Question

the following is a list of p/e ratios (current stock price divided by companys earnings per share) for 16 companies.
57, 53, 50, 46, 42, 35, 31, 56, 52, 49, 34, 34, 30, 30, 55, 55

draw the histogram for these data using an initial class boundary of 29.5 and a class width of 6. note that you can add or remove classes from the figure. label each class with its endpoints.

Explanation:

Determine the class intervals

Using the Frequency Distribution knowledge point, we construct the class intervals. The initial class boundary starts at \(29.5\) with a class width of \(6\).
The intervals are:

• Class 1: \(29.5 - 35.5\)
• Class 2: \(35.5 - 41.5\)
• Class 3: \(41.5 - 47.5\)
• Class 4: \(47.5 - 53.5\)
• Class 5: \(53.5 - 59.5\)

Count the frequencies

Using the Frequency Distribution knowledge point, we sort and count the \(16\) data points:
\(30, 30, 31, 34, 34, 35, 42, 46, 49, 50, 52, 53, 55, 55, 56, 57\)

• For \(29.5 - 35.5\): \(30, 30, 31, 34, 34, 35\) \(

ightarrow\) Frequency = \(6\)

• For \(35.5 - 41.5\): None \(

ightarrow\) Frequency = \(0\)

• For \(41.5 - 47.5\): \(42, 46\) \(

ightarrow\) Frequency = \(2\)

• For \(47.5 - 53.5\): \(49, 50, 52, 53\) \(

ightarrow\) Frequency = \(4\)

• For \(53.5 - 59.5\): \(55, 55, 56, 57\) \(

ightarrow\) Frequency = \(4\)

Construct the histogram

Using the Histogram Construction knowledge point, we define the height of each bar corresponding to its class interval:

• \(29.5 - 35.5\): Height = \(6\)
• \(35.5 - 41.5\): Height = \(0\)
• \(41.5 - 47.5\): Height = \(2\)
• \(47.5 - 53.5\): Height = \(4\)
• \(53.5 - 59.5\): Height = \(4\)

Answer:

To construct the histogram for the given P/E ratios, the class boundaries and their corresponding frequencies are:

Class Boundaries	Frequency
\(35.5 - 41.5\)	\(0\)
\(41.5 - 47.5\)	\(2\)
\(47.5 - 53.5\)	\(4\)
\(53.5 - 59.5\)	\(4\)