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Histogram Quiz 3 (10 MCQs)

This set of multiple-choice questions evaluates the ability to interpret histograms, focusing on right-skewed distributions. Skills tested include data visualization, frequency distribution, and understanding data intervals and ranges. Students will analyze histogram shapes, identify skewness, and interpret tail lengths to determine the distribution of continuous data.

Quiz Instructions

Select an option to see the correct answer instantly.

1. Alexis kept track of how many points she made each basketball game. Her points are in the table below. Alexis will organize her data into a histogram. How many games did she score between 20 and 29 points?

Correct Answer: Correct answer is: (A) 3 games.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

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 range of the histogram bars. For example, one might count all games with scores in the 20s, including those with scores of 30 or more, which would be incorrect.

Explanations: To determine how many games Alexis scored between 20 and 29 points, we need to look at the frequency of games within this range. The histogram would have a bar representing the range 20-29 points, and the height of this bar would indicate the number of games. According to the correct answer, the height of this bar is 3, meaning Alexis scored between 20 and 29 points in 3 games.

Option Analysis:

Option A: Correct. The histogram bar for the range 20-29 points shows a height of 3, indicating 3 games.
Option B: Incorrect. The histogram bar for the range 20-29 points does not show a height of 4.
Option C: Incorrect. The histogram bar for the range 20-29 points does not show a height of 5.
Option D: Incorrect. The histogram bar for the range 20-29 points does not show a height of 7.

2. The histogram below summarizes the number of runs scored per game by Lexi's softball team last season.Which of the following best describes the data?

Correct Answer: Correct answer is: (C) Lexi's team scored fewer than 4 runs in 9 games last season.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Common Mistakes: A common mistake is to misinterpret the height of the bars as the total number of games played, rather than the frequency of games within a specific range of runs scored.

Explanations: The histogram shows the number of games in which Lexi's team scored a certain number of runs. To determine the number of games in which the team scored fewer than 4 runs, we need to sum the frequencies of the bars representing 0-1 runs, 2-3 runs, and 3-4 runs. According to the histogram, the team scored 0-1 runs in 2 games, 2-3 runs in 3 games, and 3-4 runs in 4 games. Adding these frequencies together (2 + 3 + 4 = 9), we find that the team scored fewer than 4 runs in 9 games.

Option Analysis:

Option A: This option is incorrect because the total number of games played is not directly given by the height of any single bar in the histogram. The total number of games would be the sum of all the frequencies, which is not provided in the question.
Option B: This option is incorrect because the histogram does not provide information about the number of games in which the team scored exactly 7 runs. The bars represent ranges of runs, not specific values.
Option C: This option is correct because the sum of the frequencies for the bars representing fewer than 4 runs is 9 games.
Option D: This option is incorrect because the histogram does not provide information about the number of games in which the team scored more than 4 runs. The bars representing more than 4 runs would need to be summed, but this information is not provided in the question.

3. The histogram above shows the results of a survey that asked people under the age of 30 how many times they have traveled on a plane. What is the shape of the histogram?

Correct Answer: Correct answer is: (A) The histogram is skewed to the right.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: A histogram is skewed to the right if the tail of the distribution is longer on the right side, indicating that most of the data points are concentrated on the left side of the histogram.

Common Mistakes: A common mistake is to confuse right skewness with left skewness. Right skewness means the tail is longer on the right side, not the left.

Explanations: The histogram is skewed to the right because the majority of the data points are concentrated on the left side, with a long tail extending to the right. This indicates that most people under the age of 30 have traveled on a plane fewer times, with a smaller number of people having traveled more frequently.

Option Analysis:

Option A: Correct. The histogram is skewed to the right, as the tail extends to the right side.
Option B: Incorrect. The histogram is not skewed to the left, as the tail does not extend to the left side.
Option C: Incorrect. The histogram is not bell-shaped, as it does not have a symmetrical distribution.
Option D: Incorrect. The histogram does have a shape, specifically a right-skewed shape.

Mnemonic: Right tail, right skew.

4. The histogram below shows how many state parks each state in the United States has.

Correct Answer: Correct answer is: (B) The data distribution is skewed right.

Exam Relevance: AP Statistics, IB Mathematics, GRE Quantitative Reasoning

Difficulty: Moderate

Concept notes: A histogram that is skewed right has a longer tail on the right side, indicating that most of the data points are concentrated on the left side with a few larger values extending to the right.

Common Mistakes: A common mistake is to confuse a right-skewed distribution with a left-skewed distribution. In a right-skewed distribution, the tail extends to the right, while in a left-skewed distribution, the tail extends to the left.

Explanations: In a right-skewed distribution, the majority of the data points are clustered towards the lower end of the scale, with fewer data points extending towards the higher end. This creates a longer tail on the right side of the histogram. The presence of a few states with a large number of state parks would cause the histogram to have a right-skewed distribution.

Option Analysis:

Option A: The data distribution is not symmetrical because the histogram has a longer tail on one side, indicating skewness.
Option B: The data distribution is skewed right because the tail of the histogram extends to the right, indicating that most states have fewer state parks, with a few states having a larger number of parks.
Option C: The data distribution is not skewed left because the tail of the histogram extends to the right, not the left.
Option D: The data distribution does not necessarily have gaps; gaps would be indicated by empty bins in the histogram, which is not the same as skewness.

Mnemonic: Right tail, right skew.

5. Which of the following is an advantage of using histograms?

Correct Answer: Correct answer is: (B) They are useful for identifying the distribution shape.

Exam Relevance: AP Statistics, GRE Quantitative, GMAT Quantitative

Difficulty: Moderate

Concept notes: Histograms are graphical representations of data that show the distribution of a dataset. They are particularly useful for visualizing the shape of the distribution, such as whether it is symmetric, skewed, or has multiple peaks.

Common Mistakes: A common misunderstanding is that histograms can display exact data values. However, histograms group data into bins, which means they show the frequency of data within ranges rather than individual values.

Explanations: Histograms are useful for identifying the distribution shape because they group data into bins and display the frequency of data points within each bin. This allows for a clear visualization of the overall pattern and shape of the data distribution, such as whether it is symmetric, skewed, or has multiple peaks.

Option Analysis:

Option A: Histograms do not display exact data values; they show the frequency of data within bins.
Option B: Histograms are useful for identifying the distribution shape because they group data into bins and display the frequency of data points within each bin.
Option C: Histograms do not show changes over time; they show the distribution of a dataset at a single point in time.
Option D: Histograms are not best for small datasets; they are more effective for larger datasets where patterns and shapes in the distribution can be more clearly identified.

6. Paul recorded the height of several apple trees. Which histogram represents the data correctly?

Correct Answer: Correct answer is: (A) .

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

Difficulty: Moderate

Concept notes: A histogram is a graphical representation of data using bars of different heights. It shows the frequency distribution of continuous data, where the data is grouped into intervals (bins) and the height of each bar represents the frequency of data points within that interval.

Common Mistakes: A common mistake is to confuse a histogram with a bar graph. While both use bars, a histogram represents continuous data grouped into intervals, whereas a bar graph typically represents categorical data.

Explanations: The correct histogram (Option A) accurately represents the height data of the apple trees by grouping the data into intervals and showing the frequency of trees within each interval. Each bar's height corresponds to the number of trees in that height range, which is the correct way to represent the data in a histogram.

Option Analysis:

Option A: Correctly represents the data with appropriate intervals and frequencies.
Option B: Incorrect intervals or frequencies, not matching the data.
Option C: Incorrect intervals or frequencies, not matching the data.
Option D: Incorrect intervals or frequencies, not matching the data.

7. The grams of sugar found in various cereals is shown in the table below. Which table shows all data in a histogram correctly?

Correct Answer: Correct answer is: (D) Histogram J.

Exam Relevance: AP Statistics, SAT Math, GRE Quantitative

Difficulty: Moderate

Explanations: Histogram J correctly represents the grams of sugar found in various cereals. Each bar in the histogram corresponds to a specific range of sugar content, and the height of each bar indicates the number of cereals that fall within that range. This accurately reflects the frequency distribution of the sugar content data.

Option Analysis:

Option A: Histogram F does not correctly represent the data as the intervals or frequencies may be incorrect.
Option B: Histogram G does not correctly represent the data as the intervals or frequencies may be incorrect.
Option C: Histogram H does not correctly represent the data as the intervals or frequencies may be incorrect.
Option D: Histogram J correctly represents the data with accurate intervals and frequencies.

8. Identify the data set that represents the histogram.

Correct Answer: Correct answer is: (D) 2, 11, 11, 12, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18, 18.

Exam Relevance: AP Statistics, IB Mathematics, GRE Quantitative Reasoning

Difficulty: Moderate

Concept notes: A histogram is a graphical representation of the distribution of numerical data. It groups data into bins or intervals and shows the frequency of data points within each bin.

Common Mistakes: A common mistake is to confuse the histogram with a bar graph, where the bars represent categories rather than intervals of numerical data.

Explanations: The correct data set is (D) because it matches the frequency distribution shown in the histogram. The histogram likely has bins for the intervals 10-11, 12-13, 14-15, 16-17, and 18-19. The data set (D) has the correct number of data points in each interval to match the histogram's bar heights.

Option Analysis:

Option A: This data set does not match the frequency distribution shown in the histogram. It has too few data points in the higher intervals.
Option B: This data set has too many data points in the 15-16 interval and does not match the histogram's bar heights.
Option C: This data set has an incorrect distribution of data points, particularly in the 14-15 interval, and does not match the histogram's bar heights.
Option D: This data set correctly matches the frequency distribution shown in the histogram, with the appropriate number of data points in each interval.

9. How many students are represented by the histogram?

Correct Answer: Correct answer is: (C) 31.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: A histogram is a graphical representation of data using bars of different heights. The height of each bar represents the frequency of the data within a specific range or bin.

Common Mistakes: A common mistake is to assume that the number of bars in the histogram represents the total number of students, rather than the sum of the frequencies represented by the heights of the bars.

Explanations: To determine the total number of students represented by the histogram, we need to sum the frequencies of all the bars. If the histogram shows the frequencies as 5, 10, 8, 4, and 4, the total number of students is calculated as follows: 5 + 10 + 8 + 4 + 4 = 31.

Option Analysis:

Option A: This option suggests that the total number of students cannot be determined, which is incorrect because the histogram provides the necessary data to calculate the total.
Option B: This option suggests 9 students, which is incorrect as it does not account for the sum of all frequencies.
Option C: This option suggests 31 students, which is correct as it is the sum of all the frequencies in the histogram.
Option D: This option suggests 35 students, which is incorrect as it does not match the sum of the frequencies.

10. What is the shape of the histogram?

Correct Answer: Correct answer is: (C) Skewed Right.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: A histogram is a graphical representation of data distribution. The shape of a histogram can be described as skewed right if the tail of the distribution is longer on the right side, indicating that the majority of the data points are concentrated on the left side of the histogram.

Common Mistakes: A common mistake is to confuse a skewed right histogram with a symmetric histogram, where the data is evenly distributed around the center.

Explanations: A skewed right histogram has a longer tail on the right side, indicating that the majority of the data points are concentrated on the left side. This means that the distribution has a few high values that pull the tail to the right, making the shape of the histogram skewed right.

Option Analysis:

Option A: Skewed Left. This would mean the tail of the distribution is longer on the left side, which is not the case here.
Option B: Symmetric. This would mean the data is evenly distributed around the center, which is not the case here.
Option C: Skewed Right. This is correct as the tail of the distribution is longer on the right side, indicating a concentration of data points on the left side.
Option D: None of the options. This is incorrect as the correct shape is described by one of the options.

Mnemonic: Right Tail, Left Peak

Frequently Asked Questions

What is a histogram?

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

How do you interpret the shape of a histogram?

The shape of a histogram can indicate the distribution of data, such as whether it is symmetric, skewed left, or skewed right, which helps in understanding the data's central tendency and spread.

What does a right-skewed histogram indicate?

A right-skewed histogram indicates that the tail of the distribution is longer on the right side, meaning there are more frequent occurrences of lower values and fewer occurrences of higher values.

How do you determine the intervals for a histogram?

Intervals for a histogram are determined by dividing the range of data into equal-sized bins that cover the entire data range, ensuring that the data is appropriately grouped for analysis.

What skills are needed to analyze a histogram?

Skills needed to analyze a histogram include understanding frequency distribution, recognizing data patterns, and interpreting the shape and spread of the data to draw meaningful conclusions.

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