Table of contents

1. Intro to Stats and Collecting Data1h 14m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically2h 5m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables3h 6m
6. Normal Distribution and Continuous Random Variables2h 11m
7. Sampling Distributions & Confidence Intervals: Mean3h 23m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample3h 29m
10. Hypothesis Testing for Two Samples4h 50m
11. Correlation1h 6m
12. Regression1h 50m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 57m

2. Describing Data with Tables and Graphs

Frequency Distributions

Statistics

2. Describing Data with Tables and Graphs

Frequency Distributions

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2:17 minutes

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

Verified step by step guidance

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.

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.

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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Related Practice

Textbook Question

Use the ogive to approximate the

the number of black bears that weigh between 158.5 pounds and 244.5 pounds.

Textbook Question

In Exercises 17–19, use the data set, which represents the points recorded by each player on the Winnipeg Jets in the 2019–2020 NHL season. (Source: National Hockey League)

8 8 8 6 0 73 26 1

0 5 58 1 7 5 10 63

0 5 10 0 31 5 15 45

16 29 10 73 5 3 0 65

Construct a frequency distribution for the data set using eight classes. Include class limits, midpoints, boundaries, frequencies, relative frequencies, and cumulative frequencies.

Textbook Question

Construct a frequency distribution for the data set using the indicated number of classes. In the table, include the midpoints, relative frequencies, and cumulative frequencies. Which class has the greatest class frequency and which has the least class frequency.

Textbook Spending

Number of classes: 6

Data set: Amounts (in dollars) spent on textbooks for a semester 91 472 279 249 530 376 188 341 266 199 142 273 189 130 489 266 248 101 375 486 190 398 188 269 43 30 127 354 84 319

Textbook Question

Construct a frequency distribution and a frequency histogram for the data set using the indicated number of classes. Describe any patterns.

Reaction Times

Number of classes: 8

Data set: Reaction times (in milliseconds) of 30 adult females to an auditory stimulus 507 389 305 291 336 310 514 442 373 428 387 454 323 441 388 426 411 382 320 450 309 416 359 388 307 337 469 351 422 413

Textbook Question

Interpreting Percentiles In Exercises 29–32, use the ogive, which represents the cumulative frequency distribution for quantitative reasoning scores on the Graduate Record Examination in a recent range of years. (Adapted from Educational Testing Service)

What percentile is a score of 170? How should you interpret this?

Textbook Question

The data set represents the number of minutes a sample of 27 people exercise each week.

108 139 120 123 120 132 123 131 131

157 150 124 111 101 135 119 116 117

127 128 139 119 118 114 127 142 130

a. Construct a frequency distribution for the data set using five classes. Include class limits, midpoints, boundaries, frequencies, relative frequencies, and cumulative frequencies.

Textbook Question

What Would You Do? You work at a bank and are asked to recommend the amount of cash to put in an ATM each day. You do not want to put in too much (which would cause security concerns) or too little (which may create customer irritation). The daily withdrawals (in hundreds of dollars) for 30 days are listed. 72 84 61 76 104 76 86 92 80 88 98 76 97 82 84 67 70 81 82 89 74 73 86 81 85 78 82 80 91 83

Construct a relative frequency histogram for the data. Use 8 classes.

Textbook Question

Construct a cumulative frequency distribution and an ogive for the data set using six classes. Then describe the location of the greatest increase in frequency.

Retirement Ages

Data set: Retirement ages of 35 English professors 72 62 55 61 53 62 65 66 69 55 66 63 67 69 55 65 67 57 67 68 73 75 65 54 71 57 52 58 58 71 72 67 63 65 61

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