Use the frequency distribution shown below to construct an expanded frequency distribution. High Temperatures (°F) Class 17-27 28-38 39-49 50-60 61-71 72-82 83-93 Frequency, f 18 43 66 67 79 66 26 Complete the table below. High Temperatures (°F) (Round to the nearest hundredth as needed.) Curnulative frequency Relative frequency Class Frequency, f Midpoint 17-27 18 28-38 43 39-49 66 50-60 67 61-71 79 72-82 66 83-93 26

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### Constructing Expanded Frequency Distribution

#### Initial Frequency Distribution for High Temperatures (°F):

| Class   | 17-27 | 28-38 | 39-49 | 50-60 | 61-71 | 72-82 | 83-93 |
|---------|-------|-------|-------|-------|-------|-------|-------|
| Frequency, f | 18    | 43    | 66    | 67    | 79    | 66    | 26    |

#### Complete the Table Below for High Temperatures (°F):
(Round to the nearest hundredth as needed.)

| Class   | Frequency, f | Midpoint | Relative frequency | Cumulative frequency |
|---------|---------------|----------|--------------------|----------------------|
| 17-27   | 18            |          |                    |                      |
| 28-38   | 43            |          |                    |                      |
| 39-49   | 66            |          |                    |                      |
| 50-60   | 67            |          |                    |                      |
| 61-71   | 79            |          |                    |                      |
| 72-82   | 66            |          |                    |                      |
| 83-93   | 26            |          |                    |                      |

### Explanation:

- **Class**: The range of high temperatures.
- **Frequency, f**: The number of occurrences within each class.
- **Midpoint**: The central value of each class range.
- **Relative frequency**: The proportion of the total frequency represented by each class.
- **Cumulative frequency**: The sum of frequencies for the current class and all previous classes.

To complete the table:
1. **Midpoint calculation**: For each class, calculate the midpoint by averaging the lower and upper boundaries. For example, for the class 17-27, the midpoint is `(17+27)/2 = 22`.
2. **Relative frequency calculation**: Divide the frequency of each class by the total frequency. Suppose the total frequency is `365`. The relative frequency for the class 17-27 is `18/365 = 0.05` (rounded to the nearest cent).
3. **Cumulative frequency calculation**: Add the current class frequency to the sum of all previous class frequencies. For the first class, it remains the same
Transcribed Image Text:### Constructing Expanded Frequency Distribution #### Initial Frequency Distribution for High Temperatures (°F): | Class | 17-27 | 28-38 | 39-49 | 50-60 | 61-71 | 72-82 | 83-93 | |---------|-------|-------|-------|-------|-------|-------|-------| | Frequency, f | 18 | 43 | 66 | 67 | 79 | 66 | 26 | #### Complete the Table Below for High Temperatures (°F): (Round to the nearest hundredth as needed.) | Class | Frequency, f | Midpoint | Relative frequency | Cumulative frequency | |---------|---------------|----------|--------------------|----------------------| | 17-27 | 18 | | | | | 28-38 | 43 | | | | | 39-49 | 66 | | | | | 50-60 | 67 | | | | | 61-71 | 79 | | | | | 72-82 | 66 | | | | | 83-93 | 26 | | | | ### Explanation: - **Class**: The range of high temperatures. - **Frequency, f**: The number of occurrences within each class. - **Midpoint**: The central value of each class range. - **Relative frequency**: The proportion of the total frequency represented by each class. - **Cumulative frequency**: The sum of frequencies for the current class and all previous classes. To complete the table: 1. **Midpoint calculation**: For each class, calculate the midpoint by averaging the lower and upper boundaries. For example, for the class 17-27, the midpoint is `(17+27)/2 = 22`. 2. **Relative frequency calculation**: Divide the frequency of each class by the total frequency. Suppose the total frequency is `365`. The relative frequency for the class 17-27 is `18/365 = 0.05` (rounded to the nearest cent). 3. **Cumulative frequency calculation**: Add the current class frequency to the sum of all previous class frequencies. For the first class, it remains the same
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