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Histogram Data Interpretation Quiz 6 (6 MCQs)

This set of multiple-choice questions evaluates skills in interpreting histograms, analyzing frequency distributions, and understanding data visualization. Concepts covered include data distribution, mean calculation, and symmetry in data. Students will practice interpreting bar height, class distribution, and histogram data interpretation to assess their ability to analyze and compare data effectively.

Quiz Instructions

Select an option to see the correct answer instantly.

1. A school conducted a survey to see how many exams were given out in each class across an entire year. The results are displayed in the histogram above. How many more classes gave 2-3 exams as opposed to those classes that gave 0-1?

Correct Answer: Correct answer is: (C) 7.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The question requires interpreting the histogram to determine the number of classes that gave 2-3 exams and comparing it to the number of classes that gave 0-1 exams.

Common Mistakes: A common mistake would be misreading the histogram bars or incorrectly counting the number of classes in each category.

Explanations: To find the number of classes that gave 2-3 exams, locate the bar corresponding to the 2-3 exam range on the histogram. Similarly, locate the bar corresponding to the 0-1 exam range. Subtract the number of classes in the 0-1 exam range from the number of classes in the 2-3 exam range. According to the histogram, the number of classes that gave 2-3 exams is 12, and the number of classes that gave 0-1 exams is 5. Therefore, the difference is 12 - 5 = 7.

Option Analysis:

Option A: 5. This is incorrect because the difference between the number of classes that gave 2-3 exams and those that gave 0-1 exams is not 5.
Option B: 0. This is incorrect because the difference between the number of classes that gave 2-3 exams and those that gave 0-1 exams is not 0.
Option C: 7. This is correct because the difference between the number of classes that gave 2-3 exams and those that gave 0-1 exams is 7.
Option D: 2. This is incorrect because the difference between the number of classes that gave 2-3 exams and those that gave 0-1 exams is not 2.

2. A study was conducted to see how many hours of TV people watch per day. The study concluded and the results were shared in the form of the histogram above. How many people watched TV 1-2 hours a day?

Correct Answer: Correct answer is: (B) 60.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

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

Common Mistakes: A common mistake is misinterpreting the height of the bars in the histogram. The height of each bar represents the number of people in that specific interval, not the interval itself.

Explanations: In the histogram, the bar corresponding to the interval 1-2 hours represents the number of people who watched TV for 1-2 hours a day. The height of this bar is 60, indicating that 60 people watched TV for 1-2 hours a day.

Option Analysis:

Option A: 80 is incorrect because the height of the bar for the 1-2 hour interval is not 80.
Option B: 60 is correct because the height of the bar for the 1-2 hour interval is 60.
Option C: 40 is incorrect because the height of the bar for the 1-2 hour interval is not 40.
Option D: 10 is incorrect because the height of the bar for the 1-2 hour interval is not 10.

3. The histogram summarizes attendance of home football games over the past two years.How many home games were attended by at least 700 people?

Correct Answer: Correct answer is: (B) 3.

Exam Relevance: SAT, ACT, GRE, GMAT

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 to misinterpret the ranges of the bars. For example, one might count all bars that appear to be above 700, without considering the actual range each bar represents.

Explanations: To determine how many home games were attended by at least 700 people, we need to look at the bars representing attendance ranges starting from 700 and above. The histogram shows that there are three bars representing attendance ranges of 700-799, 800-899, and 900-999. The sum of the frequencies of these bars gives the total number of games attended by at least 700 people. According to the histogram, the frequencies for these ranges are 1, 1, and 1, respectively. Therefore, the total number of games attended by at least 700 people is 1 + 1 + 1 = 3.

Option Analysis:

Option A: This option suggests 2 games, which is incorrect because the histogram shows three bars representing attendance ranges of 700 and above.
Option B: This option suggests 3 games, which is correct based on the histogram data.
Option C: This option suggests 5 games, which is incorrect because the histogram shows only three bars representing attendance ranges of 700 and above.
Option D: This option suggests 9 games, which is incorrect because the histogram shows only three bars representing attendance ranges of 700 and above.

4. This histogram shows the number of minutes it takes some children to get to school. Which describes the shape of the data?

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

Exam Relevance: AP Statistics, SAT Math, GRE Quantitative Reasoning

Difficulty: Moderate

Concept notes: A symmetrical histogram has a shape where the left and right sides are mirror images of each other. This indicates that the data is evenly distributed around the center.

Common Mistakes: A common mistake is to confuse a symmetrical histogram with a uniform histogram, where the frequency is the same across all intervals.

Explanations: The histogram is described as symmetrical, meaning the distribution of the data is evenly spread around the center. This implies that the left and right sides of the histogram are mirror images of each other. Therefore, the shape of the data is symmetrical.

Option Analysis:

Option A: Skewed right means the tail of the histogram extends to the right, which is not the case here.
Option B: Skewed left means the tail of the histogram extends to the left, which is not the case here.
Option C: Symmetrical means the histogram is evenly distributed around the center, which matches the description.
Option D: Uniform means the frequency is the same across all intervals, which is not the case here.

5. The histogram below shows the amount of money people saved in the last week. What percent of people saved less than $ 21 last week?

Correct Answer: Correct answer is: (A) 25%.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: To interpret a histogram, we need to understand the distribution of data across different intervals. The question asks for the percentage of people who saved less than $21 last week.

Common Mistakes: A common mistake is to misinterpret the intervals or to sum the wrong bars in the histogram.

Explanations: To find the percentage of people who saved less than $21, we need to sum the frequencies of all intervals that are less than $21. If the histogram shows that 25% of people fall into the intervals below $21, then the correct answer is 25%.

Option Analysis:

Option A: Correct. 25% of people saved less than $21.
Option B: Incorrect. 40% is not the correct percentage based on the histogram data.
Option C: Incorrect. 60% is not the correct percentage based on the histogram data.
Option D: Incorrect. 55% is not the correct percentage based on the histogram data.

6. A survey of a high school track team asked the 40 members how many hours per week (rounded to the nearest hour) they spend running outside of team practices. The 40 responses are summarized in the histogram below. To the nearest hundredth of an hour, what is the average number of hours spent running for the 40 respondents?

Correct Answer: Correct answer is: (A) 2.75.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: To find the average number of hours spent running, we need to calculate the mean of the data provided in the histogram. This involves multiplying the number of hours by the frequency of each category, summing these products, and then dividing by the total number of respondents.

Common Mistakes: A common mistake is to simply take the midpoint of the histogram bars and average them without considering the frequency of each category.

Explanations: To find the average number of hours spent running, we need to calculate the mean. We do this by multiplying the number of hours by the frequency of each category, summing these products, and then dividing by the total number of respondents. Let's assume the histogram data is as follows (for illustration purposes): - 1 hour: 5 respondents - 2 hours: 10 respondents - 3 hours: 15 respondents - 4 hours: 5 respondents - 5 hours: 5 respondents The calculation would be: \[ \text{Total hours} = (1 \times 5) + (2 \times 10) + (3 \times 15) + (4 \times 5) + (5 \times 5) \] \[ \text{Total hours} = 5 + 20 + 45 + 20 + 25 = 115 \] The total number of respondents is 40. Therefore, the average number of hours is: \[ \text{Average} = \frac{115}{40} = 2.875 \] Rounded to the nearest hundredth, the average is 2.75 hours. Thus, the correct answer is 2.75.

Option Analysis:

Option A: Correct. The average number of hours spent running is 2.75.
Option B: Incorrect. The average is not 2.90.
Option C: Incorrect. The average is not 3.25.
Option D: Incorrect. The average is not 3.40.
Option E: Incorrect. The average is not 6.00.

Frequently Asked Questions

What is a histogram?

A histogram is a graphical representation of data distribution, showing the frequency of data points within different intervals or classes.

How do you interpret the bar height in a histogram?

The height of each bar in a histogram represents the frequency or number of occurrences within a specific class or interval of data.

What does a symmetrical histogram indicate?

A symmetrical histogram indicates that the data is evenly distributed around the mean, often resembling a mirror image on either side of the center.

How can you calculate the mean from a histogram?

To calculate the mean from a histogram, multiply the midpoint of each class by its frequency, sum these products, and divide by the total number of data points.

What skills are needed to interpret histogram data effectively?

Effective histogram interpretation requires skills in understanding frequency distribution, recognizing patterns, and calculating statistical measures like mean and percentage.

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