Step 1 :We are given a list of P/E ratios for 22 companies and we need to draw a histogram for these data. The histogram should have an initial class boundary of 30.5, an ending class boundary of 60.5, and 5 classes of equal width.
Step 2 :First, calculate the width of each class. The width can be calculated by subtracting the initial class boundary from the ending class boundary and dividing by the number of classes. In this case, the width is \(\frac{60.5 - 30.5}{5} = 6.0\).
Step 3 :Next, create the classes and count the number of data points in each class. This can be done by iterating over the data and checking in which class each data point falls.
Step 4 :The classes are [30.5, 36.5), [36.5, 42.5), [42.5, 48.5), [48.5, 54.5), and [54.5, 60.5). The counts for each class are 5, 4, 7, 4, and 2 respectively.
Step 5 :Finally, draw the histogram using these counts. The x-axis represents the P/E ratio and the y-axis represents the number of companies.
Step 6 :\(\boxed{\text{The histogram shows the distribution of P/E ratios for the 22 companies. The classes are [30.5, 36.5), [36.5, 42.5), [42.5, 48.5), [48.5, 54.5), and [54.5, 60.5). The counts for each class are 5, 4, 7, 4, and 2 respectively.}}\)