/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 48 Windy Cities Are some cities mor... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Windy Cities Are some cities more windy than others? Does Chicago deserve to be nicknamed "The Windy City"? These data are the average wind speeds (in miles per hour) for 55 selected cities in the United States: \(^{5}\) a. Construct a relative frequency histogram for the data. (HINT: Choose the class boundaries without including the value \(x=35.1\) in the range of values.) b. The value \(x=35.1\) was recorded at \(\mathrm{Mt}\) t. Washington, New Hampshire. Does the geography of that city explain the observation? c. The average wind speed in Chicago is recorded as 10.3 miles per hour. Do you consider this unusually windy?

Short Answer

Expert verified
Explain your answer using the relative frequency histogram. Answer: Chicago's average wind speed of 10.3 mph falls within one of the higher classes in the histogram, but it is not extremely far from the majority of the other cities' wind speeds. Therefore, it can be considered somewhat windy, but not unusually so compared to other cities.

Step by step solution

01

Part a: Constructing a Relative Frequency Histogram

1. Determine the number of classes: To construct the histogram, first decide on the number of classes or bins. For this dataset, let's choose 7 classes. 2. Exclude the outlier: Excluding the outlier value of 35.1 mph from the dataset, the next highest wind speed is 12.3 mph. 3. Choose class width: With the chosen 7 classes and a maximum value of 12.3 mph, let's choose a class width of 1 mph, starting from 5 and ending at 12. 4. Count the number of values within each class: Count how many wind speeds fall within each class. Calculate the relative frequency for each class by dividing the count of values in each class by the total number of values (excluding the outlier). 5. Plot the histogram: Utilizing the class boundaries and relative frequencies, construct the histogram with wind speed classes on the x-axis and relative frequency on the y-axis.
02

Part b: Geography of Mt. Washington, New Hampshire

1. Research the geography: Mt. Washington, New Hampshire, is known for its extreme weather conditions. It is the highest peak in the northeastern United States and has a prominent position in the Presidential Range. 2. Understand the reason for high wind speed: Due to its geographical position and the convergence of different air currents, Mt. Washington experiences extremely high wind speeds (recorded as 35.1 mph on average). 3. Conclusion: The geography of Mt. Washington explains why it experiences much higher wind speeds compared to other cities in the dataset.
03

Part c: Assessing Chicago's Windiness

1. Locate Chicago's wind speed in the dataset: Chicago's average wind speed is given as 10.3 mph. 2. Analyze the histogram: Observe the relative frequency histogram created in part a to see how the wind speed in Chicago compares to the wind speeds of other cities in the dataset. 3. Conclusion: Chicago's wind speed falls within one of the higher classes, but it is not extremely far from the majority of the other cities' wind speeds. Therefore, it can be considered somewhat windy, but not unusually so compared to other cities.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Average Wind Speed
Average wind speed is a crucial metric for understanding how windy a city truly is. It is calculated by summing up the daily wind speeds and dividing by the number of days. This average offers insights into the general wind conditions over a specified period.
In the recent exercise, we looked at the average wind speed across 55 cities. Among them, Chicago had an average wind speed of 10.3 mph. While this may sound low, it places the city in the higher spectrum of the dataset, confirming that Chicago is indeed windy, but not exceptionally so outside of notable outliers like Mt. Washington.
Considering wind speeds helps in understanding patterns and comparing them across different places. By knowing these averages, we can evaluate if a city's reputation, like that of "The Windy City", holds up against empirical data. This approach provides a factual basis instead of relying solely on perceptions.
Class Boundaries
Class boundaries are essential when constructing a histogram. They help categorize data into intervals or classes for easy analysis. In our exercise, we chose 7 classes to represent wind speeds across 55 U.S. cities.
To determine the class boundaries, it's vital to select classes that make the data easy to interpret. For instance, excluding the outlier of 35.1 mph (recorded in Mt. Washington) helped in setting more sensible boundaries. We decided on a class width of 1 mph, starting from the lowest observed non-outlier value, ensuring the classes were consistent and clear.
This technique helps illustrate how often different wind speeds occur, showing patterns or trends in the data. Knowing how to set class boundaries effectively can make data more digestible, facilitating accurate observations from the resulting relative frequency histogram.
Geographical Influence on Data
Geography plays a significant role in influencing wind speed data. This influence is evident in places with distinct geographical features like mountains or valleys. For instance, Mt. Washington is famously windy due to its location and altitude.
As noted in the exercise, Mt. Washington is the tallest peak in the northeastern U.S. Its prominent position in the Presidential Range leads to high wind speeds as different air currents intersect there. This geographical context justifies the recorded 35.1 mph average wind speed, which is an outlier in our dataset.
Therefore, understanding the geography of a location helps explain variations in data. For students and researchers, considering geographical influences is critical when interpreting statistical measures, ensuring a comprehensive appreciation of what affects environmental data like wind speed.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Car Colors The most popular colors for compact and sports cars in a recent year are given in the table. \({ }^{5}\) Use an appropriate graphical display to describe these data.

RBC Counts The red blood cell count of a healthy person was measured on each of 15 days. The number recorded is measured in \(10^{6}\) cells per microliter ( \(\mu \mathrm{L}\) ). $$\begin{array}{lllll}5.4 & 5.2 & 5.0 & 5.2 & 5.5 \\\5.3 & 5.4 & 5.2 & 5.1 & 5.3 \\\5.3 & 4.9 & 5.4 & 5.2 & 5.2\end{array}$$ a. Use an appropriate graph to describe the data. b. Describe the shape and location of the red blood cell counts. c. If the person's red blood cell count is measured today as \(5.7 \times 10^{6} / \mu \mathrm{L},\) would you consider this unusual? What conclusions might you draw?

Preschool The ages (in months) at which 50 children were first enrolled in a preschool are listed below. $$\begin{array}{llllllllll}38 & 40 & 30 & 35 & 39 & 40 & 48 & 36 & 31 & 36 \\\47 & 35 & 34 & 43 & 41 & 36 & 41 & 43 & 48 & 40 \\\32 & 34 & 41 & 30 &46 & 35 & 40 & 30 & 46 & 37 \\\55 & 39 & 33 & 32 & 32 & 45 & 42 & 41 & 36 & 50 \\\42 & 50 & 37 & 39 & 33 & 45 & 38 & 46 & 36 & 31\end{array}$$ a. Construct a stem and leaf display for the data. b. Construct a relative frequency histogram for these data. Start the lower boundary of the first class at 30 and use a class width of 5 months. c. Compare the graphs in parts a and b. Are there any significant differences that would cause you to choose one as the better method for displaying the data? d. What proportion of the children were 35 months (2 years, 11 months) or older, but less than 45 months ( 3 years, 9 months) of age when first enrolled in preschool? e. If one child were selected at random from this group of children, what is the probability that the child was less than 50 months old ( 4 years, 2 months) when first enrolled in preschool?

Cancer Survival Times A medical researcher wants to estimate the survival time of a patient after the onset of a particular type of cancer and after a particular regimen of radiotherapy. a. What is the yariable of interest to the medical researcher? b. Is the variable in part a qualitative, quantitative discrete, or quantitative continuous? c. Identify the population of interest to the medical researcher. d. Describe how the researcher could select a sample from the population. e. What problems might arise in sampling from this population?

Kentucky Derby The following data set shows the winning times (in seconds) for the Kentucky Derby races from 1950 to 2007 . a. Do you think there will be a trend in the winning times over the years? Draw a line chart to verify your answer. b. Describe the distribution of winning times using an appropriate graph. Comment on the shape of the distribution and look for any unusual observations.

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.