Questions: The accompanying data set lists the numbers of children of world leaders. Use the data to construct a frequency patterns. Complete the frequency distribution table below. Use the minimum data entry as the lower limit of the first class. Class, Frequency, Midpoint 0--, square, square 16-square, square, square 32-square, square, square 48-square, square, square 64-square, square, square 80-square, square, square

Solution Steps

To construct a frequency distribution table, we first need to determine the range of the data and decide on the number of classes. Then, we calculate the class width and create class intervals starting from the minimum data entry. For each class, we count the number of data points (frequency) and calculate the midpoint of each class interval.

Given the data set \( \{2, 3, 5, 1, 4, 2, 3, 5, 6, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 7\} \), we find the minimum value \( \text{min} = 1 \) and the maximum value \( \text{max} = 7 \). The data range is calculated as: \[ \text{data range} = \text{max} - \text{min} = 7 - 1 = 6 \] With \( \text{num\_classes} = 5 \), the class width is: \[ \text{class width} = \left\lfloor \frac{\text{data range}}{\text{num\_classes}} \right\rfloor + 1 = \left\lfloor \frac{6}{5} \right\rfloor + 1 = 2 \]

Using the minimum value and the calculated class width, we create the following class intervals:

• \( 1 - 2 \)
• \( 3 - 4 \)
• \( 5 - 6 \)
• \( 7 - 8 \)
• \( 9 - 10 \)

Next, we calculate the frequency and midpoint for each class interval:

• For the class \( 1 - 2 \):

  • Frequency: \( 6 \)
  • Midpoint: \( \frac{1 + 2}{2} = 1.5 \)

• For the class \( 3 - 4 \):

  • Frequency: \( 7 \)
  • Midpoint: \( \frac{3 + 4}{2} = 3.5 \)

• For the class \( 5 - 6 \):

  • Frequency: \( 6 \)
  • Midpoint: \( \frac{5 + 6}{2} = 5.5 \)

• For the class \( 7 - 8 \):

  • Frequency: \( 1 \)
  • Midpoint: \( \frac{7 + 8}{2} = 7.5 \)

• For the class \( 9 - 10 \):

  • Frequency: \( 0 \)
  • Midpoint: \( \frac{9 + 10}{2} = 9.5 \)

Final Answer