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.