Q.2.38 - Elementary Statistics

Question

The National Center for Health Statistics collects data on health insurance coverage status and coverage type. The following data from the National Health Interview Survey provides the frequency, in millions, of the current health status for persons aged$19-64$ and persons aged $65$ and over.

a. Obtain a relative-frequency distribution of health status for persons aged $19-64$and a relative-frequency distribution of health status for persons aged $65$ and over.

b. Draw a pie chart for both age groups.

c. Compare your pie charts.

Step-by-Step Solution

Answer

(a)

(b) 

(c)

Figure 1 shows that the part for "Excellent/very good" health status is higher for those aged  than for the latter group.

People aged 19-64 have a lower percentage of "fair or poor" health condition than people aged 65 and over.

Part (a) Step 1: Given information

Given in the question that, The National Center for Health Statistics collects data on health insurance coverage status and coverage type. The following data from the National Health Interview Survey provides the frequency, in millions, of the current health status for persons aged $19-64$ and persons aged $65$ and over.

We need to obtain a relative-frequency distribution of health status for persons aged$19-64$ and a relative-frequency distribution of health status for persons aged $65$ and over.

Part (a) Step 2: Explanation

The relative frequency can be calculated using the formula,

$\text{ Relative Frequency }=\frac{\text{ Frequency }}{\text{ Number of Observations }}$

The table below shows the relative frequency distribution for the age group $19-64.$

Health	Frequency	Relative Frequency
Excellent/very good	$119.7$	$\frac{119.7}{188.3}=0.6357$
Good	$48.4$	$\frac{48.4}{188.3}=0.2370$
Fair or poor	$20.2$	$\frac{20.2}{188.3}=0.1073$
Total	$188.3$	1

Part (a) Step 3: Relative frequency distribution for age group 65 and above

The table below shows the relative frequency distribution for the age group $65$ and up.

Health	Frequency	Relative Frequency
Excellent/very good	$18.1$	$\frac{18.1}{42.1}=0.4299$
Good	$14.2$	$\frac{14.2}{42.1}=0.3373$
Fair or poor	$9.2$	$\frac{9.2}{42.1}=0.2185$
Total	$42.1$	$1$

Part(b) Step 1: Given information

Given in the question that, The National Center for Health Statistics collects data on health insurance coverage status and coverage type. The following data from the National Health Interview Survey provides the frequency, in millions, of the current health status for persons aged $19-64$ and persons aged $65$ and over.

We need to draw a pie chart for both age group.

Part (b) Step 2: Explanation

MINITAB has been used to create the pie chart.

The portion for each class in a pie chart is calculated by multiplying ${360}^0$ by the corresponding relative frequencies.

The steps of drawing a pie chart are as follows:

• Choose Graph >Pie Chart.
•  Select Chart values from table.
•  Choose HEALTHunder Categorical variable.
•  Select Frequency under Summary variables.
•  Select Labels and choose Slide Labels tab.
•  Check Category name and Percent under Label pie slices with.
•  Click OK

The pie chart of the given data set is shown in figure below.

Part (c) Step 1: Given information

Given in the question that, The National Center for Health Statistics collects data on health insurance coverage status and coverage type. The following data from the National Health Interview Survey provides the frequency, in millions, of the current health status for persons aged  and persons aged $65$ and over.

We need to compare our pie charts.

Part (c) Step 2: Explanation

Figure 1 shows that the part for "Excellent/very good" health status is higher for those aged $19-64$ than for the latter group.

People aged$19-64$ have a lower percentage of "fair or poor" health condition than people aged $65$ and over.

As a result, the comparison of the two graphs has been explained.