Question

The following frequency distribution presents the five most frequent reasons for hospital admissions in U.S. community hospitals in a recent year.
Reason Frequency (in thousands)
Congestive heart failure    990
Coronary atherosclerosis 1400
Heart attack   744
Infant birth 3800

Required:
a. Construct a frequency bar graph.
b. Construct a relative frequency distribution.
c. Construct a relative frequency bar graph.
d. Construct a relative frequency Pareto chart.

Answer 1

Answer:

See Explanation

Step-by-step explanation:

Given

$Reason \to Frequency$

$Congestive\ heart\ failure \to 990$

$Coronary\ atherosclerosis\to 1400$

$Heart\ attack \to 744$

$Infant\ birth\to 3800$

Solving (a): Frequency bar graph

To do this, we simply plot the reasons (on the x-axis) against the frequency (on the y-axis).

See attachment

Solving (b): Relative frequency distribution

The relative frequency is calculated as:

$RF = \frac{F}{Total}$

Where

$Total = 990+1400+744+3800$

$Total = 6934$

So, we have:

$Congestive\ heart\ failure \to \frac{990}{6934} = 0.1427$

$Coronary\ atherosclerosis\to \frac{1400}{6934} = 0.2019$

$Heart\ attack \to \frac{744}{6934} = 0.1073$

$Infant\ birth\to \frac{3800}{6934} = 0.5481$

So, the relative distribution is:

$Reason \to Frequency \to Relative\ Frequency$

$Congestive\ heart\ failure \to 990 \to 0.1427$

$Coronary\ atherosclerosis\to 1400 \to 0.2019$

$Heart\ attack \to 744 \to 0.1073$

$Infant\ birth\to 3800 \to 0.5481$

Solving (c): Relative frequency bar graph

To do this, we simply plot the reasons (on the x-axis) against the relative frequency (on the y-axis).

See attachment

Solving (d): Relative frequency Pareto chart

First, calculate the cumulative relative frequency

This is done by adding up the previous relative frequency,

So, we have:

$Reason \to Relative\ Frequency \to Cumulative$

$Congestive\ heart\ failure \to 0.1427 \to 0.1427$

$Coronary\ atherosclerosis \to 0.2019 \to 0.2019+0.1427=0.3446$

$Heart\ attack \to 0.1073\to 0.3446+0.1073 = 0.4519$

$Infant\ birth \to 0.5481 \to 0.5481+4519 =1$

So, we have:

$Reason \to Relative\ Frequency \to Cumulative$

$Congestive\ heart\ failure \to 0.1427 \to 0.1427$

$Coronary\ atherosclerosis \to 0.2019 \to 0.3446$

$Heart\ attack \to 0.1073\to 0.4519$

$Infant\ birth \to 0.5481 \to 1$

Next, we simply plot the reasons (on the x-axis) against the cumulative relative frequency (on the right) and the left of the Pareto chart.

See attachment