Final answer:
To create a frequency distribution starting with a lower class limit of 0 and a class width of 0.50, determine the upper limits accordingly and tally the data points within each class, also calculating midpoints for graphing purposes.
Step-by-step explanation:
Constructing a Frequency Distribution
To construct a frequency distribution with a first class having a lower class limit of 0 and a class width of 0.50, you would start by determining the upper class limit for the first interval. Since the class width is 0.50, if the lower limit is 0, the upper limit would be 0 + 0.50 = 0.50. The next class would then start just above this upper limit, at 0.50, and extend to 0.50 + 0.50 = 1.00. This process would continue, defining each subsequent class with a lower limit that is 0.50 higher than the upper limit of the previous class.
The midpoint for each class can be found by taking the average of the lower and upper limits. For example, the midpoint of the first class (0 - 0.50) is 0.25. When creating a histogram or frequency polygon, these midpoints are useful for accurately plotting the frequency of each class interval.
If the frequency distribution is for a set of data, you would tally the number of data points falling within each class interval. The cumulative frequency would start with the frequency of the first class and each subsequent class's frequency would be added to the cumulative total.