Answer: 4.8.

## Explanation To find the fourth quintile (also known as the 80th percentile), we need to calculate the position of this percentile in the ordered dataset. **Step 1: Arrange the data in ascending order** The data is already in ascending order: 0, 2, 3, 4, 6 Number of observations (n) = 5 **Step 2: Calculate the position of the 80th percentile** The formula for the position of the p-th percentile is: Position = (n + 1) × p/100 For the 80th percentile (p = 80): Position = (5 + 1) × 80/100 = 6 × 0.8 = 4.8 **Step 3: Determine the value at position 4.8** Since the position is not an integer (4.8), we need to interpolate between the 4th and 5th values in the ordered dataset. The 4th value in the dataset is 4 The 5th value in the dataset is 6 **Step 4: Interpolation calculation** Value = Value at lower position + (Fractional part) × (Difference between consecutive values) Value = 4 + (0.8) × (6 - 4) Value = 4 + 0.8 × 2 Value = 4 + 1.6 = 5.6 Wait, this gives us 5.6, but that's option C. Let me double-check the calculation. Actually, I need to reconsider. The position is 4.8, which means we need the value between the 4th and 5th observations. But in statistics, when using the (n+1) method, position 4.8 means: - The integer part is 4, so we look at the 4th observation (value = 4) - The fractional part is 0.8, so we need to move 80% of the way from the 4th to the 5th observation So: 4 + 0.8 × (6 - 4) = 4 + 0.8 × 2 = 4 + 1.6 = 5.6 This suggests the answer should be C (5.6), not B (4.8). However, let me check if there's a different interpretation. Some statistical methods use different formulas for percentile calculation. The CFA curriculum typically uses the following approach: **CFA Method for Percentiles:** Position = (n + 1) × y/100 Where y is the percentile point (80 for 80th percentile) For our data: Position = (5 + 1) × 80/100 = 6 × 0.8 = 4.8 Since 4.8 is between 4 and 5: Value = Value at position 4 + 0.8 × (Value at position 5 - Value at position 4) Value = 4 + 0.8 × (6 - 4) = 4 + 1.6 = 5.6 **Conclusion:** The correct answer should be **C. 5.6**. **Why 4.8 (option B) is incorrect:** 4.8 is the position number (4.8th position), not the value at that position. The question asks for the "value" of the fourth quintile, not its position. **Why 4.0 (option A) is incorrect:** This is simply the 4th value in the dataset, which would correspond to the 4th observation, not the 80th percentile. Therefore, the correct answer is **C. 5.6**.

Author: LeetQuiz .