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The image displays an activity for constructing an ungrouped frequency distribution table based on temperature data recorded over 25 days. Here’s how to approach the task:

### Steps Breakdown:
1. **Sort the Data**: Arrange the temperatures from lowest to highest.
2. **Calculate Frequency (\(f\))**: Count how often each temperature appears.
3. **Calculate Cumulative Frequency (\(cf\))**: Sum the frequencies progressively.
4. **Calculate Relative Frequency**: Divide each frequency by the total number of observations (25).
5. **Calculate Cumulative Relative Frequency**: Add up the relative frequencies sequentially.
6. **Calculate Percentage (%)**: Convert the relative frequencies into percentages.

Let's proceed step-by-step by first sorting the data and calculating frequencies.

### Given Data:
88, 91, 84, 82, 85, 90, 88, 85, 86, 87, 88, 84, 89, 85, 90, 82, 83, 87, 86, 84, 85, 89, 84, 85, 87

I'll create the table based on these instructions.Here's the completed ungrouped frequency distribution table based on the given temperature dataHere's the completed ungrouped frequency distribution table based on the given temperature 

| Temperature (X) | Frequency (f) | Cumulative Frequency (cf) | Relative Frequency | Cumulative Rel. Frequency | Percentage (%) |
|-----------------|---------------|--------------------------|--------------------|---------------------------|----------------|
| 82              | 2             | 2                        | 0.08               | 0.08                      | 8.0            |
| 83              | 1             | 3                        | 0.04               | 0.12                      | 4.0            |
| 84              | 4             | 7                        | 0.16               | 0.28                      | 16.0           |
| 85              | 5             | 12                       | 0.20               | 0.48                      | 20.0           |
| 86              | 2             | 14                       | 0.08               | 0.56                      | 8.0            |
| 87              | 3             | 17                       | 0.12               | 0.68                      | 12.0           |
| 88              | 3             | 20                       | 0.12               | 0.80                      | 12.0           |
| 89              | 2             | 22                       | 0.08               | 0.88                      | 8.0            |
| 90              | 2             | 24                       | 0.08               | 0.96                      | 8.0            |
| 91              | 1             | 25                       | 0.04               | 1.00                      | 4.0            |
| **Total**       | **25**        |                          | **1.00**           |                           | **100.0**      |

### Key Observations:
- **Most Frequent Temperatures**: 85 (frequency of 5), followed by 84 (frequency of 4).
- **Cumulative Values**: Cumulative frequency reaches the total of 25, and cumulative relative frequency reaches 1.
- **Percentages**: All relative frequencies add up to 100%.

Would you like more details or have any questions?

#### Related Questions:
1. How is the cumulative frequency different from cumulative relative frequency?
2. Can this table be used to calculate the mean temperature?
3. How would the table change if the total observations were different?
4. What conclusions can be drawn from the temperature distribution?
5. How can we visualize this frequency distribution?

#### Tip:
For better data visualization, consider using histograms or pie charts to represent the frequency distribution and relative frequencies.

Constructing an Ungrouped Frequency Distribution Table based on temperatures recorded in a city over 25 days.

Learn how to construct an ungrouped frequency distribution table using temperature data recorded over 25 days. This guide covers statistical concepts such as frequency, cumulative frequency, relative frequency, and percentage calculations, suitable for students in Grades 6-8.

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