Q.2.87 - Elementary Statistics

Question

 Patients who undergo chronic hemodialysis often experience severe anxiety. Videotapes of progressive relaxation exercises were shown to one group of patients and neutral videotapes to another group. Then both groups took

the State-Trait Anxiety Inventory, a psychiatric questionnaire used to measure anxiety, on which higher scores correspond to higher anxiety. In the paper "The Effectiveness of Progressive Relaxation in Chronic Hemodialysis Patients" (Journal of Chronic Diseases, Vol. 35, No. 10), R. Alarcon et al. presented the results of the study. The following data give score results for the group that viewed relaxation-exercises videotapes. Use limit grouping with a first class of 12-17 and a class width of 6 .

a. determine a frequency distribution.

b. obtain a relative-frequency distribution.

c. construct a frequency histogram based on your result from part (a).

d. construct a relative-frequency histogram based on your result from part (b).

Step-by-Step Solution

Answer

(a)

 $\begin{array}{|lll|}\hline \text{ Class }& \text{ Frequency }& \begin{array}{l}\text{ Relative }\\ \text{ frequency }\end{array}\\ 12-17& 2& 0.065\\ 18-23& 3& 0.097\\ 24-29& 6& 0.194\\ 30-35& 5& 0.161\\ 36-41& 10& 0.323\\ 42-47& 4& 0.129\\ 48-53& 0& 0\\ 54-59& 0& 0\\ 60-65& 1& 0.032\\ \hline\end{array}$

(b)

$\begin{array}{|lll|}\hline \text{ Class }& \text{ Frequency }& \begin{array}{l}\text{ Relative }\\ \text{ frequency }\end{array}\\ 12-17& 2& 0.065\\ 18-23& 3& 0.097\\ 24-29& 6& 0.194\\ 30-35& 5& 0.161\\ 36-41& 10& 0.323\\ 42-47& 4& 0.129\\ 48-53& 0& 0\\ 54-59& 0& 0\\ 60-65& 1& 0.032\\ \hline\end{array}$

(c)

(d)

Part (a)Step 1: Given information

Given in the question that,  Patients who undergo chronic hemodialysis often experience severe anxiety. Videotapes of progressive relaxation exercises were shown to one group of patients and neutral videotapes to another group. Then both groups took the State-Trait Anxiety Inventory, a psychiatric questionnaire used to measure anxiety, on which higher scores correspond to higher anxiety. In the paper "The Effectiveness of Progressive Relaxation in Chronic Hemodialysis Patients" (Journal of Chronic Diseases, Vol. 35, No. 10), R. Alarcon et al. presented the results of the study. The following data give score results for the group that viewed relaxation-exercises videotapes. Use limit grouping with a first class of 12-17 and a class width of 6 .

We need to determine a frequency distribution. 

Part(a) Step 2: Explanation

The given data is,

The number of values that fall between the class's bounds is the frequency.

The data's frequency distribution is as follows:

$\begin{array}{|lll|}\hline \text{ Class }& \text{ Frequency }& \begin{array}{l}\text{ Relative }\\ \text{ frequency }\end{array}\\ 12-17& 2& 0.065\\ 18-23& 3& 0.097\\ 24-29& 6& 0.194\\ 30-35& 5& 0.161\\ 36-41& 10& 0.323\\ 42-47& 4& 0.129\\ 48-53& 0& 0\\ 54-59& 0& 0\\ 60-65& 1& 0.032\\ \hline\end{array}$

Part(b) Step 1: Given information

Given in the question that,  Patients who undergo chronic hemodialysis often experience severe anxiety. Videotapes of progressive relaxation exercises were shown to one group of patients and neutral videotapes to another group. Then both groups took the State-Trait Anxiety Inventory, a psychiatric questionnaire used to measure anxiety, on which higher scores correspond to higher anxiety. In the paper "The Effectiveness of Progressive Relaxation in Chronic Hemodialysis Patients" (Journal of Chronic Diseases, Vol. 35, No. 10), R. Alarcon et al. presented the results of the study. The following data give score results for the group that viewed relaxation-exercises videotapes. Use limit grouping with a first class of 12-17 and a class width of 6 .

We need to obtain a relative-frequency distribution. 

Part (b) Step 2: Explanation

The given data is,

The frequency is divided by the overall frequency to get the relative frequency.

The data's relative frequency distribution is as follows:

$\begin{array}{|lll|}\hline \text{ Class }& \text{ Frequency }& \begin{array}{l}\text{ Relative }\\ \text{ frequency }\end{array}\\ 12-17& 2& 0.065\\ 18-23& 3& 0.097\\ 24-29& 6& 0.194\\ 30-35& 5& 0.161\\ 36-41& 10& 0.323\\ 42-47& 4& 0.129\\ 48-53& 0& 0\\ 54-59& 0& 0\\ 60-65& 1& 0.032\\ \hline\end{array}$

Part(c) Step 1: Given information

Given in the question that,  Patients who undergo chronic hemodialysis often experience severe anxiety. Videotapes of progressive relaxation exercises were shown to one group of patients and neutral videotapes to another group. Then both groups took the State-Trait Anxiety Inventory, a psychiatric questionnaire used to measure anxiety, on which higher scores correspond to higher anxiety. In the paper "The Effectiveness of Progressive Relaxation in Chronic Hemodialysis Patients" (Journal of Chronic Diseases, Vol. 35, No. 10), R. Alarcon et al. presented the results of the study. The following data give score results for the group that viewed relaxation-exercises videotapes. Use limit grouping with a first class of 12-17 and a class width of 6 .

We need to construct a frequency histogram based on the result from part (a) 

Part(c) Step 2: Explanation

The given data is,

On a horizontal axis, the histogram shows the quantitative data classes, and on a vertical axis, the frequencies of those classes.

The bars must all be the same width and must be bordered by the lower class limitations.

The frequency must be represented by the height of the bars.

The frequency distribution histogram is shown below:

Part(d) Step 1: Given information

Given in the question that,  Patients who undergo chronic hemodialysis often experience severe anxiety. Videotapes of progressive relaxation exercises were shown to one group of patients and neutral videotapes to another group. Then both groups took the State-Trait Anxiety Inventory, a psychiatric questionnaire used to measure anxiety, on which higher scores correspond to higher anxiety. In the paper "The Effectiveness of Progressive Relaxation in Chronic Hemodialysis Patients" (Journal of Chronic Diseases, Vol. 35, No. 10), R. Alarcon et al. presented the results of the study. The following data give score results for the group that viewed relaxation-exercises videotapes. Use limit grouping with a first class of 12-17 and a class width of 6 .

We need to construct a relative-frequency histogram based on the result from part (b) 

Part(d) Step 2: Explanation

The given data is,

On a horizontal axis, the histogram shows the quantitative data classes, and on a vertical axis, the frequencies of those classes.

The bars must all be the same width and must be bordered by the lower class limitations.

The frequency must be represented by the height of the bars.

The relative frequency distribution histogram is shown below: