Chapter 2, Problem 1PS

A categorical variable has three categories, with the following frequencies of occurrence:

a. Compute the percentage of values in each category.

b. What conclusions can you reach concerning the categories?

To determine

Determine the percentage of values in each category.

Answer to Problem 1PS

The required percentages of categories A, B and C are $\text{26\%}$ , $56\%$ and $18\%$ , respectively.

Explanation of Solution

The frequency summary table is given.

The total frequency of all categories is:

$\begin{array}{c}\text{Total Frequency = Frequency of A + Frequency of B + Frequency of C}\\ =13+28+9\\ =50\end{array}$

The percentage of values in category A is:

$\begin{array}{c}\text{Percentage of A =}\frac{\text{Frequency of category A}}{\text{Total Frequency}}\times 100\%\\ =\frac{13}{50}\times 100\%\\ =26\%\end{array}$

The percentage of values in category B is:

$\begin{array}{c}\text{Percentage of B =}\frac{\text{Frequency of category B}}{\text{Total Frequency}}\times 100\%\\ =\frac{28}{50}\times 100\%\\ =56\%\end{array}$

The percentage of values in category C is:

$\begin{array}{c}\text{Percentage of C =}\frac{\text{Frequency of category C}}{\text{Total Frequency}}\times 100\%\\ =\frac{9}{50}\times 100\%\\ =18\%\end{array}$

The percentages of categories A, B and C are $\text{26\%}$ , $56\%$ and $18\%$ , respectively.

To determine

Write the conclusion about the different categories.

Explanation of Solution

The percentage of each category is calculated above.

By looking at the percentage of each category, it can be concluded that more than half of the values are in category B and about a quarter of the values are in category A while are comparatively less values, that is, $18\%$ in category C.