Assignment: Measures of Central Tendency and Variability
Last week, you learned how to summarize a distribution by using frequency distribution tables and various graphs. The shape the frequency distribution forms is important, but frequency tables and graphs are not always the most efficient or meaningful way to summarize large amounts of data. In addition to graphing the shape of the distribution, statistics can be computed to provide even more information about the scores. Measures of central tendency tell us how the scores in the data set “hang together.” What score or scores are “typical” for the data set? Measures of variability help us understand how scores are spread out. How big are the distances between scores? Computing measures of central tendency, such as the mean, median, and mode, and measures of variability, such as the range and standard deviation, is often the first step researchers take after collecting data for a study.
This assignment will allow you to practice computing and interpreting some common measures of central tendency and measures of variability. Be sure to watch this week’s instructional videos in the Learning Resources tab of Week 2 before beginning your Assignment.
Download the scenario and data set that you will use for this assignment from the Weekly Data Set forum. This Assignment has two Parts: 1) Computation and Interpretation and 2) Conceptual Understanding. Write your responses in your own words. It is acceptable to number your answers, but do not copy and paste the questions into your answer document.
By Day 7
Part 1: Computation and Interpretation. Use SPSS to compute the following measures of central tendency, then interpret what those results tell you about the sample:
Mean
Median
Mode
Range
Standard deviation
In your written answer document, include the following for each statistic:
The answer you obtained from SPSS
An interpretation of what each statistic tells you about the variable
For example, each of your answers might look something like this: “The mean of this sample is ______. The mean is important because it tells me that ____________.” Be sure to also include supporting evidence from the text and/or class resources to support each answer.
Part 2: Conceptual Understanding. Answer the following questions about the dataset and resulting distribution, again, making sure to support each answer with evidence from the text and/or class resources and explaining each answer thoroughly.
6. Without redoing any calculations, think critically about how each measure would be affected if the highest score was eliminated from the data set. Explain if each measure (mean, median, mode, range, and standard deviation) would increase, decrease, or stay the same.
7. Use the relative positions of the mean, median, and mode to identify the shape of the distribution (positive skew, negative skew, or normal distribution). Explain what the shape of this distribution tells you about the sample.
Provide an APA reference list.
Submit three documents for grading:
Your text (Word) document with your answers and explanations to the assignment questions, your SPSS Data file, and your SPSS Output file.
Scenario: A school psychologist at Henry D. Thoreau High School wants to know how many times students drink caffeinated beverages during the school year. The information will help her determine if she should do a school-wide information session about the effects of caffeine use on physical and mental health. She collects data from a sample of 100 students. You will find the data in the spreadsheet attached here. Copy and paste it into SPSS for analysis.
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