Construct a grouped frequency distribution for the given data values using 5
classes. Include the class limits, frequencies, relative frequencies, and the
midpoints.
Scores on a math midterm examination.
33, 35, 45, 48, 60, 62, 63, 67, 71, 72, 75, 75, 77, 77, 79, 82, 84, 86, 87, 87,
89, 90, 93, 94, 94, 94, 96, 97, 98, 99      Draw the relative frequency polygon for the data

To construct a grouped frequency distribution for the given data values with 5 classes, we will follow these steps:

### Steps:
1. **Range of the dataTo construct a grouped frequency distribution for the given data values with 5 classes, we will follow these steps:

### Steps:
1. **Range of the **
   \[
   \text{Range} = \text{Maximum value} - \text{Minimum value} = 99 - 33 = 66
   \]

2. **Class width:**
   The formula for class width is:
   \[
   \text{Class width} = \frac{\text{Range}}{\text{Number of classes}} = \frac{66}{5} \approx 13.2
   \]
   We'll round this value up to 14 to ensure the entire range of the data is covered.

3. **Class limits:**
   Using a class width of 14, we can determine the lower and upper limits of each class. We'll start the first class with the minimum value of 33.

4. **Midpoints:** 
   The midpoint for each class is calculated using:
   \[
   \text{Midpoint} = \frac{\text{Lower class limit} + \text{Upper class limit}}{2}
   \]

5. **Frequencies:**
   Count the number of data points that fall within each class interval.

6. **Relative frequencies:**
   The relative frequency for each class is calculated as:
   \[
   \text{Relative frequency} = \frac{\text{Frequency}}{\text{Total number of data points}}
   \]

### Data Distribution:

| Class Limits | Frequency (f) | Midpoints (x) | Relative Frequency (f/n) |
|--------------|---------------|---------------|--------------------------|
| 33 - 46      | 4             | 39.5          | 4/30 = 0.133             |
| 47 - 60      | 3             | 53.5          | 3/30 = 0.100             |
| 61 - 74      | 5             | 67.5          | 5/30 = 0.167             |
| 75 - 88      | 13            | 81.5          | 13/30 = 0.433            |
| 89 - 102     | 5             | 95.5          | 5/30 = 0.167             |

### Drawing the Relative Frequency Polygon:
To draw the relative frequency polygon, plot the midpoints (39.5, 53.5, 67.5, 81.5, 95.5) on the x-axis and the corresponding relative frequencies on the y-axis. Then connect the points with straight lines.

I can help you with the polygon. Would you like me to draw it for you?

Construct a grouped frequency distribution for the given data values using 5 classes. Include the class limits, frequencies, relative frequencies, and the midpoints. Scores on a math midterm examination: 33, 35, 45, 48, 60, 62, 63, 67, 71, 72, 75, 75, 77, 77, 79, 82, 84, 86, 87, 87, 89, 90, 93, 94, 94, 94, 96, 97, 98, 99. Draw the relative frequency polygon for the data.

Learn how to construct a grouped frequency distribution with 5 classes for a set of math exam scores. This problem covers class limits, frequencies, midpoints, and relative frequencies. It also includes instructions on how to draw a relative frequency polygon. Suitable for Grades 9-12.

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