Categorical Data. In Exercises 23 and 24, use the given categorical data to construct the relative frequency distribution.

Clinical Trial When XELJANZ (tofacitinib) was administered as part of a clinical trial for this rheumatoid arthritis treatment, 1336 subjects were given 5 mg doses of the drug, and here are the numbers of adverse reactions: 57 had headaches, 21 had hypertension, 60 had upper respiratory tract infections, 51 had nasopharyngitis, and 53 had diarrhoea. Does any one of these adverse reactions appear to be much more common than the others? (Hint: Find the relative frequencies using only the adverse reactions, not the total number of treated subjects.)

The frequency distribution of the adverse reactions of a drug as a part of a treatment is provided.

The relative frequency of a class interval in a grouped frequency distribution is obtained using the given formula:

$\text{Relative}\text{frequency}\text{of}\text{a}\text{class}\text{interval}=\frac{\text{Frequency}\text{of}\text{a}\text{class}\text{interval}}{\text{Sum}\text{of}\text{all}\text{frequencies}}\times 100\%$

The table below shows the frequencies of different adverse reactions:

The sum of all frequencies is shown below:

$$\begin{gathered} \text{Sum}\text{of}\text{all}\text{frequencies}=57+21+60+51+53 \\ =242 \end{gathered}$$

Using the formula mentioned above, the relative frequencies for the different categories are calculated as shown below:

$$\begin{gathered} \text{Relative}{\text{freq}}_1=\frac{57}{242}\times 100\% \\ =23.55\% \\ \text{Relative}{\text{freq}}_2=\frac{21}{242}\times 100\% \\ =8.68\% \end{gathered}$$

$$\begin{gathered} \text{Relative}{\text{freq}}_3=\frac{60}{242}\times 100\% \\ =24.79\% \\ \text{Relative}{\text{freq}}_4=\frac{51}{242}\times 100\% \\ =21.07\% \end{gathered}$$

$$\begin{gathered} \text{Relative}{\text{freq}}_5=\frac{53}{242}\times 100\% \\ =21.9\% \end{gathered}$$

It can be observed that the highest relative frequency,equal to 224.79%, is not very high as compared to the other frequencies.

Therefore, there is not one particular adverse reaction that appears to occur much more frequently than others.