Q.2.85 - Elementary Statistics

Question

Dementia is a person's loss of intellectual and social abilities that is severe enough to interfere with judgment, behavior, and daily functioning. Alzheimer's disease is the most common type of dementia. In the article "Living with Early Onset Dementia: Exploring the Experience and Developing EvidenceBased Guidelines for Practice" (Alzheimer's Care Quarterly, Vol. 5 , Issue 2, pp. 111-122), P. Harris and J. Keady explored the experience and struggles of people diagnosed with dementia and their families. A simple random sample of 21 people with early-onset dementia gave the following data on age, in years, at diagnosis. Use limit grouping with a first class of $40-44$ and a class width of 5 .

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)

$\begin{array}{|lll|}\hline \text{ Class }& \text{ Frequency }& \begin{array}{l}\text{ Relative }\\ \text{ frequency }\end{array}\\ 40-44& 4& 0.167\\ 45-49& 3& 0.125\\ 50-54& 4& 0.167\\ 55-59& 8& 0.333\\ 60-64& 2& 0.083\\ \text{ Total }& 24& 1\\ \hline\end{array}$

(b)

$\begin{array}{|lll|}\hline \text{ Class }& \text{ Frequency }& \begin{array}{l}\text{ Relative }\\ \text{ frequency }\end{array}\\ 40-44& 4& 0.167\\ 45-49& 3& 0.125\\ 50-54& 4& 0.167\\ 55-59& 8& 0.333\\ 60-64& 2& 0.083\\ \text{ Total }& 24& 1\\ \hline\end{array}$

(c)

(d)

Part (a)Step 1: Given information

Given in the question that,  Dementia is a person's loss of intellectual and social abilities that is severe enough to interfere with judgment, behavior, and daily functioning. Alzheimer's disease is the most common type of dementia. In the article "Living with Early Onset Dementia: Exploring the Experience and Developing EvidenceBased Guidelines for Practice" (Alzheimer's Care Quarterly, Vol. 5 , Issue 2, pp. 111-122), P. Harris and J. Keady explored the experience and struggles of people diagnosed with dementia and their families. A simple random sample of 21 people with early-onset dementia gave the following data on age, in years, at diagnosis. Use limit grouping with a first class of 40-44 and a class width of 5 .

We need to determine a frequency distribution. 

Part(a) Step 2: Explanation

The given data

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

The data's frequency distribution is as follows:

$\begin{array}{|lll|}\hline \text{ Class }& \text{ Frequency }& \begin{array}{l}\text{ Relative }\\ \text{ frequency }\end{array}\\ 40-44& 4& 0.167\\ 45-49& 3& 0.125\\ 50-54& 4& 0.167\\ 55-59& 8& 0.333\\ 60-64& 2& 0.083\\ \text{ Total }& 24& 1\\ \hline\end{array}$

Part(b) Step 1: Given information

Given in the question that,  Dementia is a person's loss of intellectual and social abilities that is severe enough to interfere with judgment, behavior, and daily functioning. Alzheimer's disease is the most common type of dementia. In the article "Living with Early Onset Dementia: Exploring the Experience and Developing EvidenceBased Guidelines for Practice" (Alzheimer's Care Quarterly, Vol. 5 , Issue 2, pp. 111-122), P. Harris and J. Keady explored the experience and struggles of people diagnosed with dementia and their families. A simple random sample of 21 people with early-onset dementia gave the following data on age, in years, at diagnosis. Use limit grouping with a first class of 40-44 and a class width of 5 .

We need to obtain a relative-frequency distribution. 

Part (b) Step 2: Explanation

The given data

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

The data's relative frequency distribution is as follows:

$\begin{array}{|lll|}\hline \text{ Class }& \text{ Frequency }& \begin{array}{l}\text{ Relative }\\ \text{ frequency }\end{array}\\ 40-44& 4& 0.167\\ 45-49& 3& 0.125\\ 50-54& 4& 0.167\\ 55-59& 8& 0.333\\ 60-64& 2& 0.083\\ \text{ Total }& 24& 1\\ \hline\end{array}$

Part(c) Step 1: Given information

Given in the question that,  Dementia is a person's loss of intellectual and social abilities that is severe enough to interfere with judgment, behavior, and daily functioning. Alzheimer's disease is the most common type of dementia. In the article "Living with Early Onset Dementia: Exploring the Experience and Developing EvidenceBased Guidelines for Practice" (Alzheimer's Care Quarterly, Vol. 5 , Issue 2, pp. 111-122), P. Harris and J. Keady explored the experience and struggles of people diagnosed with dementia and their families. A simple random sample of 21 people with early-onset dementia gave the following data on age, in years, at diagnosis. Use limit grouping with a first class of 40-44 and a class width of 5 .

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

Part(c) Step 2: Explanation

The given data

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,  Dementia is a person's loss of intellectual and social abilities that is severe enough to interfere with judgment, behavior, and daily functioning. Alzheimer's disease is the most common type of dementia. In the article "Living with Early Onset Dementia: Exploring the Experience and Developing EvidenceBased Guidelines for Practice" (Alzheimer's Care Quarterly, Vol. 5 , Issue 2, pp. 111-122), P. Harris and J. Keady explored the experience and struggles of people diagnosed with dementia and their families. A simple random sample of 21 people with early-onset dementia gave the following data on age, in years, at diagnosis. Use limit grouping with a first class of 40-44 and a class width of 5 .

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

Part(d) Step 2: Explanation

The given data

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: