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can you do the assessment about this percentiles 

The image you provided discusses how to calculate percentiles, specifically finding the 60th percentile of a given set of data.

### Here's a breakdown of the problem from the image:

1. **Given Data:**
   - Ages of teachers in CES: 20, 21, 23, 25, 27, 51, 55, 56.
   
2. **Find:**
   - The 60th percentile.

### Step-by-Step Solution:

1. **Formula for Percentile:**
   \[
   P = \frac{n \cdot k}{100}
   \]
   where:
   - \(P\) is the position of the percentile in the data set.
   - \(n\) is the total number of data points.
   - \(k\) is the desired percentile (in this case, 60).

2. **Applying the Formula:**
   - Total number of data points \(n = 8\).
   - For the 60th percentile: \(k = 60\).

   Substituting the values:
   \[
   P = \frac{8 \times 60}{100} = 4.8
   \]

3. **Interpreting the Position:**
   - The result, 4.8, suggests that the 60th percentile lies between the 4th and 5th data points.

4. **Finding the Percentile Value:**
   - Arrange the data in ascending order: 20, 21, 23, 25, 27, 51, 55, 56.
   - The 4th data point is 25, and the 5th data point is 27.

   To find the 60th percentile, interpolate between these two values:
   \[
   \text{Percentile value} = 25 + (4.8 - 4) \times (27 - 25)
   \]
   \[
   = 25 + 0.8 \times 2 = 25 + 1.6 = 26.6
   \]

5. **Interpretation:**
   - The 60th percentile is approximately 26.6 years. This means that 60% of the teachers are younger than or equal to 26.6 years.

Would you like to see more details or have any questions about this? Here are a few related questions for further practice:

1. What is the 25th percentile of the given data set?
2. How would you find the median (50th percentile) of this data?
3. What is the difference between percentiles and quartiles?
4. How do you compute the 90th percentile for the data?
5. If a new teacher aged 30 joins, how does it affect the 60th percentile?

**Tip:** Percentiles are useful in understanding the distribution of data points within a set, particularly in statistics and data analysis.

Can you do the assessment about this percentiles?

Learn how to calculate the 60th percentile of a given data set of teacher ages (20, 21, 23, 25, 27, 51, 55, 56). This problem uses the percentile position formula and interpolation to find that 60% of teachers are younger than 26.6 years. Suitable for students in Grades 10-12.

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