Statistical Reasoning Worksheet

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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, 20

24, 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 or 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 41.7

4. 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 %

1972 43

1982 42

1992 48

2002 40

2012 43

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: