Questions: The accompanying data set lists the numbers of children of world leaders. Use the data to construct a frequency distribution using six classes and to create a frequency polygon. Describe any patterns.

Solution Steps

To solve this problem, we need to follow these steps:

1. Organize the data into six classes.
2. Count the frequency of numbers of children in each class.
3. Create a frequency distribution table.
4. Plot a frequency polygon to visualize the distribution.

We need to organize the given data into six classes. The class intervals are: \[ \begin{align_} 0-2 \\ 3-5 \\ 6-8 \\ 9-11 \\ 12-14 \\ 15-17 \\ \end{align_} \]

We count the number of data points that fall into each class interval: \[ \begin{align_} 0-2: & \quad 11 \\ 3-5: & \quad 17 \\ 6-8: & \quad 7 \\ 9-11: & \quad 5 \\ 12-14: & \quad 2 \\ 15-17: & \quad 1 \\ \end{align_} \]

We create a frequency distribution table based on the counted frequencies: \[ \begin{array}{|c|c|} \hline \text{Class Interval} & \text{Frequency} \\ \hline 0-2 & 11 \\ 3-5 & 17 \\ 6-8 & 7 \\ 9-11 & 5 \\ 12-14 & 2 \\ 15-17 & 1 \\ \hline \end{array} \]

We calculate the midpoints for each class interval: \[ \begin{align_} \text{Midpoint of } 0-2: & \quad \frac{0+2}{2} = 1.0 \\ \text{Midpoint of } 3-5: & \quad \frac{3+5}{2} = 4.0 \\ \text{Midpoint of } 6-8: & \quad \frac{6+8}{2} = 7.0 \\ \text{Midpoint of } 9-11: & \quad \frac{9+11}{2} = 10.0 \\ \text{Midpoint of } 12-14: & \quad \frac{12+14}{2} = 13.0 \\ \text{Midpoint of } 15-17: & \quad \frac{15+17}{2} = 16.0 \\ \end{align_} \]

We plot the frequency polygon using the class midpoints and their corresponding frequencies.

Final Answer