Problem 23 - BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

Question

OPEN-ENDED Find a newspaper or magazine article that describes a survey. Identify the population and sample. Describe the sample.

Step-by-Step Solution

Answer

In the chosen article, the population is all high school students in Town A. The sample, meanwhile, is a group of 500 students randomly selected from various high schools within the town, representing a diverse and fair reflection of the population.

Step 1: Identification of the Survey

Locate a newspaper or magazine article that talks about a survey. Read it carefully. Here, let's consider a hypothetical article which talks about a survey conducted among high school students of Town A to determine their favorite pastime activities.

Step 2: Identification of the Population

The population often refers to a large group about whom conclusions are to be drawn based on the survey. After reading our hypothetical article, it could be established that the population in this context are all the high school students in Town A.

Step 3: Identification of the Sample

The sample is a subset of the population that is being surveyed. In the article, it says that 500 students were randomly selected from various high schools in Town A. Hence, the sample in this context is the group of 500 students selected.

Step 4: Description of the Sample

The article states that these 500 students were selected randomly across several high schools and various grades within Town A. This would mean a fair representation of the population as it accounts for different ages and social backgrounds.

Key Concepts

Survey Methods

Surveys are a popular method for collecting data about a population by asking questions to a group of people. Understanding survey methods is key to evaluating the quality of the data collected. Surveys can be conducted in various ways:

• Questionnaires: Written responses are collected through paper forms or online.
• Interviews: Data is gathered through direct interaction, either face-to-face or over the phone.
• Online Surveys: Rapidly growing, these use digital platforms to reach participants.

Choosing the right method depends on the survey's goals, budget, and the target population's accessibility. It is also important to design clear and unbiased questions to ensure reliable results. Proper survey design can influence the accuracy and credibility of the findings.

Random Sampling

Random sampling is an essential technique for ensuring that survey results are valid and applicable to the entire population. By using random sampling, every individual in the population has an equal chance of being selected, which minimizes biases and provides a representative sample.

For example, if a survey aims to understand high school students' favorite activities, randomly selecting a diverse group, such as 500 students from various schools and grades, can offer a glimpse into broader student trends. There are different types of random sampling, including:

• Simple Random Sampling: Each member of the population has an equal probability of selection. This can be achieved through methods like drawing names from a hat or using random number generators.
• Stratified Random Sampling: The population is divided into subgroups (strata) based on important characteristics, and samples are taken from each stratum.
• Systematic Sampling: Picks every nth member of the population from a randomly ordered list, ensuring a spread across the entire population.

Using these methods helps ensure the sample accurately reflects the population's characteristics, making conclusions drawn from the data more robust.

Data Interpretation

Data interpretation involves analyzing collected data to find patterns or insights and drawing conclusions. This is a critical step in making sense of the information gathered during a survey.

Several key factors play into effective data interpretation:

• Identify Patterns and Trends: Look for common responses or trends in the data, such as which activities are the most popular among surveyed students.
• Consider Variability: Understand the range and diversity of the responses, accounting for different demographics and subgroups.
• Contextual Understanding: Place the data within the broader context, considering factors like cultural or local influences impacting the results.

Results must be carefully assessed, keeping in mind any limitations in the survey method or sample size. Accurate interpretation leads to informed conclusions and helps guide decision-making based on the survey's findings.