https://file.aiquickdraw.com/mathbot/file/1726708912734q2zu0f90.jpg

The image shows a table summarizing the scores of respondents from a questionnaire. The task is to determine the value of **P24**, which likely refers to the 24th percentile of the data.

### Here's how we approach it:

1. **Interpret the Data:**
   - The first row represents the **total score** out of 40 (since each question has a maximum score of 4, and there are 10 questions).
   - The second row represents the **number of respondents** corresponding to each total score.

#### Table Recap:
| **Jumlah Skor (Total Score)** | 20 | 23 | 25 | 26 | 27 | 28 | 30 | 33 | 34 | 35 | 36 | 37 | 38 | 39 |
|-------------------------------|----|----|----|----|----|----|----|----|----|----|----|----|----|----|
| **Banyaknya Responden (Respondents)** | 2  | 5  | 3  | 10 | 12 | 9  | 16 | 16 | 20 | 23 | 21 | 14 | 10 | 10 |

2. **Calculate the Total Number of Respondents:**
   We sum the total number of respondents to understand the dataset's size.
   
   \[
   \text{Total respondents} = 2 + 5 + 3 + 10 + 12 + 9 + 16 + 16 + 20 + 23 + 21 + 14 + 10 + 10
   \]

3. **Find the Position for P24:**
   The percentile position can be found using the formula:
   \[
   \text{Position of P24} = \left(\frac{24}{100} \times \text{Total respondents}\right)
   \]

4. **Determine the Score Corresponding to P24:**
   Once we have the position, we can use the cumulative frequency to find the total score that corresponds to this percentile.

Let me calculate that for you.The total number of respondents is **171**.

The position of the 24th percentile (P24) is approximately **41.04**. This means we are looking for the score that corresponds to the 41st respondent in the cumulative frequency.

Looking at the cumulative frequency:

- The cumulative frequency reaches **41** at a score of **28**.

Thus, the value of **P24** is **28**.

Would you like any further details or clarifications? Here are five related questions that could deepen your understanding:

1. How is a percentile calculated in larger datasets?
2. What is the difference between percentiles and quartiles?
3. How can we estimate other percentiles from the same data set?
4. What is the significance of cumulative frequency in percentile calculations?
5. How does the distribution of data affect percentile rankings?

**Tip:** When dealing with percentiles, always ensure that the dataset is sorted and cumulative frequencies are correctly calculated to avoid misinterpretations.

A questionnaire consists of 10 questions, each with a maximum score of 4. The image shows a summary of scores from respondents. The task is to determine the value of P24, representing the 24th percentile of the data.

Calculate the 24th percentile (P24) using cumulative frequency from a dataset of respondent scores. The data includes scores for 10 questions, with a detailed step-by-step solution provided. Suitable for Grades 10-12.

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