Table of contents
- 1. Intro to Stats and Collecting Data55m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically1h 45m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables2h 33m
- 6. Normal Distribution and Continuous Random Variables1h 38m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample1h 1m
- 10. Hypothesis Testing for Two Samples2h 8m
- 11. Correlation48m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
2. Describing Data with Tables and Graphs
Frequency Distributions
Problem 2.3.14
Textbook Question
Matching In Exercises 13–16, match the distribution with one of the graphs in Exercises 9–12. Justify your decision.
The frequency distribution of mileages of service vehicles at a business where a few vehicles have much higher mileages than the majority of vehicles

1
Identify the key characteristics of the distribution described in the problem. The problem mentions that a few vehicles have much higher mileages than the majority, which suggests the data is skewed to the right (positively skewed).
Review the graphs provided in Exercises 9–12. Look for a graph that shows a right-skewed distribution, where the majority of the data is concentrated on the left side, and the tail extends to the right.
Understand the relationship between the frequency distribution and the graph. A frequency distribution summarizes the data into intervals, and the graph visually represents this distribution. Match the graph that aligns with the description of the data.
Justify your choice by explaining how the shape of the graph corresponds to the description of the data. For example, the presence of a long tail on the right side of the graph aligns with the description of a few vehicles having much higher mileages.
Conclude by confirming that the selected graph accurately represents the frequency distribution of the mileages, based on the characteristics of the data provided in the problem.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Frequency Distribution
A frequency distribution is a summary of how often each value occurs in a dataset. It organizes data into categories or intervals, showing the number of observations within each category. This helps in visualizing the data's overall shape and identifying patterns, such as skewness or the presence of outliers.
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Skewness
Skewness refers to the asymmetry of a probability distribution. A distribution is positively skewed (right-skewed) when a few high values pull the mean to the right, while the majority of values cluster on the left. Understanding skewness is crucial for interpreting data distributions, especially when identifying outliers or making predictions.
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Outliers
Outliers are data points that significantly differ from other observations in a dataset. They can arise from variability in the data or may indicate measurement errors. In the context of the given question, the presence of a few vehicles with much higher mileages suggests that outliers are influencing the overall distribution, which is essential for matching it to the correct graph.
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