Use the data set and the indicated number of classes to construct

(c) a frequency polygon,


Hospitals
Number of classes: 8
Data set: Number of hospitals in each of the 50 U.S. states and 5 inhabited territories (Source: American Hospital Directory) 10 90 51 1 77 341 56 34 8 214 111 3 14 40 18 142 102 55 75 108 72 53 19 105 55 83 1 69 19 108 10 27 14 78 37 31 186 146 90 37 177 52 11 67 25 100 361 35 91 2 7 61 78 33 14

Verified step by step guidance

1. Step 1: Organize the data by sorting the number of hospitals in ascending order to better understand the range and distribution.
2. Step 2: Determine the class width using the formula: \(\text{Class Width} = \frac{\text{Maximum value} - \text{Minimum value}}{\text{Number of classes}}\). Here, the number of classes is 8.
3. Step 3: Create the class intervals starting from the minimum value, adding the class width each time to form 8 classes that cover the entire data range without overlap.
4. Step 4: Tally the frequency of data points falling into each class interval to build the frequency distribution table.
5. Step 5: To construct the frequency polygon, plot the midpoints of each class interval on the x-axis and their corresponding frequencies on the y-axis, then connect these points with straight lines.

Key Concepts

Frequency Polygon

A frequency polygon is a graphical representation of a data distribution, created by plotting the midpoints of class intervals against their frequencies and connecting these points with straight lines. It helps visualize the shape and trends of the data, making it easier to compare distributions or identify patterns.

Class Intervals and Number of Classes

Class intervals divide continuous data into equal-sized groups or bins, and the number of classes determines how many such intervals are used. Choosing the correct number of classes (here, 8) is essential for summarizing data effectively without losing important details or creating too much noise.

Frequency Distribution

A frequency distribution organizes data by showing how often each value or range of values occurs. It forms the basis for constructing histograms and frequency polygons, allowing for a clear summary of data patterns and helping to identify central tendencies and variability.