/*! 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 15 Eating at Fast Food Restaurants ... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Eating at Fast Food Restaurants A survey was taken of 50 individuals. They were asked how many days per week they ate at a fast-food restaurant. Construct a frequency distribution using 8 classes \((0-7) .\) Based on the distribution, how often did most people eat at a fastfood restaurant? $$ \begin{array}{lllll} 1 & 3 & 4 & 0 & 4 \\ 5 & 2 & 2 & 3 & 1 \\ 2 & 2 & 2 & 2 & 2 \\ 2 & 2 & 2 & 2 & 3 \\ 2 & 2 & 5 & 2 & 4 \\ 2 & 4 & 5 & 2 & 1 \\ 4 & 1 & 3 & 2 & 2 \\ 2 & 0 & 7 & 2 & 3 \\ 2 & 2 & 2 & 5 & 2 \\ 3 & 3 & 4 & 1 & 3 \end{array} $$

Short Answer

Expert verified
Most people ate at a fast-food restaurant 2 days a week.

Step by step solution

01

Tally Data

Examine the data set with 8 classes (0 to 7) and create an initial tally chart to count the frequency of occurrence for each day value from 0 to 7. This helps us track how many individuals ate at a fast-food restaurant each day of the week.
02

Create Frequency Distribution Table

Once the tallying is complete, total up the tallies to form a frequency distribution table. This table will show each day (0 to 7) and the corresponding number of individuals who ate at a fast-food restaurant that number of times during the week.
03

Analyze the Frequency Distribution

Examine the frequency distribution to identify the day (or range of days) that has the highest frequency. This will show how often most individuals in the survey ate at a fast-food restaurant.

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Key Concepts

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

Tally Chart
A tally chart is a simple yet effective tool used to organize and count data. In the context of the survey asking about fast-food consumption, a tally chart helps visualize how frequently individuals eat out during the week. Tally marks are used to represent data values, with each mark generally representing one unit of data. When we tally numbers according to their frequency, we can quickly see how many people fall into each category. To create a tally chart, follow these steps:
  • Review your data set. In our example, we have numbers ranging from 0 to 7.
  • Draw a column with numbers representing your classes (0, 1, 2, etc.).
  • Next to each number, mark a tally for each occurrence of the number in the data set.
Grouping tally marks in sets of five (four vertical lines followed by a diagonal line through them) makes it easy to count them quickly. This method provides a clear visual representation and serves as a foundation for creating further data analysis tools, like frequency distribution tables.
Data Analysis
Data analysis involves examining, cleaning, and transforming data to highlight helpful results and support decision-making. This process enables you to understand the insights hidden within your data. In our problem, we analyze how often people visit fast-food restaurants each week. Key steps in data analysis include:
  • Collection: Gather all relevant data, like survey responses.
  • Organization: Use tools like tally charts to organize data into easier-to-digest formats.
  • Interpretation: Create and review frequency distribution tables to identify patterns or conclusions.
The frequency distribution table from our tally chart shows how many people fall into each frequency category (0-7 days). By comparing these frequencies, you can identify the most common behavior, informing which days are more popular for fast-food visits.
Survey Analysis
Survey analysis involves interpreting data collected from survey responses to draw meaningful conclusions and provide insights. In this case, the survey asked participants how many days per week they ate at fast-food restaurants. By analyzing these responses, we can paint a picture of typical fast-food eating habits. Here's how to conduct survey analysis effectively:
  • Design surveys with clear and concise questions to gather precise data.
  • Collect responses consistently to ensure data accuracy.
  • Analyze data using visual aids such as tally charts and frequency distribution tables to identify trends.
From our data, we saw that a particular range (e.g., 2 days) might be the most popular choice, suggesting that individuals commonly eat fast food twice a week. Understanding these patterns helps businesses and policymakers make informed decisions about marketing, health initiatives, and resource allocation.

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Most popular questions from this chapter

Show frequency distributions that are incorrectly constructed. State the reasons why they are wrong. $$ \begin{array}{lc} \text { Class } & \text { Frequency } \\ \hline 10-19 & 1 \\ 20-29 & 2 \\ 30-34 & 0 \\ 35-45 & 5 \\ 46-51 & 8 \end{array} $$

The frequency distribution represents the cost (in cents) for the utilities of states that supply much of their own power. Construct a histogram, frequency polygon, and ogive for the data. Is the distribution skewed? $$ \begin{array}{lc} \text { Class limits } & \text { Frequency } \\ \hline 6-8 & 12 \\ 9-11 & 16 \\ 12-14 & 3 \\ 15-17 & 1 \\ 18-20 & 0 \\ 21-23 & 0 \\ 24-26 & \frac{1}{33} \end{array} $$

The math and reading achievement scores from the National Assessment of Educational Progress for selected states are listed below. Construct a back- to-back stem and leaf plot with the data, and compare the distributions. $$ \begin{array}{lllll|lllll} &&&{\text { Math }} &&&{\text { Reading }} \\ \hline 52 & 66 & 69 & 62 & 61 & 65 & 76 & 76 & 66 & 67 \\ 63 & 57 & 59 & 59 & 55 & 71 & 70 & 70 & 66 & 61 \\ 55 & 59 & 74 & 72 & 73 & 61 & 69 & 78 & 76 & 77 \\ 68 & 76 & 73 & & & 77 & 77 & 80 & & \end{array} $$

The frequency distribution shows the blood glucose levels (in milligrams per deciliter) for 50 patients at a medical facility. Construct a histogram, frequency polygon, and ogive for the data. Comment on the shape of the distribution. What range of glucose levels did most patients fall into? $$ \begin{array}{lr} \text { Class limits } & \text { Frequency } \\ \hline 60-64 & 2 \\ 65-69 & 1 \\ 70-74 & 5 \\ 75-79 & 12 \\ 80-84 & 18 \\ 85-89 & 6 \\ 90-94 & 5 \\ 95-99 & \frac{1}{50} \end{array} $$

Name the three types of frequency distributions, and explain when each should be used.

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