Question

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

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

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.

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.

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.

Key concepts

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.