Q.2.83 - Elementary Statistics

Question

Every year since 1998, Arbitron and Edison Research have conducted a nationally representative survey focusing on trends in digital platforms. According to their publication The Infinite Dial, in 2002 , there were an average of \(1.2\) working computers in the U.S. home. A random sample of 45 households taken this year yielded the following data on number of working computers. Use single-value grouping.

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)

$\begin{array}{rr}Single value& Frequency\\ 0& 5\\ 1& 22\\ 2& 11\\ 3& 2\\ 4& 4\\ 5& 1\\ & \\ Total& 45\end{array}\begin{array}{}\\ \\ \\ \\ \\ \\ \end{array}$

(b)

$\begin{array}{|lllll|}\hline \begin{array}{l}\text{ Single }\\ \text{ value }\end{array}& \text{ Frequency }& \begin{array}{l}\text{ Relative }\\ \text{ frequency }\end{array}& & \\ 0& 5& 5/45& =& 0.1111\\ 1& 22& 22/45& =& 0.4889\\ 2& 11& 11/45& =& 0.2444\\ 3& 2& 2/45& =& 0.0444\\ 4& 4& 4/45& =& 0.0889\\ 5& 1& 1/45& =& 0.0222\\ & & & & \\ & & & & \\ \text{ Total }& 45& & & 1\\ \hline\end{array}$

(c)

  

(d)

Part (a)Step 1: Given information

Given in the question that, every year since 1998, Arbitron and Edison Research have conducted a nationally representative survey focusing on trends in digital platforms. According to their publication The Infinite Dial, in 2002 , there were an average of $1.2$working computers in the U.S. home. A random sample of 45 households taken this year yielded the following data on number of working computers. Use single-value grouping.

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:

$\begin{array}{rr}Single value& Frequency\\ 0& 5\\ 1& 22\\ 2& 11\\ 3& 2\\ 4& 4\\ 5& 1\\ & \\ Total& 45\end{array}\begin{array}{}\\ \\ \\ \\ \\ \\ \end{array}$

Part(b) Step 1: Given information

Given in the question that, every year since 1998, Arbitron and Edison Research have conducted a nationally representative survey focusing on trends in digital platforms. According to their publication The Infinite Dial, in 2002 , there were an average of $1.2$ working computers in the U.S. home. A random sample of 45 households taken this year yielded the following data on number of working computers. Use single-value grouping.

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:

$\begin{array}{|lllll|}\hline \begin{array}{l}\text{ Single }\\ \text{ value }\end{array}& \text{ Frequency }& \begin{array}{l}\text{ Relative }\\ \text{ frequency }\end{array}& & \\ 0& 5& 5/45& =& 0.1111\\ 1& 22& 22/45& =& 0.4889\\ 2& 11& 11/45& =& 0.2444\\ 3& 2& 2/45& =& 0.0444\\ 4& 4& 4/45& =& 0.0889\\ 5& 1& 1/45& =& 0.0222\\ & & & & \\ & & & & \\ \text{ Total }& 45& & & 1\\ \hline\end{array}$

Part(c) Step 1: Given information

Given in the question that, every year since 1998, Arbitron and Edison Research have conducted a nationally representative survey focusing on trends in digital platforms. According to their publication The Infinite Dial, in 2002 , there were an average of $1.2$ working computers in the U.S. home. A random sample of 45 households taken this year yielded the following data on number of working computers. Use single-value grouping.

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.

Calculation: The bars must be of the same width and must be bordered by the lower class limits.

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, every year since 1998, Arbitron and Edison Research have conducted a nationally representative survey focusing on trends in digital platforms. According to their publication The Infinite Dial, in 2002 , there were an average of $1.2$ working computers in the U.S. home. A random sample of 45 households taken this year yielded the following data on number of working computers. Use single-value grouping.

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.

Calculation: The bars must be of the same width and must be bordered by the lower class limits.

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

The relative frequency distribution histogram is shown below: