Final answer:
The upper limits of a frequency distribution are generated by determining the range of data, deciding the number of intervals, dividing the range by the number of intervals to find interval width, and then adding this width to the minimum value for each subsequent interval, often with a small value adjustment to maintain distinct intervals.
Step-by-step explanation:
To generate the upper limits of a frequency distribution, you must first determine the range of your data set by finding the difference between the maximum and minimum values. Then decide on the number of intervals (classes) you wish to use, which typically depends on the data size. The range is divided by the number of intervals to determine the width of each interval. From there, you add the interval width to the minimum value to find the upper limit of the first interval and proceed similarly for subsequent intervals. It's crucial to decide whether to use the upper boundary method (where the upper limit of one interval is the lower limit of the next) or to add a small value to define distinct intervals.
For example, if we have a minimum value of 10, a maximum value of 100, and we choose five intervals, we would have intervals of width 18 ((100 - 10) / 5). Starting at 10, the first interval would be 10-28, the second would be 28-46, and so on, until the last interval encompasses values up to 100. Adjust the upper limits by adding a small value such as 0.5 to avoid overlapping. If we take the first interval 10-28 and add 0.5, the first interval would become 10-28.5, ensuring there are distinct upper limits for each interval.