Quantitative Methods - 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:
- Option : C
- Explanation : 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:
- Option : A
- Explanation : 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:
- Option : B
- Explanation : 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:
- Option : B
- Explanation : 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:
