Question

The data below give the number of hurricanes classified as major hurricanes in the Atlantic Ocean each year from 1944 through 2006 , as reported by NOAA (www.nhc.noaa.gov): \(\begin{aligned} &3,2,1,2,4,3,7,2,3,3,2,5,2,2,4,2,2,6,0,2,5,1,3,1,0, \\ &3,2,1,0,1,2,3,2,1,2,2,2,3,1,1,1,3,0,1,3,2,1,2,1,1, \\ &0,5,6,1,3,5,3,3,2,3,6,7,2 \end{aligned}\) a) Create a dotplot of these data. b) Describe the distribution.

Short answer

a) Create a dotplot ranging from 0 to 7 with dots representing frequency. b) The distribution is slightly skewed right with a peak around 2-3, showing variability in hurricane counts.

Step-by-step solution

- Understand the Dotplot

A dotplot is a simple graphical representation used to display the distribution of data points. Each dot represents one or more occurences of a specific value.

- Determine the Range of Data

Identify the smallest and largest numbers in the dataset. From the provided data, the smallest value is 0 and the largest is 7.

- Set Up the Dotplot Axis

Draw a horizontal line to represent the values from the minimum to the maximum of the data set. This means you should have marks for 0, 1, 2, 3, 4, 5, 6, and 7.

- Plot Each Data Point as a Dot

Place a dot above the number on the axis for each occurrence in the dataset. For instance, if the number 3 appears, place a dot above the number 3. If 3 appears multiple times, stack the dots.

- Analyze the Distribution

Once all data points are plotted, describe the distribution by observing the shape, center, spread, and any unusual features. Look for patterns, such as clustering, symmetry, or outliers.

Key concepts

Data Visualization

Data visualization is the art of representing data in a visual format, making it easier to see patterns and trends. One of the simplest and most effective tools for visualizing data is the dotplot. In a dotplot, each data point is represented as a dot on a number line. This allows us to quickly assess the frequency of each value in a dataset.
Creating a dotplot involves a few basic steps:

• First, identify the smallest and largest numbers in your data. This will help define the range of your dotplot.
• Once you have the range, draw a horizontal line and mark it with the numbers within this range.
• For each data point, place a dot above the corresponding number on the number line.
• If a number appears more than once, stack the dots vertically.

By visually displaying data, dotplots help in seeing the overall shape and spread of the data almost immediately.

Distribution Analysis

Distribution analysis involves examining how data points are spread out across different values. It's about understanding the shape, center, and spread of the data, as well as identifying any outliers. When analyzing a dotplot, we first look for clustering, which is when data points are bunched together. This can indicate a common trend or tendency in the data.
The center of the data can often be seen where the most dots are concentrated. For example, if most data points center around the number 3, we can say 3 is a central value or mode.
The spread of the data tells us how much the data varies. A wider spread indicates more variability. In contrast, a narrow spread indicates that most values are similar to each other. Also, look for outliers, which are data points that deviate significantly from the rest of the dataset. Understanding these aspects helps in gaining insights into the data's behavior and characteristics.

Graphical Representation

Graphical representation of data transforms complex datasets into understandable visual formats. Dotplots are just one way to achieve this, providing a straightforward method to observe data distribution.
With a graphical tool like a dotplot, we harness the visual strength of graphs to aid in quicker comprehension. The simplicity of dotplots makes them accessible. Unlike other graphs, a dotplot requires minimal prior knowledge to interpret, making it a great choice for beginners.

• It highlights the frequency of occurrences directly.
• It simplifies comparing different values at a glance.
• It can reveal insights like clustering and symmetry without extensive calculations.

By using graphical representation, we bridge the gap between raw data and insightful understanding, turning numbers into visually meaningful stories.