Quantitative Methods - Quantitative Methods Section 1
51. The table below shows some sample figures:
| - 25 | - 12 | -2 | 0 | 1 |
| 2 | 6 | 7 | 9 | 11 |
| 13 | 19 | 20 | 21 | 25 |
| 29 | 39 | 41 | 55 | 65 |
The median value of the above items is closest to:
- Option : B
- Explanation : Median is the value of the middle item of a set of items. The value of the 10th item is 11; the value of the 11th item is 13. The mean of 11 and 13 is 12.
52. The discount rate set by the central bank of country XYZ for the past 6 quarters is shown below:
| Quarter | Discount Rate | Quarter | Discount Rate |
| 1 | 10.0% | 4 | 8.5% |
| 2 | 10.5% | 5 | 9.6% |
| 3 | 11.4% | 6 | 11.5% |
The sample mean rate for the 6 quarters is closest to:
- Option : A
- Explanation : Sample Mean = ∑t=Xi / N = (10.0 + 10.5 + 11.4 + 8.5 + 9.6 + 11.5) / 6 = 10.25%
53. Which of the following statements about arithmetic mean is most accurate?
- Option : A
- Explanation : B is incorrect because the sum of the deviations around the mean is equal to 0. C is incorrect because the advantage of an arithmetic mean is that it makes use of all data.
54. The discount rate set by the central bank of Romulus for the past 6 quarters is shown below:
| Quarter | Discount Rate | Quarter | Discount Rate |
| 1 | 10.0% | 4 | 8.5% |
| 2 | 10.5% | 5 | 9.6% |
| 3 | 11.4% | 6 | 11.5% |
The median is closest to:
- Option : A
- Explanation : Arrange the data in ascending order as: 8.5, 9.6, 10.0, 10.5, 11.4, 11.5 Since there are an even number of observations, take the average of the two middle values to calculate median: (10.0 + 10.5) / 2 = 10.25 Median = 10.25 percent
| Interval | Frequency |
| 0 ≤ r ≤ 10 | 29 |
| 10 < r ≤ 20 | 37 |
| 20 < r ≤ 30 | 31 |
| 30 < r ≤ 40 | 35 |
| 40 < r ≤ 50 | 33 |
The modal interval of this distribution is most likely:
- Option : B
- Explanation : The modal interval is the interval with the highest frequency, which in this case, is 10 < r ≤ 20.
