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The task requires computing the percentiles, deciles, and quartiles from ungrouped data using the scores provided. The data set is:

\[ 10, 11, 12, 14, 16, 18, 19, 20, 21, 22, 24, 25 \]

Let's go step by step to calculate each:

1. **Percentiles** (\( P_k \)):
   Percentiles divide the data into 100 equal parts. The formula for the percentile rank is:
   \[
   P_k = \left( \frac{k}{100} \right) \times (N + 1)
   \]
   where \( N \) is the number of observations and \( k \) is the percentile rank.

2. **Deciles** (\( D_k \)):
   Deciles divide the data into 10 equal parts. The formula for the decile rank is:
   \[
   D_k = \left( \frac{k}{10} \right) \times (N + 1)
   \]

3. **Quartiles** (\( Q_k \)):
   Quartiles divide the data into 4 equal parts. The formula for the quartile rank is:
   \[
   Q_k = \left( \frac{k}{4} \right) \times (N + 1)
   \]

Let me calculate the requested values for:
1. \( P_{60} \)
2. \( P_{40} \)
3. \( D_9 \)
4. \( Q_2 \)
5. \( D_8 \)

I'll perform the calculations now.Here are the calculated values for the requested percentiles, deciles, and quartiles:

1. \( P_{60} \) (60th Percentile) = **19.8**
2. \( P_{40} \) (40th Percentile) = **16.4**
3. \( D_9 \) (9th Decile) = **24.7**
4. \( Q_2 \) (2nd Quartile, or Median) = **18.5**
5. \( D_8 \) (8th Decile) = **22.8**

Let me know if you'd like more details or if you have any questions.

Here are some related questions:
1. How do percentiles help in data analysis?
2. What's the difference between quartiles and deciles?
3. Why is interpolation used in calculating percentiles?
4. What does the second quartile (median) represent in a dataset?
5. Can the same method be used for grouped data?

**Tip:** Percentiles, deciles, and quartiles help describe the distribution of data and locate values relative to the entire dataset.

Using the scores below, compute the percentile, decile, and quartile using ungrouped data. Scores: 10, 11, 12, 14, 16, 18, 19, 20, 21, 22, 24, 25. Find P60, P40, D9, Q2, D8.

Learn how to calculate percentiles, deciles, and quartiles using ungrouped data. This guide covers step-by-step solutions for finding P60, P40, D9, Q2, and D8 with a given dataset. Suitable for Grades 9-12.

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