Find the value What’s the 53rd percentile 

What’s the 100th percentile 

Class
366-386
387-407
408-428
429-449
450-470
471-491
492-512
513-533

Frequency
3
3
3
1
1
1
2
7

To find the 53rd and 100th percentiles for a frequency distribution, we first need to calculate the cumulative frequency for each class and use these values to find the respective percentiles.

Here is the process for finding percentiles step by step:

### Step 1: Calculate the Cumulative Frequency
The cumulative frequency is the running total of the frequency as you move down the classes. Let's calculate it for each class:

| Class   | Frequency | Cumulative Frequency |
|---------|-----------|----------------------|
| 366-386 | 3         | 3                    |
| 387-407 | 3         | 6                    |
| 408-428 | 3         | 9                    |
| 429-449 | 1         | 10                   |
| 450-470 | 1         | 11                   |
| 471-491 | 1         | 12                   |
| 492-512 | 2         | 14                   |
| 513-533 | 7         | 21                   |

The total cumulative frequency is 21, which represents all the data points.

### Step 2: Calculate the 53rd Percentile
To find the position of the 53rd percentile, we calculate:

\[
P_{53} = \left( \frac{53}{100} \right) \times \text{Total Frequency} = 0.53 \times 21 = 11.13
\]

This means the 53rd percentile lies between the 11th and 12th data points. From the cumulative frequency, we see that the 11th and 12th data points are in the class **471-491**.

Thus, the 53rd percentile corresponds to the class interval **471-491**.

### Step 3: Calculate the 100th Percentile
The 100th percentile corresponds to the highest value in the data, which will always fall in the last class. In this case, the 100th percentile is in the class interval **513-533**, as it represents the highest possible value in this dataset.

### Summary:
- The **53rd percentile** lies in the class **471-491**.
- The **100th percentile** lies in the class **513-533**.

Would you like more details on the method, or help with another question?

Here are 5 related questions to expand on the topic:
1. How do you calculate percentiles for continuous data?
2. Can you explain how to calculate the exact value within a class for a specific percentile?
3. What is the difference between percentiles and quartiles?
4. How do percentiles help in interpreting frequency distributions?
5. What is the process for calculating percentiles in grouped data with unequal class widths?

**Tip:** Percentiles help identify the position of data points relative to the entire dataset, offering insight into data distribution and comparison.

Find the value What’s the 53rd percentile What’s the 100th percentile Class 366-386 387-407 408-428 429-449 450-470 471-491 492-512 513-533 Frequency 3 3 3 1 1 1 2 7

Learn how to calculate the 53rd and 100th percentiles for a given frequency distribution. This example demonstrates cumulative frequency calculations and percentile positioning, perfect for students in Grades 9-12. Understand key statistical concepts and formulas with detailed solutions.

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