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The data provided is a list of numbers:

**31, 31, 35, 36, 39, 40, 43, 47, 50, 53, 53, 55, 55, 55, 59, 60, 62, 69, 70, 75, 79, 82, 85, 87, 87, 88, 90**

You are asked to calculate:
- **K_3** (quartile 3)
- **D_4** (decile 4)
- **P_67** (percentile 67)

Also, calculate:
- **K_2** (quartile 2)
- **D_5** (decile 5)
- **P_50** (percentile 50)

Let me explain the steps, and then I will calculate the values.

### Steps:
1. **Quartiles (K)** divide the data into four equal parts.
   - \( K_1 \) is the first quartile (25th percentile)
   - \( K_2 \) is the second quartile (median or 50th percentile)
   - \( K_3 \) is the third quartile (75th percentile)

2. **Deciles (D)** divide the data into ten equal parts.
   - \( D_1 \) is the 10th percentile
   - \( D_2 \) is the 20th percentile, and so on.
   - \( D_4 \) is the 40th percentile.
   - \( D_5 \) is the 50th percentile (same as median).

3. **Percentiles (P)** divide the data into 100 equal parts.
   - \( P_50 \) is the median (same as \( K_2 \)).
   - \( P_67 \) is the 67th percentile.

Let's calculate these now.Here are the calculated values based on the given dataHere are the calculated values based on the given 

- \( K_3 \) (Third Quartile or 75th percentile) = **77.0**
- \( D_4 \) (Fourth Decile or 40th percentile) = **53.8**
- \( P_{67} \) (67th Percentile) = **69.42**

Additionally:
- \( K_2 \) (Second Quartile or Median) = **55.0**
- \( D_5 \) (Fifth Decile or Median) = **55.0**
- \( P_{50} \) (50th Percentile or Median) = **55.0**

Let me know if you would like further details or have any questions.

### Related Questions:
1. What are the differences between quartiles, deciles, and percentiles?
2. How can we calculate these values for a larger dataset?
3. Why is the 50th percentile the same as the median?
4. Can we calculate the interquartile range using the \( K_1 \) and \( K_3 \) values?
5. How does the interpretation of percentiles change depending on the dataset?

### Tip:
When interpreting percentiles, they indicate the percentage of data points that fall below a given value, which is useful for understanding the distribution of data.

Data tersebar 31, 31, 35, 36, 39, 40, 43, 47, 50, 53, 53, 55, 55, 55, 59, 60, 62, 69, 70, 75, 79, 82, 85, 87, 87, 88, 90. Hitung nilai K3, D4 dan P67. hitung pula nilai K2, D5 dan P50.

Learn how to calculate the 3rd quartile (K3), 4th decile (D4), and 67th percentile (P67) for the data set: 31, 31, 35, 36, 39, 40, 43, 47, 50, 53, 53, 55, 55, 55, 59, 60, 62, 69, 70, 75, 79, 82, 85, 87, 87, 88, 90. Also, find K2, D5, and P50.

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