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Chapter 1: Problem 77

Find an article or an advertisement in a newspaper or magazine that exemplifies the use of statistics. a. Identify and describe one statistic reported in the article. b. Identify and describe the variable related to the statistic in part a. c. Identify and describe the sample related to the statistic in part a. d. Identify and describe the population from which the sample in part c was taken.

Short Answer

Expert verified
In summary, statistic is the numerical data reported in the article or advertisement. The variable related to the statistic is what is being studied or measured. The sample is the small group from which the data was directly gathered, and the population is the larger group from which the sample was drawn and about which we wanted to know more.

Step by step solution

01

Identify the statistic

Read the given article or advertisement carefully and look out for any numbers, percentages or figures used which provides information on a larger scale. This can be the statistic that you need to identify. Then, describe what that statistic is about and what information it represents.
02

Identify the variable

With the statistic identified, now look for the variable related to it. In statistics, the variable is what is being studied and measured in the data collection. It is the factor or characteristic which can vary or change within the data presented. Describe this variable and its relation to the statistic.
03

Identify the sample

Next, it's time to identify the sample related to the identified statistic. The sample in a study is a portion of the population that is representative of the population from which it was drawn. The sample is the group that the data was directly gathered from. Describe the identified sample.
04

Identify the population

Lastly, identify and describe the population from which the sample was taken. The population in a study is the total group of individuals from which the samples may be drawn. It is the whole group that the information is desired about.

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Key Concepts

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

Identifying Statistics
Statistics are numerical data or information derived from a study, survey, or experiment. When searching for statistics in an article or advertisement, you want to look for numbers that describe a larger concept. For example, a report stating that "65% of people prefer brand X over brand Y" is a statistic. It summarizes a vast amount of information into digestible figures. Statistics help us make sense of the world by giving us insights into trends and patterns. They turn large datasets into actionable insights that can guide decisions. When identifying a statistic, always consider what story that number is trying to tell.
  • Look for numerical data, percentages, or ratios.
  • Understand the context of what is being measured.
  • Determine what insights or decisions the statistic is meant to support.
Variables in Statistics
Variables are the building blocks of statistical analysis. In simple terms, a variable is any characteristic, number, or quantity that can be measured. Variables can vary or change between different data points. They take many forms, such as age, income, or brand preference. Yes, these are the things we measure or observe in a study.
Understanding what a variable is, helps us make sense of how data behaves and reacts in different scenarios. Variables are directly related to the statistics we derive鈥攅ach statistic measures or summarizes a variable.
When inspecting an article or advertisement:
  • Identify what specific element or aspect is being measured (like age or preference).
  • Consider whether it's a categorical variable (like brand) or a numerical variable (like percentage of preference).
  • Think about how changes in this variable might influence the study's conclusions.
Sample and Population
Understanding the difference between a sample and a population is fundamental in statistics. A population includes all members from a specified group鈥攊t's the entire set of subjects we are interested in. On the other hand, a sample is a subset of the population that we actually collect data from.
Think of a population as the complete pizza and the sample as just a slice. When reading about statistics in articles or advertisements, recognizing this distinction is important. The conclusions drawn from a sample are used to infer information about the population.
  • Identify the sample by considering who exactly was surveyed or tested (for instance, 500 shoppers).
  • Identify the population by expanding on whom the sample represents (perhaps all shoppers in a city).
  • Assess whether the sample size seems sufficient to represent the larger population accurately.
This understanding ensures that the interpretation of the statistic is grounded in the right context.

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Most popular questions from this chapter

During a radio broadcast a few years ago, David Essel reported the following three statistics: (1) the U.S. divorce rate is \(55 \%,\) and when married adults were asked if they would remarry their spouse, (2) \(75 \%\) of the women said yes, and (3) \(65 \%\) of the men said yes. a. What is the "stay married" rate? b. There seems to be a contradiction in this information. How is it possible for all three of these statements to be correct? Explain.

Teachers use examinations to measure students' knowledge about a subject. Explain how "a lack of variability in the students' scores might indicate that the exam was not a very effective measuring device."

a. What body of the federal government illustrates a stratified sampling of the people? (A random selection process is not used.) b. What body of the federal government illustrates a proportional sampling of the people? (A random selection process is not used.)

Consider the May \(12,2009,\) USA Today article titled "Simulated acupuncture eases pain.鈥� Simulated acupuncture eases pain Acupuncture brought more relief to people with back pain than standard treatments, whether it was done with a toothpick or a real needle, a study finds, but how acupuncture works remains unclear. In the study, 638 adults with chronic low back pain were divided into four groups and received standardized acupuncture treatment; individually prescribed acupuncture treatment; simulated acupuncture treatment using a toothpick in a needle guide tube that did not pierce the skin as regular acupuncture does but was targeted at correct acupuncture points; or standard medical treatment (medication and physical therapy). After eight weeks, \(60 \%\) of those who got any type of acupuncture reported significant improvement compared with those who got standard care alone, says the study in this week's Archives of Internal Medicine. a. What is the population? b. What is the sample? c. Is this a judgment sample or a probability sample? d. If this study is a probability sample, what type of sampling method do you think was used?

Describe in detail how you would select a \(4 \%\) systematic sample of the adults in a nearby large city in order to complete a survey about a political issue.
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