Question

the following data are the \favorite numbers\ (single digits, 1 through 9) of the 24 pupils of a second - grade class. complete parts (a) through (c) below. click the icon to view the data. (c) construct a frequency polygon. choose the correct graph below.

Explanation:

1. Explanation of constructing a frequency - polygon:

• A frequency polygon is constructed by first finding the mid - points of each class interval (in this case, the single - digit numbers 1 through 9 are the “classes”). Then, the frequency of each class is plotted at the mid - point of the class, and the points are connected with straight lines.
• To determine the correct frequency polygon, we need to look at the frequencies of each number from 1 to 9 in the data set (not shown here, but we can assume we have counted the frequencies correctly).
• We plot the frequency of the number 1 at 1, the frequency of the number 2 at 2, and so on, and then connect these points with line segments.

1. Without the actual frequency data, we can't calculate the exact values, but we can analyze the general shape:

• We need to match the pattern of frequencies in the frequency polygon with the pattern of frequencies in the frequency distribution of the “favorite numbers”.
• Let's assume we have counted the frequencies of each number from 1 to 9. For example, if the frequency of 1 is 3, we plot a point at (1, 3), if the frequency of 2 is 5, we plot a point at (2, 5), and then connect these points with line segments.
• Looking at the options:
• We check the peaks and troughs of the frequency polygon. If a particular number has a high frequency, there should be a high point in the frequency polygon at that number's position on the x - axis. If a number has a low frequency, the point in the frequency polygon at that number's position should be low.

1. Let's assume we have the following frequency counts (for illustration purposes only):

• Suppose the frequencies of the numbers 1 - 9 are [3, 5, 4, 2, 6, 3, 4, 2, 5] respectively.
• We plot the points (1, 3), (2, 5), (3, 4), (4, 2), (5, 6), (6, 3), (7, 4), (8, 2), (9, 5) and connect them.
• After comparing with the given options, we can find the correct frequency polygon.

Since we don't have the actual data to calculate the frequencies precisely, we can't give a definite answer. But the general process to find the answer is as above. If we had the frequency data, we would follow these steps:

Step1: Count frequencies

Count the frequency of each number from 1 to 9 in the data set.

Step2: Plot points

Plot the points (number, frequency) for each number from 1 to 9 on the coordinate plane.

Step3: Connect points

Connect the plotted points with straight - line segments to form the frequency polygon.

Step4: Match with options

Compare the resulting frequency polygon with the given options to find the correct one.

Answer:

We need the actual frequency data of each number from 1 to 9 to determine the correct option among A, B, C, and D.