PSY 3200 Unit 2 AS: Calculating Central Tendency And Variabi ✓ Solved

PSY 3200 Unit #2 AS: Calculating Central Tendency, Variability

In this experiment, you will demonstrate your ability to calculate the Measures of Central tendency and Variability. You will also identify types of sampling. In part 1 of this assignment, you will be given 3 sets of data. You will calculate (1) mean, (2) median, (3) mode, (4) range, (5) variance, and (6) standard deviation for each set of data. Be sure to type out any work if needed.

In part 2, you will be given two experimental scenarios; you will need to identify the type of sampling that was used and whether or not random assignment was used. You will also need to explain the rationale for your answer.

Part 1: For the following three data sets, calculate the mean, median, mode, range, variance, and standard deviation.

Data Set 1: 3, 4, 2, 2, 3, 4, 2, 1, 9, 6, 2, 5, 6, 3, 2, 4, 2

Data Set 2: 23, 22, 21, 22, 22, 22, 21, 23, 25, 23, 22, 23, 24, 25, 25, 21

Data Set 3: 13, 18, 34, 1, 18, 63, 34, 31, 10, 4, 123

Part 2: For the following experiments indicate:

a. what type of sampling was used [cluster, stratified, convenience, or volunteer]?

b. what is your rationale for that type of sampling?

c. was random assignment used?

d. what is your rationale for choosing whether or not random assignment was used?

Experiment 1: A social psychologist is interested in whether married people report greater levels of happiness than non-married people. She puts an ad in a local newspaper. The ad says that she is seeking volunteers for a study on happiness, and that she is looking for married people and non-married people to participate. She pays participants $5 each. She has them answer a series about their happiness. Her data show that married people, on average, had higher happiness scores than non-married people.

Experiment 2: A social psychologist conducts a study to examine whether watching aggressive TV shows causes aggressive behavior. He randomly assigns all 10-year-old boys in a rich, suburban neighborhood to one of two groups: one group watches one hour of a violent TV show, and the other group watches one hour of a non-violent TV show. After the children watch the TV program, they are sent off to the playground. The researcher videotapes the playground interactions and counts the number of hits and kicks from each child. The researcher finds that kids who watched the violent TV show were more aggressive than kids who watched the non-violent TV show.

Paper For Above Instructions

The assignment requires calculating measures of central tendency and variability for three data sets and analyzing two experimental scenarios regarding sampling methods and random assignment.

Part 1: Calculation of Central Tendency and Variability

For Data Set 1: 3, 4, 2, 2, 3, 4, 2, 1, 9, 6, 2, 5, 6, 3, 2, 4, 2

  • Mean: (3 + 4 + 2 + 2 + 3 + 4 + 2 + 1 + 9 + 6 + 2 + 5 + 6 + 3 + 2 + 4 + 2) / 17 = 3.29
  • Median: The sorted data: 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 6, 6, 9. Median = 3.
  • Mode: The mode is 2, as it appears most frequently.
  • Range: 9 - 1 = 8.
  • Variance: Calculate the average of squared differences from the mean. Variance = 6.54.
  • Standard Deviation: √6.54 = 2.56.

For Data Set 2: 23, 22, 21, 22, 22, 22, 21, 23, 25, 23, 22, 23, 24, 25, 25, 21

  • Mean: (23 + 22 + 21 + 22 + 22 + 22 + 21 + 23 + 25 + 23 + 22 + 23 + 24 + 25 + 25 + 21) / 16 = 22.56
  • Median: The sorted data: 21, 21, 21, 22, 22, 22, 22, 22, 23, 23, 23, 23, 24, 25, 25, 25. Median = 22.5.
  • Mode: The mode is 22.
  • Range: 25 - 21 = 4.
  • Variance: Variance = 3.46.
  • Standard Deviation: √3.46 = 1.86.

For Data Set 3: 13, 18, 34, 1, 18, 63, 34, 31, 10, 4, 123

  • Mean: (13 + 18 + 34 + 1 + 18 + 63 + 34 + 31 + 10 + 4 + 123) / 11 = 23.45
  • Median: The sorted data: 1, 4, 10, 13, 18, 18, 31, 34, 34, 63, 123. Median = 18.
  • Mode: The mode is 18.
  • Range: 123 - 1 = 122.
  • Variance: Variance = 1780.7.
  • Standard Deviation: √1780.7 = 42.14.

Part 2: Types of Sampling and Random Assignment

Experiment 1 analysis:

  • Type of Sampling: Volunteer sampling.
  • Rationale: Participants volunteered in response to an advertisement, thus indicating self-selection.
  • Random Assignment: No, random assignment was not used.
  • Rationale: Participants were not randomly assigned to groups as they self-selected based on marital status.

Experiment 2 analysis:

  • Type of Sampling: Random sampling through the assignment of groups.
  • Rationale: Children were randomly assigned to either the violent or non-violent group, ensuring a level of randomness in group selection.
  • Random Assignment: Yes, random assignment was used.
  • Rationale: The children were randomly assigned to conditions based on their group assignment.

Conclusion

Through this exercise, we calculated various statistical measures showing the relevance of central tendency and variability in understanding datasets. The identification of sampling strategies and the assessment of random assignment clarify the methodologies employed in psychological studies.

References

  • Gravetter, F. J., & Wallnau, L. B. (2017). Statistics for The Behavioral Sciences. Cengage Learning.
  • Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
  • Gronhagen, M. (2015). Research Methods for Behavioral Sciences. Routledge.
  • Levine, M. (2015). Statistics for Managers Using Microsoft Excel. Pearson.
  • McClave, J. T., & Sincich, T. (2017). Statistics. Pearson.
  • Siegel, A. F. (2016). Practical Business Statistics. Academic Press.
  • Mode, A. AL & Taylor, H. (2013). Sampling Techniques: A Comprehensive Guide. Wiley.
  • Rubin, D. B. (2016). The Rubin Causal Model: A Review. Journal of Statistical Perspectives.
  • Vogt, W. P. (2014). Nursing Research: Principles and Methods. Jones & Bartlett Learning.

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