Question

The article "The Need to Be Plugged In" (Associated Press, December 22,2005 ) described the results of a survey of 1006 adults who were asked about various technologies, including personal computers, cell phones, and DVD players. The accompanying table summarizes the responses to questions about how essential these technologies were. \begin{tabular}{lccc} & \multicolumn{3}{c} { Relative Frequency } \\ \cline { 2 - 4 } Response & Personal Computer & Cell Phone & DVD Player \\ \hline Cannot imagine living without & .46 & .41 & .19 \\ Would miss but could do without & .28 & .25 & .35 \\ Could definitely live without \\ \hline \end{tabular} Construct a comparative bar chart that shows the distribution of responses for the three different technologies.

Short answer

Begin by creating a bar chart with the three technology categories on the x-axis and the relative frequency on the y-axis. For every technology category, plot three bars corresponding to the three responses and their respective relative frequencies. Make sure the y-axis is accurately scaled and each bar is labeled with the correct relative frequency. Each category must have a clear title, and the chart itself should also be titled.

Step-by-step solution

Understand the Data

Start by understanding the data presented. It is clear that the table provides relative frequencies of different responses on how essential the three technologies are to the respondents.

Set up the Chart

Setup a comparative bar chart with each technology category (Personal Computer, Cell Phone, and DVD Player) on the x-axis and relative frequency on the y-axis. Each technology category will have three bars corresponding to the three responses.

Plot the Bars

Now plot the relative frequencies into their respective categories. For instance, Personal Computer had a relative frequency of 0.46 for the response 'Cannot imagine living without'. This will be represented as the first bar in this category and its height should correspond to the frequency of 0.46. Do this for every response and for each of the technology categories.

Label the Chart

Label each bar with the correct relative frequency. Make sure the y-axis is properly labeled, along with the title of the chart and each category on the x-axis

Key concepts

Relative Frequency

Relative frequency is a way to express data as a proportion of the whole. Represented as decimals in the given survey data, it indicates how common each response was relative to the total number surveyed. For example, a relative frequency of 0.46 in the category 'Cannot imagine living without' for Personal Computers means 46% of respondents considered PCs essential. Relative frequency helps create a clear and straightforward understanding of survey results.
It allows comparison across different categories and responses without needing the actual count of participants. Instead of seeing the number of people, we see the proportion of each response. This is especially useful in visual representations like bar charts.
When constructing a comparative bar chart, the relative frequency values determine the height of the bars, making it easier to visualize and compare the significance of each technology to the participants.

Survey Data

Survey data is collected by asking questions to a group and recording their responses. In this exercise, survey data was collected from 1006 adults regarding the importance of certain technologies. By analyzing this data, researchers can understand trends and patterns in people's attitudes and preferences.
Surveys are often used in social sciences, marketing, and any field where understanding people's opinions and behaviors is valuable. The data can be presented in different formats, including tables and charts. This allows for a comprehensive analysis of the topic being investigated. In surveys like the one described, it’s crucial to consider how question phrasing and response options may affect outcomes and interpretations.

• Quantitative Data: Provides numbers, like relative frequencies, effectively summarizing the importance of each technology.
• Qualitative Data: Captures opinions, describing why certain technologies might be considered essential or dispensable.

Technology Usage

The survey described gives insights into technology usage and its perceived importance in daily life. In 2005, technologies such as personal computers, cell phones, and DVD players were at varying importance levels among adults. The survey responses reflect these varying levels of necessity, often influenced by personal and professional demands.
Personal computers and cell phones, for instance, show higher relative frequencies of being essential. This could relate to their diverse functionalities, including communication, work, and entertainment. Technology usage is dynamic, with different demographics showing varying dependences on technology. Surveys like this help us understand the evolving role of technology over time and among different groups of people.
These insights are critical for businesses, policymakers, and researchers who study technology trends and their impacts on society.

Data Visualization

Data visualization involves presenting data in graphical format. It helps convey information clearly and efficiently. Comparative bar charts, like those recommended in the solution steps, are one way to visualize the survey data on technology importance.
These bar charts make the survey results visually accessible, highlighting the relative importance of each technology category. By assigning different colors or patterns to each category and response, viewers can quickly grasp complex information. The comparative bar chart organizes data so viewers can easily compare responses across different technologies.

• Enhances understanding by turning data into a visual story.
• Allows quick comparisons of different data points visually, showing trends and patterns.
• Facilitates identifying which technology was perceived as most versus least essential.

In summary, data visualization transforms abstract numbers into meaningful visual insights, making it easier to see what the data says at a glance.