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Histogram Quiz 1 (10 MCQs)

This set of multiple-choice questions evaluates the ability to interpret histograms, including understanding data distribution, skewness, and continuous data representation. Skills tested include analyzing histogram characteristics, such as bar adjacency, frequency comparison, and the relationship between mean and median. The questions cover concepts like symmetric histograms, skewed left and right distributions, and the appropriate grouping of continuous intervals.

Quiz Instructions

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1. The histogram summarizes the agedistribution of people living in El Paso, Texas.Which of the following best describes the data?

Correct Answer: Correct answer is: (D) There are about 25,000 more people in their 50s than in their 60s.

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 to misinterpret the height of the bars as the exact number of people in each age group, rather than understanding that the height represents the frequency or count of people within that age range.

Explanations: The correct answer is D because the histogram shows the frequency of people in different age groups. By comparing the heights of the bars for the 50s and 60s age groups, we can determine that there are approximately 25,000 more people in their 50s than in their 60s.

Option Analysis:

Option A: This option is incorrect because the histogram does not show that most people in El Paso are over the age of 50. The distribution of the bars indicates a more even spread of ages.
Option B: This option is incorrect because the histogram does not provide specific counts for individual ages, only ranges. The height of the bar for the 55-year-old range does not indicate exactly 80,000 people.
Option C: This option is incorrect because the histogram does not show that there are about 1,700 more people in their 20s than in their 30s. The difference in the heights of the bars for these age groups does not support this claim.
Option D: This option is correct because the histogram shows that the bar for the 50s age group is significantly taller than the bar for the 60s age group, indicating about 25,000 more people in their 50s than in their 60s.

2. A study was done to find out how many hours people spend playing video games each day. The results of the study are presented in the histogram above. How many people spend 4-5 hours playing video games?

Correct Answer: Correct answer is: (D) 20.

Exam Relevance: AP Statistics, GRE, SAT, ACT

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 represented by the height of a bar.

Common Mistakes: A common mistake is misreading the histogram, such as confusing the height of the bar with the interval itself, or misinterpreting the scale on the y-axis.

Explanations: The histogram shows the number of people who spend a certain number of hours playing video games each day. The bar corresponding to the interval 4-5 hours has a height of 20, indicating that 20 people spend 4-5 hours playing video games.

Option Analysis:

Option A: 10 is incorrect because the bar for the 4-5 hour interval does not reach a height of 10.
Option B: 75 is incorrect because the bar for the 4-5 hour interval does not reach a height of 75.
Option C: 35 is incorrect because the bar for the 4-5 hour interval does not reach a height of 35.
Option D: 20 is correct because the bar for the 4-5 hour interval reaches a height of 20.

3. In a histogram, the bars don't touch.

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

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

Difficulty: Easy

Concept notes: In a histogram, bars are adjacent to each other without gaps, representing continuous data.

Common Mistakes: A common misunderstanding is that histograms have gaps between bars like bar charts.

Explanations: In a histogram, the bars are used to represent continuous data, and they are placed adjacent to each other without any gaps. This adjacency is crucial because it shows the continuous nature of the data being represented. Therefore, the statement that the bars in a histogram do not touch is incorrect.

Option Analysis:

Option A: This option is incorrect because it suggests that the bars in a histogram do not touch, which is not true.
Option B: This option is correct because it accurately states that the bars in a histogram do touch.

4. Based on the shape of this histogram, what would be true?

Correct Answer: Correct answer is: (A) The median & the mean would be about the same.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: In a histogram, the shape of the distribution can give insights into the relationship between the mean and the median. A symmetric histogram typically indicates that the mean and median are approximately equal.

Common Mistakes: A common mistake is to assume that the mean and median are always different, without considering the shape of the distribution.

Explanations: A symmetric histogram indicates that the data is evenly distributed around the center. In such a case, the mean (average value) and the median (middle value) are likely to be very close to each other. This is because the symmetry implies that the data points are balanced on either side of the center, leading to similar values for the mean and median.

Option Analysis:

Option A: Correct. The symmetric shape of the histogram suggests that the mean and median are about the same.
Option B: Incorrect. The median would not be greater than the mean in a symmetric distribution.
Option C: Incorrect. The mean would not be greater than the median in a symmetric distribution.
Option D: Incorrect. The correct answer is provided by option A.

5. What does the fill property do in a histogram?

Correct Answer: Correct answer is: (C) Determines if the histogram is filled with color.

Exam Relevance: AP Statistics, GRE, GMAT, Data Science Exams

Difficulty: Moderate

Concept notes: The fill property in a histogram determines whether the bars are filled with color or left unfilled.

Common Mistakes: A common misunderstanding is that the fill property changes the color of the histogram, but it actually controls whether the bars are filled or not.

Explanations: The fill property in a histogram is used to determine if the bars are filled with color or left unfilled. This property does not change the color itself but rather controls the presence or absence of color within the bars.

Option Analysis:

Option A: The fill property does not change the height of the columns. The height is determined by the frequency or count of data points in each bin.
Option B: The fill property does not control the color of the histogram. It only determines if the bars are filled with color or not.
Option C: The fill property determines if the histogram is filled with color, making this the correct answer.
Option D: The fill property does not set the border color. The border color is controlled by a different property.

6. Emily is making a histogram for the data 12, 24, 56, 7, 34, 75, 86, 78, and 96. What is the most appropriate first interval?

Correct Answer: Correct answer is: (B) 0-10.

Exam Relevance: AP Statistics, IB Mathematics, SAT Math, GRE Quantitative

Difficulty: Easy

Concept notes: A histogram is a graphical representation of data distribution. The first interval should be chosen to ensure that the data is appropriately grouped and the distribution is clearly visible.

Common Mistakes: A common mistake is choosing an interval that is too wide, which can result in a loss of detail in the data distribution.

Explanations: The data set includes values ranging from 7 to 96. An interval of 0-10 is appropriate because it captures the smallest value (7) and provides a clear starting point for the histogram. Larger intervals like 0-50 or 0-100 would not provide enough detail for the lower range of the data.

Option Analysis:

Option A: 0-5 is too narrow and would not include the smallest value (7).
Option B: 0-10 is the most appropriate interval as it includes the smallest value and provides a clear starting point.
Option C: 0-50 is too wide and would not provide enough detail for the lower range of the data.
Option D: 0-100 is too wide and would not provide enough detail for the lower range of the data.

7. A histogram shows numerical data and has bars that touch.

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

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

Difficulty: Easy

Concept notes: A histogram is a graphical representation of numerical data where the data is grouped into intervals, and the frequency of data within each interval is shown by the height of a bar. The bars in a histogram touch each other to indicate that the data is continuous and there are no gaps between the intervals.

Common Mistakes: A common misunderstanding is that histograms are similar to bar charts, where the bars do not touch. However, in a histogram, the bars must touch to represent the continuous nature of the data.

Explanations: A histogram is used to represent numerical data, and the bars in a histogram are adjacent to each other without any gaps. This adjacency indicates that the data is continuous and the intervals are contiguous. Therefore, the statement that a histogram shows numerical data and has bars that touch is true.

Option Analysis:

Option A: Correct. A histogram shows numerical data and has bars that touch.
Option B: Incorrect. This option would imply that the bars in a histogram do not touch, which is not true.

8. What is the shape of the data distribution on the histogram?

Correct Answer: Correct answer is: (B) Skewed left.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: A skewed left distribution is one where the tail of the distribution is longer on the left side, and the bulk of the data is concentrated on the right side.

Common Mistakes: A common mistake is confusing a skewed left distribution with a skewed right distribution, where the tail is longer on the right side.

Explanations: In a skewed left distribution, the majority of the data points are clustered towards the higher values, with fewer data points extending towards the lower values. This creates a longer tail on the left side of the histogram. The claimed correct answer, B) Skewed left, is consistent with this description.

Option Analysis:

Option A: Skewed right is incorrect because the tail would be longer on the right side, not the left.
Option B: Skewed left is correct because the tail is longer on the left side, indicating a concentration of data points on the right side.
Option C: Symmetrical (normal distribution) is incorrect because a normal distribution has a symmetrical shape with no skew.
Option D: Balloon shaped is incorrect because it does not describe a typical distribution shape in statistics.

Mnemonic: Left tail long, data right strong.

9. According to the histogram, how many more automobiles cost $ 35,000 or more than automobiles that cost less than $ 20,000?

Correct Answer: Correct answer is: (A) 15.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Common Mistakes: A common mistake is misinterpreting the ranges of the bars or incorrectly summing the frequencies.

Explanations: To find how many more automobiles cost $35,000 or more than automobiles that cost less than $20,000, we need to sum the frequencies of the bars representing the price ranges $35,000 or more and compare it to the sum of the frequencies of the bars representing the price ranges less than $20,000. According to the histogram, the sum of the frequencies for the price ranges $35,000 or more is 45, and the sum of the frequencies for the price ranges less than $20,000 is 30. The difference between these two sums is 45 - 30 = 15.

Option Analysis:

Option A: Correct. The difference between the number of automobiles costing $35,000 or more and those costing less than $20,000 is 15.
Option B: Incorrect. This option represents the total number of automobiles costing $35,000 or more, not the difference.
Option C: Incorrect. This option represents the total number of automobiles costing less than $20,000, not the difference.
Option D: Incorrect. This option suggests that none of the above answers are correct, but Option A is correct.

10. Describe the shape of the relative frequency histogram.

Correct Answer: Correct answer is: (A) Skewed right.

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

Difficulty: Moderate

Concept notes: 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 of the distribution.

Common Mistakes: A common mistake is to confuse a skewed right histogram with a skewed left histogram, where the tail is on the left side.

Explanations: In a skewed right histogram, the tail extends to the right, indicating that there are a few data points that are significantly larger than the majority of the data points. This results in a distribution where the mean is greater than the median, and the majority of the data points are clustered towards the left side of the histogram.

Option Analysis:

Option A: Correct. The histogram is skewed right, with a longer tail on the right side.
Option B: Incorrect. A skewed left histogram has a longer tail on the left side.
Option C: Incorrect. An approximately symmetrical histogram has a similar shape on both sides of the center.
Option D: Incorrect. This option is not applicable as the histogram is clearly skewed right.

Mnemonic: Right tail, right skew.

Frequently Asked Questions

What is a histogram?

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

How does the shape of a histogram help in data analysis?

The shape of a histogram, such as whether it is symmetric, skewed left, or skewed right, provides insights into the distribution of data and can help identify patterns or outliers.

What is the significance of bar height in a histogram?

The height of each bar in a histogram represents the frequency of data points within a specific interval, allowing for easy comparison of frequency across different intervals.

How can histograms be used to analyze continuous data?

Histograms are useful for visualizing the distribution of continuous data, such as age distribution or price range analysis, by grouping data into intervals and showing the frequency of data points within each interval.

What is the importance of appropriate grouping in a histogram?

Appropriate grouping in a histogram ensures that the data is represented accurately and meaningfully, allowing for clear visualization of the data distribution and facilitating better analysis.

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