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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.)

Short Answer

Expert verified

The relative frequency distribution is constructed as follows:

Adverse reactions

Relative Frequency

Headache

23.55%

Hypertension

8.68%

Upper respiratory tract infection

24.79%

Nasopharyngitis

21.07%

Diarrhea

21.9%

There is no adverse reaction that occurs much frequently than others.

Step by step solution

01

Given information

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

02

Define relative frequency

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

Relativefrequencyofaclassinterval=FrequencyofaclassintervalSumofallfrequencies×100%

03

Calculate the relative frequencies

The table below shows the frequencies of different adverse reactions:

Adverse reactions

Frequency

Headache

57

Hypertension

21

Upper respiratory tract infection

60

Nasopharyngitis

51

Diarrhea

53

The sum of all frequencies is shown below:

Sumofallfrequencies=57+21+60+51+53=242

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

Relativefreq1=57242×100%=23.55%Relativefreq2=21242×100%=8.68%

Relativefreq3=60242×100%=24.79%Relativefreq4=51242×100%=21.07%

Relativefreq5=53242×100%=21.9%

Adverse reactions

Relative Frequency

Headache

23.55%

Hypertension

8.68%

Upper respiratory tract infection

24.79%

Nasopharyngitis

21.07%

Diarrhea

21.9%

Total

99.99%

04

Analysis

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.

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