Quantitative Methods MCQ - Quantitative Methods Section 1

61 The table below shows data on the volatility of a series of funds:

Fund	Volatility (%)
Fund 1	5.05
Fund 2	6.20
Fund 3	6.93
Fund 4	7.56
Fund 5	8.25
Fund 6	10.11
Fund 7	11.36
Fund 8	14.52
Fund 9	15.02
Fund 10	15.66
Fund 11	15.98
Fund 12	16.01
Fund 13	19.25

The value of the second quintile is closest to:

62 Which of the following statements is least accurate?

The first quintile is the 20th percentile and the third quintile is the 60th percentile. The first decile is the 10th percentile, the first quartile is the 25th percentile, and the median is the 50th percentile. While it is possible that these various percentiles or some subsets of them might be equal (for example the10th percentile possibly could be equal to the 20th percentile), in general the order from smallest to largest would be: first decile, first quintile, first quartile, median.

63 The following ten observations are a sample drawn from a normal population: 6, 12, 32, -12, 10, 3, -21, 15, 8, and 11. The third quintile (60th percentile) of the sample is closest to:

First we need to sort the data in ascending order: -21, -12, 3, 6, 8, 10, 11, 12, 15, 32. The third quintile corresponds to the 60th percentile. The location of the 60th percentile is given by: L60 = (10 + 1)60/100 = 6.6. The value is estimated using linear interpolation: P60 = 10 + 0.6(11– 10) = 10.6.

64 Which of the following statements is least likely accurate?

Linear interpolation is used when the location, L, is not a whole number and lies between two closest integers

65 The following table shows the earnings per share (EPS) of 20 hypothetical companies.

Company	EPS	Company	EPS
AB	$4.50	AAA	$13.22
CDE	$14.50	BBB	$13.25
FG	$9.33	CCC	$12.98
HIJ	$7.21	DDD	$11.54
KLM	$6.44	EEE	$11.73
NO	$6.99	FFF	$15.00
PQR	$6.27	GGG	$10.49
STU	$8.11	HHH	$5.78
VWX	$5.25	III	$6.50
YZ	$12.15	JJJ	$4.75

The 30th percentile is closest to:

The 30th percentile is the value at or below which 30 percent of observations lie. To solve this problem, we first arrange the 20 data points in ascending order: 4.50, 4.75, 5.25, 5.78, 6.29, 6.44, 6.50, 6.99, 7.21, 8.11, 9.33, 10.49, 11.54, 11.73, 12.15, 12.98, 13.22, 13.25, 14.50, and 15.00. The location of the 30th percentile is 30% of 20 = 6. The 6th data point is 6.44. The two numbers (6.44 and 6.46) are different because the percentile calculations using the location formula gives an approximate answer when n is small.