Question 1
Multiple ChoiceThe table below shows the standard deviation of a set of 12 equity funds, ranked in ascending order:
Fund | Volatility (%) |
|---|---|
Fund A | 8.72 |
Fund B | 9.41 |
Fund C | 10.05 |
Fund D | 10.63 |
Fund E | 11.44 |
Fund F | 12.20 |
Fund G | 13.67 |
Fund H | 14.12 |
Fund I | 14.78 |
Fund J | 15.31 |
Fund K | 16.09 |
Fund L | 17.43 |
What is the approximate value of the third quartile?
Explanation
To find the third quartile (Q3), which is the 75th percentile, use the formula for the location of a percentile:
L _{y} = (n+1) × ( \frac{y}{100} )
Here:
n=12 (number of funds)
y=75 (for the 75th percentile)
L _{25} = (12 + 1) × \frac{75}{100} = 13 × 0.75 =9.75
So, the third quartile lies between the 9th and 10th positions in the sorted list:
9th = 14.78%
10th = 15.31%
We interpolate between these two values:
Q3 = 14.78 + 0.75 × (15.31 − 14.78) = 14.78 + 0.3975 = 15.18%
So the value is closet to 15.31%.
Key takeaway:
When using percentiles or quartiles in ordered data, always:
Use the percentile location formula.
Interpolate between values if needed.
Choose the closest option.