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Survey analysis is a method used to gather and interpret data from a specific group or sample to understand trends, behavior, and opinions. In the example of retailers surveyed about the use of electronic tags as antitheft devices, we gather data from 176 retailers.
- A survey consists of structured questions aimed at extracting quantitative data, like percentages, to infer conclusions. - Surveys can be conducted through various methods such as online questionnaires, face-to-face interviews, or phone calls. - Important considerations in survey analysis include sample size, question clarity, and respondent honesty.
In our exercise, the survey's outcome shows that 46% of retailers have adopted electronic tags. This data is critical for understanding industry trends and making informed business decisions, like adopting similar security measures or analyzing the effectiveness of these devices.

Percentage calculation is a fundamental math skill used to express a number as a fraction of 100. In numerous real-life scenarios, such as surveys, percentages help present data efficiently. To find out how many retailers out of 176 use electronic tags: Multiply the total number of retailers (176) by the percentage using tags (46%). The formula is: \[ \text{Number of retailers using tags} = \left( \frac{46}{100} \right) \times 176 \]
This yields approximately 81 retailers using electronic tags. Knowing how to perform percentage calculations enables you to quickly convert survey data into actionable insights. It's a valuable skill for analyzing probability and making everyday decisions.

Antitheft devices are tools designed to prevent or reduce theft in businesses and retail stores. Among these, electronic tags are common due to their effectiveness and ease of use. Here's why electronic tags are preferred: - They deter potential shoplifters by alerting store personnel when an item is being removed without authorization. - These devices enable stores to secure merchandise without encasing items in bulky security boxes. - Electronic tags are economical for large retailers, who can tag thousands of products efficiently.
Understanding the use of antitheft devices like electronic tags can inform retailers in making decisions about inventory protection and loss prevention strategies, which are vital for maintaining profitability.

Simplifying fractions is a method to reduce a fraction to its simplest form where the numerator and denominator have no common factors other than 1. In the given exercise, simplifying the fraction representing the probability involves: The probability that a randomly selected retailer uses electronic tags is given by the fraction: \[ \frac{81}{176} \] To simplify, find the greatest common divisor (GCD) of 81 and 176, and divide both the numerator and the denominator by this GCD. This fraction simplifies the representation of probabilities, making them easier to understand and communicate, especially in reviewing survey results or making predictions based on data.
Simplifying fractions is essential not only in probability but also in general mathematics, ensuring clarity and efficiency in calculations and decision-making.