https://file.aiquickdraw.com/mathbot/file/1730810896529nu8n06up.jpg

To construct the table based on the data provided in the activity, I will go through the steps outlined in the image:

### Step-by-Step Solution:

1. **Identify the Data Set**:
   The data provided indicates three classes of performance appraisal: High, Average, and Low.

2. **Count the Frequency of Each Category**:
   Based on the list of appraisals:
   - **High**: Count how many times "High" appears.
   - **Average**: Count how many times "Average" appears.
   - **Low**: Count how many times "Low" appears.

3. **Calculate the Frequency and Percentage for Each Category**:
   - The frequency \( f \) for each category is the number of times it appears.
   - The percentage for each category can be calculated using the formula:
     \[
     \text{Percentage} = \frac{f}{\text{Total Number of Applicants}} \times 100
     \]
   - Given that the total number of applicants is 20, each percentage is calculated relative to this total.

Let’s tally the data and compute the table:

### Tallying Results:

- **High** appears 9 times.
- **Average** appears 7 times.
- **Low** appears 4 times.

### Constructing the Table:

| Class   | Tally         | Frequency (f) | Percentage (%)            |
|---------|---------------|---------------|----------------------------|
| High    | |||||||||     | 9             | \(\frac{9}{20} \times 100 = 45\%\) |
| Average | |||||||       | 7             | \(\frac{7}{20} \times 100 = 35\%\) |
| Low     | ||||          | 4             | \(\frac{4}{20} \times 100 = 20\%\) |
| **Total** |               | **20**        | **100%**                  |

### Final Table Summary:

| Class   | Tally         | Frequency (f) | Percentage (%) |
|---------|---------------|---------------|----------------|
| High    | 9             | 9             | 45%           |
| Average | 7             | 7             | 35%           |
| Low     | 4             | 4             | 20%           |
| **Total** |               | **20**        | **100%**      |

Let me know if you would like a deeper explanation of each step or have questions!

---

### Additional Questions:

1. How would you calculate the percentage if the total number of applicants changed?
2. What would happen to the percentages if there were an additional "High" rating?
3. Can you explain why the percentages add up to 100%?
4. How does the tally method help in counting data more effectively?
5. If a new category was added (e.g., "Very High"), how would it affect the table?

#### Tip:
When calculating percentages, ensure that all class counts are accurate before applying the formula, as this avoids calculation errors.

Construct a table from the given data showing performance appraisal ratings of twenty applicants (High, Average, Low) and calculate the frequency and percentage for each rating.

Learn how to create a frequency distribution table for performance appraisals of twenty applicants, tallying and calculating the percentage for each category: High, Average, and Low. This activity is ideal for middle school students, covering data collection, frequency, and percentage calculations.

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