21, 31, 33, 41, 18, 27, 52, 62, 72, 73, 69, 55, 37, 31, 18, 22,
25, 26, 29, 30, 36, 37, 42, 47, 58, 64, 57, 77, 76, 74, 71, 67       Find the 63 percentile

To find the 63rd percentile of a data set, we can follow these steps:

### Steps:
1. **Order the data** from least to greatest.
2. **Determine the index** corresponding to the 63rd percentile using the formula:
   
   \[
   \text{Index} = \frac{63}{100} \times (n + 1)
   \]
   
   where \(n\) is the number of data points.

3. If the index is a whole number, the percentile is the value at that index. If the index is not a whole number, interpolate between the values surrounding that index.

### Step 1: Order the data

The data ordered from least to greatest is:

\[
18, 18, 21, 22, 25, 26, 27, 29, 30, 31, 31, 33, 36, 37, 37, 41, 42, 47, 52, 55, 57, 58, 62, 64, 67, 69, 71, 72, 73, 74, 76, 77
\]

### Step 2: Calculate the index
There are 32 data points, so:

\[
\text{Index} = \frac{63}{100} \times (32 + 1) = 0.63 \times 33 = 20.79
\]

### Step 3: Interpolation
The 63rd percentile lies between the 20th and 21st data points (since the index is 20.79).

- 20th value: 55
- 21st value: 57

Now interpolate:

\[
\text{Percentile value} = 55 + 0.79 \times (57 - 55) = 55 + 0.79 \times 2 = 55 + 1.58 = 56.58
\]

### Conclusion:
The 63rd percentile of the data set is approximately **56.58**.

Would you like more details or have any questions about this?

Here are 5 related questions to expand on the topic:
1. How do you calculate other percentiles in a data set?
2. What is the difference between percentile rank and percentile value?
3. How is percentile used in standardized testing?
4. Can percentiles be used in non-numeric data sets?
5. What is the relationship between percentiles and quartiles?

**Tip**: Interpolation is used to estimate values between data points when the index is not a whole number!

Find the 63rd percentile of the data set: 21, 31, 33, 41, 18, 27, 52, 62, 72, 73, 69, 55, 37, 31, 18, 22, 25, 26, 29, 30, 36, 37, 42, 47, 58, 64, 57, 77, 76, 74, 71, 67

Learn how to calculate the 63rd percentile of the data set: 21, 31, 33, 41, 18, 27, 52, 62, 72, 73, 69, 55, 37, 31, 18, 22, 25, 26, 29, 30, 36, 37, 42, 47, 58, 64, 57, 77, 76, 74, 71, 67. This step-by-step solution explains how to order data, find the percentile index, and use interpolation to get the percentile value. Perfect for students in Grades 8-10.

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