Final answer:
To construct a frequency distribution with five classes, first calculate the class width, then count the number of data points per class. A relative frequency histogram can then be created, with the y-axis reflecting the proportion of data points in each class to identify the classes with the greatest and least relative frequency.
Step-by-step explanation:
To construct a frequency distribution for a dataset using five classes, first determine the range of the data by subtracting the smallest data point from the largest. Then, divide the range by the number of desired classes to find the class width. After rounding up to an appropriate level of precision, create the classes ensuring that they are mutually exclusive and exhaustive. Then, count the number of data points that fall into each class to find the frequency.
For the relative frequency histogram, the y-axis will represent the relative frequency, which is calculated by dividing the frequency of each class by the total number of data points in the dataset. Plot vertical bars for each class without gaps between them to create the histogram.
The class with the greatest relative frequency is the one with the highest proportion of the data points, while the class with the least relative frequency has the smallest proportion.