In Exercises 15 and 16, construct the frequency polygons.
Presidents Use the frequency distribution from Exercise 14 in Section 2-1 to construct a frequency polygon. Does the graph suggest that the distribution is skewed? If so, how?

Verified step by step guidance

1. Step 1: Understand the concept of a frequency polygon. A frequency polygon is a graphical representation of a frequency distribution. It is created by plotting points corresponding to the midpoints of each class interval and their respective frequencies, and then connecting these points with straight lines.
2. Step 2: Identify the class midpoints from the frequency distribution provided in Exercise 14. The midpoint of a class interval is calculated as the average of the lower and upper boundaries of the interval. Use the formula: $\mathrm{Midpoint}=\frac{\mathrm{Lower}+\mathrm{Upper}}{2}$.
3. Step 3: Plot the midpoints on the x-axis and the corresponding frequencies on the y-axis. For each class interval, locate the midpoint on the x-axis and plot a point at the height corresponding to the frequency of that class.
4. Step 4: Connect the plotted points with straight lines to form the frequency polygon. Optionally, extend the lines to the x-axis at the beginning and end of the graph to close the polygon.
5. Step 5: Analyze the shape of the frequency polygon to determine if the distribution is skewed. If the graph is symmetric, the distribution is not skewed. If the graph has a longer tail on the right, it is positively skewed. If the graph has a longer tail on the left, it is negatively skewed.

Key Concepts

Frequency Distribution

A frequency distribution is a summary of how often each value occurs in a dataset. It organizes data into categories or intervals, showing the number of observations within each category. This helps in visualizing the data's overall shape and identifying patterns, such as central tendency and variability.

Frequency Polygon

A frequency polygon is a graphical representation of a frequency distribution. It is created by plotting points for the frequency of each category and connecting them with straight lines. This type of graph provides a clear visual of the distribution's shape, making it easier to identify trends, peaks, and potential skewness in the data.

Skewness

Skewness refers to the asymmetry of a probability distribution. A distribution is considered skewed if one tail is longer or fatter than the other. Positive skewness indicates that the tail on the right side is longer, while negative skewness indicates a longer left tail. Analyzing skewness helps in understanding the data's behavior and potential outliers.