Quantitative Methods MCQ - Quantitative Methods Section 1

66 The following observations are drawn from an approximately normal population:

Observation	1	2	3	4	5
Value	13	- 5	1	3	- 8

The sample standard deviation is closest to:

The sample variance is given by s2 = 264.8/5-1 = 66.2 The sample standard deviation is simple the square root of the sample variance. The sample standard deviation is 8.13.

67 UBL Fund’s return for the last five years are as follow:

Year	Return (%)
2009	-12
2010	10
2011	15
2012	17
2013	19

The mean absolute deviation of returns for this fund is closest to:

The Mean Absolute Deviation (MAD) is calculated through the following formula: Mean = (-12+10+15+17+19)/5 = 9.8% MAD = (|-12 - 9.8| + |10 - 9.8| + |15 – 9.8| + |17 – 9.8| + |19 – 9.8|)/5=8.72%.

68 The annual returns of a stock portfolio since its inception on 1 January 2008 is given below:

Year	Portfolio return
2008	7.5%
2009	9.0%
2010	11.5%
2011	-5.3%
2012	9.7%

The portfolio’s mean absolute deviation for the five-year period is closest to:

Compute the mean: (7.5 + 9.0 + 11.5 – 5.3 + 9.7) / 5 = 6.48% and compute MAD, (|7.5 – 6.48| + |9.0 – 6.48| + |11.5 – 6.48| + | –5.3 – 6.48| + |9.7 – 6.48|) / 5 = 4.71%.Compute the mean: (7.5 + 9.0 + 11.5 – 5.3 + 9.7) / 5 = 6.48% and compute MAD, (|7.5 – 6.48| + |9.0 – 6.48| + |11.5 – 6.48| + | –5.3 – 6.48| + |9.7 – 6.48|) / 5 = 4.71%.

69 The returns of a fund are given below:

Year	Return %
2009	5.0
2010	-3.2
2011	6.1
2012	4.5
2013	1.3

The mean absolute deviation of returns for this fund is closest to:

Mean is 2.74. MAD is the mean of the absolute deviations from 2.74: (2.26 + 5.94 + 3.36 + 1.76 + 1.44) / 5 = 2.95.

70 The table below shows the temperatures recorded at different places:

Place	Temperature (degree Celsius)	Place	Temperature (degree Celsius)
A	48	E	51
B	21	F	35
C	10	G	16
D	-8	H	-15

The range for this data is closest to:

Range = Maximum value - Minimum value Range = 51 - (-15 ) = 66.