Certainly! Let's create a frequency polygon for the given data.
### Step-by-Step Solution:
1. Identify the age groups and their corresponding midpoints:
- The age groups given are: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, and 60-70.
- The midpoint of each age group can be calculated by taking the average of the lower and upper bounds of the age group.
- Midpoint of 0-10: [tex]\((0 + 10) / 2 = 5.0\)[/tex]
- Midpoint of 10-20: [tex]\((10 + 20) / 2 = 15.0\)[/tex]
- Midpoint of 20-30: [tex]\((20 + 30) / 2 = 25.0\)[/tex]
- Midpoint of 30-40: [tex]\((30 + 40) / 2 = 35.0\)[/tex]
- Midpoint of 40-50: [tex]\((40 + 50) / 2 = 45.0\)[/tex]
- Midpoint of 50-60: [tex]\((50 + 60) / 2 = 55.0\)[/tex]
- Midpoint of 60-70: [tex]\((60 + 70) / 2 = 65.0\)[/tex]
- Therefore, the midpoints are: [tex]\([5.0, 15.0, 25.0, 35.0, 45.0, 55.0, 65.0]\)[/tex].
2. List the number of people corresponding to each age group:
- The number of people corresponding to each age group is given: [5, 14, 25, 30, 35, 40, 20].
3. Construct the frequency polygon:
- The frequency polygon is constructed by plotting the midpoints against their corresponding frequencies (number of people).
- Pairing the midpoints with their corresponding frequencies:
- (5.0, 5)
- (15.0, 14)
- (25.0, 25)
- (35.0, 30)
- (45.0, 35)
- (55.0, 40)
- (65.0, 20)
- Therefore, the points to be plotted to construct the frequency polygon are: [tex]\((5.0, 5)\)[/tex], [tex]\((15.0, 14)\)[/tex], [tex]\((25.0, 25)\)[/tex], [tex]\((35.0, 30)\)[/tex], [tex]\((45.0, 35)\)[/tex], [tex]\((55.0, 40)\)[/tex], [tex]\((65.0, 20)\)[/tex].
4. Plotting the frequency polygon:
- On a graph, mark the midpoints on the X-axis: 5.0, 15.0, 25.0, 35.0, 45.0, 55.0, 65.0.
- Mark the frequencies on the Y-axis: 5, 14, 25, 30, 35, 40, 20.
- Plot the points: (5.0, 5), (15.0, 14), (25.0, 25), (35.0, 30), (45.0, 35), (55.0, 40), (65.0, 20).
- Connect these points with straight lines to form the frequency polygon.
### Summary:
The midpoints are [5.0, 15.0, 25.0, 35.0, 45.0, 55.0, 65.0], the frequencies are [5, 14, 25, 30, 35, 40, 20], and the points to plot are [(5.0, 5), (15.0, 14), (25.0, 25), (35.0, 30), (45.0, 35), (55.0, 40), (65.0, 20)]. Using these points, you can construct the frequency polygon by plotting these on a graph and connecting the dots with straight lines.
