A qualitative variable is measured for 20 companies randomly sampled and the data are classified into three classes, small (S), medium (M), and large (L), based on the number of employees in each company. The data (observed class for each company) are listed below. ______________________________________ SSL M SM M S M S L M S SSS M L S L ----------------------------------------------------------------

a. Compute the frequency for each of the three classes.

b. Compute the relative frequency for each of the three classes.

c. Display the results, part a, in a frequency bar graph.

d. Display the results, part b, in a pie chart.

In the array of data, it can be observed that there is a total of 10 small (S) size companies. Other than small companies, there are 4 large (L) size companies and 6 medium (M) size companies.

The calculation of relative frequencies of small (S), large (L), and medium (M) companies are shown below:

$$\begin{gathered} \mathbf{Relative} \mathbf{frequency} \mathbf{of} \mathbf{S}\mathbf{=}\frac{\mathbf{Frequency} \mathbf{of} \mathbf{S}}{\mathbf{Frequency} \mathbf{of} \mathbf{S}\mathbf{+}\mathbf{Frequency} \mathbf{of} \mathbf{L}\mathbf{+}\mathbf{Frequency} \mathbf{of} \mathbf{M}} \\ \mathbf{=}\frac{\mathbf{10}}{\mathbf{10}\mathbf{+}\mathbf{4}\mathbf{+}\mathbf{6}} \\ \mathbf{=}\frac{\mathbf{10}}{\mathbf{20}} \\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{5} \\ \mathbf{Relative} \mathbf{frequency} \mathbf{of} \mathbf{L}\mathbf{=}\frac{\mathbf{Frequency} \mathbf{of} \mathbf{L}}{\mathbf{Frequency} \mathbf{of} \mathbf{S}\mathbf{+}\mathbf{Frequency} \mathbf{of} \mathbf{L}\mathbf{+}\mathbf{Frequency} \mathbf{of} \mathbf{M}} \\ \mathbf{=}\frac{\mathbf{4}}{\mathbf{10}\mathbf{+}\mathbf{4}\mathbf{+}\mathbf{6}} \\ \mathbf{=}\frac{\mathbf{4}}{\mathbf{20}} \\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{2} \\ \mathbf{Relative} \mathbf{frequency} \mathbf{of} \mathbf{M}\mathbf{=}\frac{\mathbf{Frequency} \mathbf{of} \mathbf{M}}{\mathbf{Frequency} \mathbf{of} \mathbf{S}\mathbf{+}\mathbf{Frequency} \mathbf{of} \mathbf{L}\mathbf{+}\mathbf{Frequency} \mathbf{of} \mathbf{M}} \\ \mathbf{=}\frac{\mathbf{6}}{\mathbf{10}\mathbf{+}\mathbf{4}\mathbf{+}\mathbf{6}} \\ \mathbf{=}\frac{\mathbf{6}}{\mathbf{20}} \\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{3} \end{gathered}$$

In the bar graph, the classes are plotted on the horizontal axis, and the frequencies are plotted on the vertical axis. The tallest bar represents the frequency of the small (S) companies, the medium-sized bar represents the medium (M) sized companies, and the shortest one represents the large (L) companies.

In the pie chart, the section showing the dark grey color represents the small companies that acquired the largest portion of the pie chart followed by the other two. Amongst the other two, the section showing aqua green color represents the large (L) companies, and the section showing light blue color represents the medium (M) sized companies.