https://file.aiquickdraw.com/mathbot/file/1726681834550z7sty3f1.jpg

I see that you need to find the 25th, 50th, and 75th percentiles from a list of 33 observations, which is displayed in the image. Let's solve it step by step.

### 1. **Arrange the Data in Order**
The data is already listed from smallest to largest in the image, so no need to rearrange it:
```
6, 7, 8, 11, 12, 14, 18, 19, 21, 25, 40, 42, 43, 44, 47, 
49, 51, 52, 57, 58, 61, 62, 63, 67, 75, 77, 82, 84, 87, 
95, 97, 98, 100
```

### 2. **Percentile Calculations**

- **25th Percentile (Q1):**
  The formula for percentile rank is:
  \[
  P = \frac{n}{100} \times \text{(Percentile Rank)}
  \]
  For the 25th percentile:
  \[
  P = \frac{33 + 1}{4} = 8.5
  \]
  We round this to the nearest rank, which is the 8th and 9th numbers in the list, i.e., 19 and 21. The average of these two values is:
  \[
  \frac{19 + 21}{2} = 20
  \]
  So, the 25th percentile is **20**.

- **50th Percentile (Median, Q2):**
  The 50th percentile is the median, which corresponds to the middle value:
  \[
  \text{Median Rank} = \frac{33 + 1}{2} = 17
  \]
  The 17th value in the list is **51**, so the 50th percentile is **51**.

- **75th Percentile (Q3):**
  For the 75th percentile:
  \[
  P = \frac{3(33 + 1)}{4} = 25.5
  \]
  This corresponds to the 25th and 26th values in the list, i.e., 75 and 77. The average of these two values is:
  \[
  \frac{75 + 77}{2} = 76
  \]
  So, the 75th percentile is **76**.

### Final Results:
- **25th percentile (Q1): 20**
- **50th percentile (Q2): 51**
- **75th percentile (Q3): 76**

Would you like further details or clarifications on this? 

Here are 5 related questions to consider:
1. How are percentiles used in interpreting data sets?
2. What is the significance of quartiles in statistics?
3. Can the percentile formula change for a non-equidistant data set?
4. How does the number of observations affect the calculation of percentiles?
5. What is the relationship between percentiles and standard deviation?

**Tip:** Always check whether the data set is arranged in ascending order before calculating percentiles.

Find the 25th, 50th, and 75th percentile from the following list of 33 observations: [6, 7, 8, 11, 12, 14, 18, 19, 21, 25, 40, 42, 43, 44, 47, 49, 51, 52, 57, 58, 61, 62, 63, 67, 75, 77, 82, 84, 87, 95, 97, 98, 100].

Find the 25th, 50th (median), and 75th percentiles from a set of 33 observations. This detailed step-by-step solution covers key concepts like percentiles and median, showing the calculations for each quartile. Suitable for Grades 9-12 students studying descriptive statistics.

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