Q.2.84 - Elementary Statistics

Question

The U.S. Energy Information Administration collects data on residential energy consumption and expenditures. Results are published in the document

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)

 $\begin{array}{|lll|}\hline \text{ Class }& \text{ Frequency }& \begin{array}{l}\text{ Relative }\\ \text{ frequency }\end{array}\\ 40-49& 1& 0.02\\ 50-59& 7& 0.14\\ 60-69& 7& 0.14\\ 70-79& 3& 0.06\\ 80-89& 6& 0.12\\ 90-99& 10& 0.2\\ 100-109& 5& 0.1\\ 110-119& 4& 0.08\\ 120-129& 2& 0.04\\ 130-139& 3& 0.06\\ 140-149& 0& 0\\ 150-159& 2& 0.04\\ \hline\end{array}$

(b)

$\begin{array}{|lll|}\hline \text{ Class }& \text{ Frequency }& \begin{array}{l}\text{ Relative }\\ \text{ frequency }\end{array}\\ 40-49& 1& 0.02\\ 50-59& 7& 0.14\\ 60-69& 7& 0.14\\ 70-79& 3& 0.06\\ 80-89& 6& 0.12\\ 90-99& 10& 0.2\\ 100-109& 5& 0.1\\ 110-119& 4& 0.08\\ 120-129& 2& 0.04\\ 130-139& 3& 0.06\\ 140-149& 0& 0\\ 150-159& 2& 0.04\\ \hline\end{array}$

(c)

(d) 

Part (a)Step 1: Given information

Given in the question that,  The U.S. Energy Information Administration collects data on residential energy consumption and expenditures. Results are published in the document

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:

$\begin{array}{|lll|}\hline \text{ Class }& \text{ Frequency }& \begin{array}{l}\text{ Relative }\\ \text{ frequency }\end{array}\\ 40-49& 1& 0.02\\ 50-59& 7& 0.14\\ 60-69& 7& 0.14\\ 70-79& 3& 0.06\\ 80-89& 6& 0.12\\ 90-99& 10& 0.2\\ 100-109& 5& 0.1\\ 110-119& 4& 0.08\\ 120-129& 2& 0.04\\ 130-139& 3& 0.06\\ 140-149& 0& 0\\ 150-159& 2& 0.04\\ \hline\end{array}$

Part(b) Step 1: Given information

Given in the question that,  The U.S. Energy Information Administration collects data on residential energy consumption and expenditures. Results are published in the document

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:

$\begin{array}{|lll|}\hline \text{ Class }& \text{ Frequency }& \begin{array}{l}\text{ Relative }\\ \text{ frequency }\end{array}\\ 40-49& 1& 0.02\\ 50-59& 7& 0.14\\ 60-69& 7& 0.14\\ 70-79& 3& 0.06\\ 80-89& 6& 0.12\\ 90-99& 10& 0.2\\ 100-109& 5& 0.1\\ 110-119& 4& 0.08\\ 120-129& 2& 0.04\\ 130-139& 3& 0.06\\ 140-149& 0& 0\\ 150-159& 2& 0.04\\ \hline\end{array}$

Part(c) Step 1: Given information

Given in the question that,  The U.S. Energy Information Administration collects data on residential energy consumption and expenditures. Results are published in the document

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,  The U.S. Energy Information Administration collects data on residential energy consumption and expenditures. Results are published in the document

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: