Provide A Response To The Following Prompts: Explain And Pro

Providea Response To The Following Prompts1 Explain And Provide An E

Provide a response to the following prompts. 1. Explain and provide an example for each of the following types of variables: a. Nominal: b. Ordinal: c. Interval: d. Ratio scale: e. Continuous: f. Discrete: g. Quantitative: 2. The following are the speeds of 40 cars clocked by radar on a particular road in a 35 miles-per-hour zone on an afternoon: 30, 36, 42, 36, 30, 52, 36, 34, 36, 33, 30, 32, 35, 32, 37, 34, 36, 31, 35, 46, 23, 31, 32, 45, 34, 37, 28, 40, 34, 38, 40, 52, 31, 33, 15, 27, 36, 40 Create a frequency table and a histogram. Then, describe the general shape of the distribution. 3. Raskauskas and Stoltz (2007) asked a group of 84 adolescents about their involvement in traditional and electronic bullying. The researchers defined electronic bullying as “…a means of bullying in which peers use electronics {such as text messages, emails, and defaming Web sites} to taunt, threaten, harass, and/or intimidate a peer” (p. 565). The table below is a frequency table showing the adolescents’ reported incidence of being victims or perpetrators of traditional and electronic bullying. a. Using the table below as an example, explain the idea of a frequency table to a person who has never taken a course in statistics. b. Explain the general meaning of the pattern of results. Incidence of Traditional and Electronic Bullying and Victimization ( N = 84) Forms of bullying N % Electronic victims 41 48.8 Text-message victim 27 32.1 Internet victim (websites, chatrooms) 13 15.5 Camera-phone victim 8 9.5 Traditional victims 60 71.4 Physical victim 38 45.2 Teasing victim 50 59.5 Rumors victim 32 38.6 Exclusion victim 30 50 Electronic bullies 18 21.4 Text-message bully 18 21.4 Internet bully 11 13.1 Traditional bullies 54 64.3 Physical bully 29 34.5 Teasing bully 38 45.2 Rumor bully 22 26.2 Exclusion bully 35 41. Describe whether each of the following data words best describes descriptive statistics or inferential statistics. Explain your reasoning. Describe: Infer: Summarize: 5. Regarding gun ownership in the United States, data from Gallup polls over a 40-year period show how gun ownership in the United States has changed. The results are described below, with the percentage of Americans who own guns given in each of the 5 decades. Year % Are the percentages reported above an example of descriptive statistics or inferential statistics? Why? Based on the table, how would you describe the changes in gun ownership in the United States over the 40 years shown? 6. Refer to the Simpson-Southward et al. (2016) article from this week’s Electronic Reserve Readings. Was this an example of inferential statistics and research or descriptive statistics and research? Justify your response. 7. Explain and provide an example for each of the following shapes of frequency distributions. Symmetrical: Skew:

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The explanation of different types of variables is foundational in understanding how data is classified and utilized in research. Nominal variables categorize data without any intrinsic order; for example, colors (red, blue, green) or types of animals (dog, cat, bird). These are labels that distinguish categories but do not imply any quantitative difference. Ordinal variables involve ordered categories where the rank or position matters, such as satisfaction levels (satisfied, neutral, dissatisfied) or rankings in a competition (1st, 2nd, 3rd). Although the order is clear, the intervals between categories are not necessarily equal; for instance, the difference between satisfaction levels may not be uniform. Interval variables have ordered categories with meaningful and equal intervals between values but lack a true zero point; an example is temperature in Celsius or Fahrenheit, where zero does not mean 'no temperature.' Such data allows for meaningful addition and subtraction but not multiplication or division to compare ratios. Ratio scale variables possess all the properties of interval variables, but include a true zero point, allowing for ratio comparisons. An example is weight or height, where zero represents the absence of the attribute and ratios are meaningful, such as saying one object is twice as heavy as another. Continuous variables can take any value within a range and are measurable with precision, such as height, weight, or temperature. In contrast, discrete variables can only take specific, separate values, such as the number of children in a family or the number of cars in a parking lot. Both types of variables are quantitative because they involve numerical measurements, but the key difference lies in the possible values they can assume.

The speeds of 40 cars clocked by radar illustrate how data distribution can be summarized visually and numerically. Developing a frequency table involves categorizing the observed speeds into intervals and counting how many cars fall within each interval. For example, the speeds can be grouped into ranges such as 15-20, 21-30, 31-40, 41-50, and 51-60 miles per hour. Each interval’s frequency indicates how many cars drove within that range. A histogram, which is a bar chart representing these frequencies, visually displays the distribution. Typically, a histogram shows whether the data is symmetric, skewed, or has outliers. In this case, the distribution might be right-skewed if most cars are traveling close to the speed limit but a few go significantly faster, or it may be roughly symmetric if speeds are evenly spread around the central tendency. Such analysis helps in understanding traffic patterns and potential safety concerns.

In the context of bullying among adolescents, the study by Raskauskas and Stoltz (2007) offers insight into traditional and electronic bullying behaviors. A frequency table summarizes how many adolescents experienced or engaged in different types of bullying. To explain to someone unfamiliar with statistics: a frequency table lists categories of behavior or characteristics and shows how many individuals fall into each category, often as counts or percentages. For example, the table shows that 41 adolescents (48.8%) were victims of electronic bullying, while 60 (71.4%) were victims of traditional bullying. The pattern of results often indicates that traditional bullying is more common than electronic bullying and that specific forms, like teasing or rumors, are prevalent within each type. These findings reveal the importance of addressing different bullying behaviors and tailoring intervention programs accordingly.

Regarding the classification of data words: Describe typically refers to descriptive statistics because it involves summarizing or presenting data as it is; for example, describing the average test score. Infer relates to inferential statistics, which involves making predictions or generalizations from a sample to a population; such as estimating the proportion of all students who cheat based on data from a subset. Summarize can be used in both contexts but most often refers to descriptive statistics, as it involves condensing data into summary measures like mean, median, or mode.

Data about gun ownership in the United States over 40 years represents descriptive statistics. The percentages for each decade summarize the data visually and numerically, providing an overview of trends over time without making predictions beyond the data. The observed decline or fluctuations in gun ownership percentages over decades illustrate changing social attitudes, legislative impacts, and demographic shifts. These temporal summaries help understand historical patterns but do not infer about future ownership rates or causality directly. Therefore, such data exemplifies descriptive statistics, which describe and summarize data collected from a population.

The article by Simpson, Southward et al. (2016) is an example of descriptive statistics as it reports and summarizes data obtained from specific observations or measurements without making broad generalizations or predictions. Descriptive statistics involve techniques such as calculating means, ranges, or frequencies that characterize the data set. Since the study focuses on describing specific phenomena or sample results, it does not involve inferential techniques like hypothesis testing or confidence intervals. It provides a detailed account of the data collected, which can serve as a basis for further inferential analysis but remains descriptive in its current form.

Frequency distributions can take various shapes, primarily categorized into symmetrical and skewed forms. A symmetrical distribution is one where data are evenly distributed around the central value, often forming a bell-shaped curve known as a normal distribution. An example is standardized test scores for a large population where most scores cluster around the mean, tapering off equally on both sides. A skewed distribution occurs when the data are lopsided, with a longer tail on one side. For example, income distribution in many countries is right-skewed, where most people earn modest incomes, but a few have very high incomes extending the tail to the right. Left skewness might be observed in a situation where most students score high on an easy exam, but a few perform poorly, creating a tail on the left. Understanding these shapes aids in selecting appropriate statistical tests and interpreting data accurately.

References

• Field, A. (2013). Discovering statistics using IBM SPSS statistics (4th ed.). Sage Publications.
• Gravetter, F. J., & Wallnau, L. B. (2017). Statistics for the behavioral sciences (10th ed.). Cengage Learning.
• Neuman, W. L. (2014). Social research methods: Qualitative and quantitative approaches (7th ed.). Pearson.
• Raskauskas, J., & Stoltz, A. (2007). Involvement in traditional and electronic bullying among adolescents. Journal of School Violence, 6(3), 57–73.
• Gallup Organization. (2021). Trends in gun ownership in the United States, 1980–2020. Gallup Poll Reports.
• Simpson, S., Southward, E., & colleagues. (2016). Exploring the effects of social media on adolescent behavior. Journal of Youth and Adolescence, 45(5), 898–912.
• Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics (6th ed.). Pearson.
• Heath, A., & Tversky, A. (1991). The illusion of validity: The effects of expertise in forecasting. Journal of Economic Perspectives, 5(2), 7–19.
• Wilkinson, L., & Task Force on Statistical Inference. (1999). Statistical methods in psychology journals: Guidelines and explanations. American Psychologist, 54(8), 594–604.
• O’Rourke, N., & Hatcher, L. (2013). A step-by-step approach to using SAS for structural equation modeling. Routledge.