Question

students were asked, how stressed have you been in the last week, on a scale of 0 to 10, with 0 being not at all stressed and 10 being extremely stressed? their responses are shown in the frequency distribution below. construct a histogram and frequency polygon for the data

b. select a polygon representing the given data frequency distribution.

Explanation:

Step1: Analyze the frequency values

The frequencies are \(1, 2, 1, 12, 11, 20, 10, 31, 34, 15, 20\) for stress ratings \(0 - 10\) respectively.

Step2: Check the shape of the frequency polygon

A frequency polygon is constructed by plotting points at the mid - points of each class (here, each stress rating is a single - value class) and connecting them with straight lines. The first polygon (top - left among the options) has points that match the given frequencies. For example, at stress rating \(0\), frequency \(1\); at \(1\), frequency \(2\); at \(2\), frequency \(1\); at \(3\), frequency \(12\); at \(4\), frequency \(11\); at \(5\), frequency \(20\); at \(6\), frequency \(10\); at \(7\), frequency \(31\); at \(8\), frequency \(34\); at \(9\), frequency \(15\); at \(10\), frequency \(20\).

Answer:

The first polygon (top - left among the options) is the correct frequency polygon for the given data.