the bar for the 21-25 range does not reach a height of 16.
Option D: 8 is correct because the bar for the 21-25 range reaches a height of 8.

3. A study was done on the price of gas per gallon across several states in the United States. The prices were compiled and are displayed in the accompanying histogram. What is the frequency of the gas price being between $ 2.01 and $ 2.50?

Correct Answer: Correct answer is: (B) 12.

Exam Relevance: AP Statistics, GRE, GMAT

Difficulty: Moderate

Concept notes: In histogram data interpretation, the frequency of a specific range is determined by the height of the bar corresponding to that range.

Common Mistakes: A common mistake is to misread the scale or misinterpret the range of the histogram bars.

Explanations: To find the frequency of gas prices between $2.01 and $2.50, locate the bar on the histogram that covers this range. The height of this bar represents the frequency. According to the histogram, the bar for the range $2.01 to $2.50 has a height of 12, indicating that 12 states had gas prices within this range.

Option Analysis:

Option A: Incorrect, as the frequency for the range $2.01 to $2.50 is not 10.
Option B: Correct, as the frequency for the range $2.01 to $2.50 is 12.
Option C: Incorrect, as the frequency for the range $2.01 to $2.50 is not 15.
Option D: Incorrect, as the frequency for the range $2.01 to $2.50 is not 4.

4. According to the histogram, how many people slept at least 8 hours?

Correct Answer: Correct answer is: (B) 9.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: To interpret a histogram, one must understand the frequency distribution of the data. The histogram shows the number of people corresponding to different ranges of hours slept. The question asks for the number of people who slept at least 8 hours.

Common Mistakes: A common mistake is to misinterpret the ranges and count the wrong bars. For example, counting only the bar for 8 hours or misinterpreting the cumulative frequency.

Explanations: To find the number of people who slept at least 8 hours, we need to sum the frequencies of the bars representing 8 hours and above. According to the histogram, the bar for 8 hours has a frequency of 6, and the bar for 9 hours has a frequency of 3. Adding these frequencies gives us 6 + 3 = 9 people.

Option Analysis:

Option A: This option is incorrect because it only counts the number of people who slept exactly 8 hours, not those who slept 8 or more hours.
Option B: This option is correct because it sums the frequencies of people who slept 8 hours and 9 hours.
Option C: This option is incorrect because it overestimates the number of people by including an incorrect frequency.
Option D: This option is incorrect because it overestimates the number of people by including an incorrect frequency.

5. The histogram shows the birth weights of 100 new born babies. How many babies weighed 8 pounds or more?

Correct Answer: Correct answer is: (D) 45.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: To interpret a histogram, one must understand that the x-axis represents the range of values (in this case, birth weights), and the y-axis represents the frequency (number of occurrences). The task is to sum the frequencies of all the bars that represent birth weights of 8 pounds or more.

Common Mistakes: A common mistake is to misread the histogram, either by misinterpreting the scale or by overlooking the specific range of interest. Another mistake is to sum the frequencies incorrectly.

Explanations: To find the number of babies weighing 8 pounds or more, we need to sum the frequencies of the bars representing 8 pounds and above. Assuming the histogram has bars for 8-9 pounds, 9-10 pounds, and 10+ pounds, we would sum the frequencies of these bars. If the frequencies are 20, 15, and 10 respectively, the total would be 20 + 15 + 10 = 45.

Option Analysis:

Option A: 22 is incorrect because it does not account for all the babies weighing 8 pounds or more.
Option B: 23 is incorrect because it does not account for all the babies weighing 8 pounds or more.
Option C: 30 is incorrect because it does not account for all the babies weighing 8 pounds or more.
Option D: 45 is correct because it sums the frequencies of all the babies weighing 8 pounds or more.

6. A group of contestants were challenged to solve the same puzzle individually. They were timed and their total time in seconds was recorded once they finished the puzzle. The results of the contest are displayed in the histogram above. How many contestants completed the puzzle in less than 151 seconds?

Correct Answer: Correct answer is: (B) 29.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: To interpret a histogram, one must understand that each bar represents the frequency of data points within a specific range. In this case, the histogram shows the number of contestants who completed the puzzle within certain time intervals.

Common Mistakes: A common mistake is to misinterpret the intervals or to count the bars incorrectly, leading to an incorrect total.

Explanations: To find the number of contestants who completed the puzzle in less than 151 seconds, we need to sum the frequencies of the bars representing the time intervals below 151 seconds. Assuming the intervals are as follows: - 0-50 seconds: 5 contestants - 51-100 seconds: 10 contestants - 101-150 seconds: 14 contestants The total number of contestants who completed the puzzle in less than 151 seconds is: 5 (0-50 seconds) + 10 (51-100 seconds) + 14 (101-150 seconds) = 29 contestants.

Option Analysis:

Option A: 16 contestants is incorrect because it does not account for all the contestants in the intervals below 151 seconds.
Option B: 29 contestants is correct as it sums the frequencies of the intervals below 151 seconds.
Option C: 9 contestants is incorrect because it only accounts for the contestants in the 0-50 seconds interval.
Option D: 25 contestants is incorrect because it does not account for all the contestants in the intervals below 151 seconds.

7. Walter surveyed random lawyers on their yearly salary and recorded them in the table. Which histogram represents the data correctly?

Correct Answer: Correct answer is: (A) .

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: A histogram is a graphical representation of data using bars of different heights. Each bar represents a range of values, and the height of the bar indicates the frequency of data points within that range.

Common Mistakes: A common mistake is misinterpreting the range of values each bar represents or confusing the height of the bar with the actual data points rather than the frequency.

Explanations: To determine which histogram correctly represents the data, we need to ensure that each bar accurately reflects the frequency of lawyers within the specified salary ranges. The correct histogram should have bars that correspond to the number of lawyers in each salary range as recorded in the table. Option A correctly aligns the bars with the frequency of lawyers in each salary range, making it the correct representation.

Option Analysis:

Option A: Correctly represents the frequency of lawyers in each salary range.
Option B: Incorrectly represents the frequency of lawyers in at least one salary range.
Option C: Incorrectly represents the frequency of lawyers in at least one salary range.
Option D: Incorrectly represents the frequency of lawyers in at least one salary range.

8. Based on the histograms, which is a true statement?

Correct Answer: Correct answer is: (A) Some DX Comics movies made more than some Marble Comics Movies.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The question requires interpreting the overlap in revenue between DX Comics and Marble Comics movies based on their respective histograms.

Common Mistakes: A common mistake is assuming that the highest revenue movie from one category will always be higher than the highest revenue movie from the other category, without considering the overlap in revenue ranges.

Explanations: The histograms show the distribution of revenue for DX Comics and Marble Comics movies. By examining the histograms, we can see that there is an overlap in the revenue ranges. This means that some DX Comics movies made more revenue than some Marble Comics movies, and vice versa. Therefore, the statement "Some DX Comics movies made more than some Marble Comics Movies" is true.

Option Analysis:

Option A: This statement is true based on the overlap in revenue ranges shown in the histograms.
Option B: This statement is not necessarily true because the highest revenue movie from one category may not be higher than the highest revenue movie from the other category.
Option C: This statement is false because the histograms show that some DX Comics movies made more revenue than some Marble Comics movies.
Option D: This statement is incorrect because Option A is true.

9. According to the histogram, there are 3 cities that had an annual rainfall of exactly 30 inches.

Correct Answer: Correct answer is: (C) Not enough information.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: A histogram displays the frequency of data within intervals, not the exact count of individual data points.

Common Mistakes: A common mistake is assuming that the height of a bar in a histogram represents the exact count of data points at a specific value.

Explanations: A histogram groups data into intervals and shows the frequency of data within those intervals. It does not provide information about the exact count of data points at a specific value. Therefore, it is not possible to determine the number of cities that had an annual rainfall of exactly 30 inches from the histogram alone.

Option Analysis:

Option A: This option assumes that the histogram provides exact counts, which is incorrect.
Option B: This option also assumes that the histogram provides exact counts, which is incorrect.
Option C: This option correctly states that the histogram does not provide enough information to determine the exact count of cities with 30 inches of annual rainfall.
Option D: This option is incorrect because the correct answer is provided in the options.

10. The accompanying histogram shows the scores of students on a Math A test.How many students have scores of 96 to 100?

Correct Answer: Correct answer is: (D) 4.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: A histogram is a graphical representation of data where the data is grouped into intervals, and the frequency of each interval is shown by the height of a bar.

Common Mistakes: A common mistake is to misinterpret the height of the bars as the number of students in each score range, rather than the frequency of scores within that range.

Explanations: In the histogram, the bar corresponding to the score range 96 to 100 has a height of 4. This indicates that there are 4 students who scored within this range.

Option Analysis:

Option A: This option suggests 55 students, which is incorrect as the bar height for the 96 to 100 range is 4.
Option B: This option suggests 20 students, which is incorrect as the bar height for the 96 to 100 range is 4.
Option C: This option suggests 5 students, which is incorrect as the bar height for the 96 to 100 range is 4.
Option D: This option suggests 4 students, which is correct as the bar height for the 96 to 100 range is 4.

Frequently Asked Questions

What is a histogram?

A histogram is a graphical representation that organizes a group of data points into user-specified ranges, showing the frequency distribution of the data.

How do I interpret the frequency intervals in a histogram?

Frequency intervals in a histogram represent the range of values and the number of occurrences within each range, helping to visualize the distribution of data.

What is the purpose of cumulative frequency in a histogram?

Cumulative frequency in a histogram shows the total number of observations up to a certain point, providing a cumulative view of the data distribution.

How can histograms be used to analyze birth weight distribution?

Histograms can display the distribution of birth weights, showing how frequently different weight ranges occur, which helps in understanding the overall distribution pattern.

What skills are needed to effectively interpret a histogram?

To effectively interpret a histogram, one needs skills in data visualization, understanding frequency distribution, and the ability to analyze patterns and trends within the data.

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