Quantitative Methods - Quantitative Methods Section 1
41. The actual number of observations in a given interval is known as the:
- Option : A
- Explanation : The actual number of observations in a given interval is known as the absolute frequency. Relative frequency is the absolute frequency of each interval divided by the total number of observations. the absolute frequency for an interval is calculated as the sum of the absolute frequencies of all intervals lower than and including that interval.
42. Which of the following statements about frequency distribution is most accurate?
- Option : C
- Explanation : The cumulative relative frequency is the fraction of the observations that are less than the upper limit of each interval. A is incorrect as an observation cannot fall in more than one interval. B is incorrect as the data is sorted in ascending order for the construction of a frequency distribution.
43. Which of the following statements about histograms is least likely accurate?
- Option : C
- Explanation : In the histogram, the height represents the absolute frequency for each interval.
- Option : A
- Explanation : For a frequency polygon, the mid points for each interval are plotted on the x-axis and the absolute frequency for that interval on the y-axis.
45. The following table shows the average monthly returns of a portfolio over the past one year:
| Month  | Return(%) | Month | Return(%) |
| January  | 10% | July | 5% |
| February | 15% | August | 6% |
| March  | 14% | September |  7.5% |
| April  | 11% | October | 9% |
| May | 8% | November | 12% |
| June  | 3% | December | 11% |
The following intervals are used for the construction of the frequency polygon:
| Interval |
| 1 < r < 3 |
| 4 < r < 6 |
| 7 < r < 9 |
| 10 < r < 12 |
| 13 < r < 15 |
The cumulative relative frequency for the interval ‘10 ≤ r ≤ 12’ is equal to:
- Option : C
- Explanation :
Interval  Frequency RelativeFrequency Cumulative Relative Frequency 1 < r < 3 1 8.33% 8.33% 4 < r < 6  2 16.67% 25% 7 < r < 9 3 25% 50% 10 < r < 12  4 33.33% 83.33% 13 < r < 15 2 16.67% 100% Relative Frequency = Frequency / Total Observations
Cumulative relative frequency is the sum of subsequent relative frequencies. Thus the cumulative relative frequency is 83.33% for the interval 10 < r <12. The cumulative frequency distribution allows us to see how many or what percent of the observations lie below a certain value.
