/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 14 Use the following data. In a ran... [FREE SOLUTION] | 91Ó°ÊÓ

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Use the following data. In a random sample, 800 smartphone owners were asked which type of smartphone they would choose with their next purchase (if they could only choose one). The results are summarized below: $$\begin{array}{l|l} \text {Smartphone} & \text {Frequency} \\ \hline \text { iPhone } & 320 \\ \text { Samsung } & 284 \\ \text { LG } & 82 \\ \text { Motorola } & 35 \\ \text { Other } & 79 \end{array}$$ Make a bar graph of these data using the frequencies.

Short Answer

Expert verified
Draw a bar graph with smartphone categories along the x-axis and frequencies along the y-axis.

Step by step solution

01

Understand the Data

The data provides frequencies for the preferred smartphone brands in a sample of 800 users. There are five categories: iPhone, Samsung, LG, Motorola, and Other, with respective frequencies of 320, 284, 82, 35, and 79.
02

Set Up the Bar Graph Axes

Draw the horizontal axis (x-axis) to list the smartphone categories (iPhone, Samsung, LG, Motorola, Other). Label the vertical axis (y-axis) to depict the frequency of the responses, ranging from 0 to the maximum frequency, in this case, 320.
03

Plot the Bars

For each smartphone category, draw a vertical bar whose height corresponds to the frequency of that category. For iPhone, draw a bar up to 320; for Samsung, up to 284; for LG, up to 82; for Motorola, up to 35; and for Other, up to 79.
04

Label the Graph

Add a title to the graph, such as 'Smartphone Preferences in a Sample of 800 Users'. Also, label the x-axis as 'Smartphone' and the y-axis as 'Frequency'. Ensure each bar is labeled at the top with its respective frequency for clarity.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Frequency Distribution
Frequency distribution is a way of organizing data to show how often different values or categories occur in a dataset. In our smartphone survey, this involves tallying the number of respondents who prefer each smartphone brand. By setting up a frequency distribution, you can easily see which smartphone brand is the most popular and which is the least among the sampled users.
It involves simple calculations of counting occurrences and can be represented in a straightforward chart or table. This is a fundamental step prior to creating visual representations, as it provides the basis upon which data visualization is built. In this exercise, the frequencies are:
  • iPhone: 320
  • Samsung: 284
  • LG: 82
  • Motorola: 35
  • Other: 79
These numbers help us understand the preferences and facilitate the creation of a bar graph.
Data Visualization
Data visualization is the process of converting data into a visual context, such as a chart or graph, to make the information easier to understand. This transformation is crucial as it allows patterns, trends, and outliers to be quickly discerned, improving comprehension for even complex datasets.
With our smartphone data example, the shift from a numeric frequency distribution to a bar graph is a perfect instance of data visualization. By visualizing the data, we make it much easier for an observer to immediately grasp which smartphone brand leads the preferences and which trails behind.
  • Quickly identify the most and least preferred smartphone brands
  • Observe notable differences in preferences at a glance
Overall, effective data visualization makes data analysis accessible to a broader audience, enabling quicker and more informed decision-making.
Bar Chart
A bar chart is a type of graph that uses bars to display and compare quantities corresponding to different categories. Each category in the data is represented by a bar, the length or height of which is proportional to the frequency of responses in that category.
In the context of our survey, the categories are different smartphone brands, and we plot a bar for each corresponding to its frequency:
  • iPhone: 320
  • Samsung: 284
  • LG: 82
  • Motorola: 35
  • Other: 79
To construct a bar chart:
1. Draw the horizontal axis (x-axis) for smartphone brands.
2. Draw the vertical axis (y-axis) for the frequency of customers.
3. Plot the bars so each brand's bar reaches up to its frequency.
These bars visually compare preferences and truly highlight the dominance of iPhone in this survey.
Survey Results
Survey results serve as a source of data by capturing preferences, opinions, or behaviors of a specific population. In this exercise, how respondents expressed their interest in different smartphone brands gives us valuable information about consumer preferences.
This data collection method is powerful because it provides insights from real user perspectives. It helps businesses, like smartphone companies, understand market trends, guide product development, and tailor marketing strategies.
Considerations from the survey results in our exercise:
  • iPhone leads with 40% (320 out of 800 users)
  • Samsung and LG have substantial user bases but are smaller than iPhone
  • Motorola and Other have comparatively smaller interest
These results enable strategic planning and give an inside look into potential shifts and fads in tech preferences.

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