use the frequency polygon to identify the class with the greatest, and the class with the least, frequency.

Verified step by step guidance

1. Examine the frequency polygon, which is a line graph connecting points that represent the frequency of students commuting certain distances.
2. Identify the point on the graph with the highest vertical position, as this corresponds to the class with the greatest frequency. Note the distance value on the horizontal axis at this peak.
3. Identify the point on the graph with the lowest vertical position (excluding zero frequency if present), as this corresponds to the class with the least frequency. Note the distance value on the horizontal axis at this lowest point.
4. Confirm the frequencies by reading the values on the vertical axis (frequency) corresponding to these points to ensure accuracy.
5. Summarize the classes (distance intervals) with the greatest and least frequencies based on the identified points from the graph.

Key Concepts

Frequency Polygon

A frequency polygon is a line graph that represents the frequencies of different classes or intervals. Points are plotted at the midpoint of each class interval with their corresponding frequencies and connected by straight lines. It helps visualize the distribution and identify peaks and troughs in the data.

Frequency

Frequency refers to the number of observations or data points that fall within a particular class or category. In this context, it shows how many students commute a certain distance. Identifying the highest and lowest frequencies helps determine the most and least common commuting distances.

Class Interval

A class interval groups data into ranges or categories, such as distances in miles. Each class interval has a frequency representing how many data points fall within that range. Understanding class intervals is essential for interpreting the frequency polygon and identifying which classes have the greatest or least frequency.