Order Central Tendency And Dispersion Assignment

Note to the Instructor: This is the seventh in a series of 13 exercises that were written for an introductory research methods class. The first exercise focuses on the research design which is your plan of action that explains how you will try to answer your research questions. Exercises two through four focus on sampling, measurement, and data collection. The fifth exercise discusses hypotheses and hypothesis testing. The last eight exercises focus on data analysis. In these exercises we’re going to analyze data from one of the Monitoring the Future Surveys (i.e., the 2017 survey of high school seniors in the United States). This data set is part of the collection at the Inter-university Consortium for Political and Social Research at the University of Michigan. This data set is freely available to the public and you do not have to be a member of the Consortium to use it. We’re going to use SDA (Survey Documentation and Analysis) to analyze the data which is an online statistical package written by the Survey Methods Program at UC Berkeley and is available without cost wherever one has an internet connection. A weight variable is automatically applied to the data set so it better represents the population from which the sample was selected. You have permission to use this exercise and to revise it to fit your needs. Please send a copy of any revision to the author so I can see how people are using the exercises. Included with this exercise (as separate files) are more detailed notes to the instructors and the exercise itself. Please contact the author for additional information.

This page in MS Word (.docx) format is attached.

Goal of Exercise

The goal of this exercise is to explore measures of central tendency (mode, median, and mean) and dispersion (range, standard deviation, and variance). The exercise also gives you practice in using FREQUENCIES in SDA.

Order Central Tendency And Dispersion Assignment

Part I – Measures of Central Tendency

Data analysis always starts with describing variables one-at-a-time. Sometimes this is referred to as univariate (one-variable) analysis. Central tendency refers to the center of the distribution.

There are three commonly used measures of central tendency – the mode, median, and mean of a distribution. The mode is the most common value or values in a distribution.[1] The median is the middle value of a distribution.[2] The mean is the sum of all the values divided by the number of values.

We’re going to use the Monitoring the Future (MTF) Survey of high school seniors for this exercise. The MTF survey is a multistage cluster sample of all high school seniors in the United States. The survey of seniors started in 1975 and has been an annual survey ever since. To access the MTF 2017 survey follow the instructions in the Appendix. Your screen should look like Figure 7-1. Notice that a weight variable has already been entered in the WEIGHT box. This will weight the data so the sample better represents the population from which the sample was selected.

This the SDA dialog box that you will get when you open SDA.

Figure 7-1

Order Central Tendency And Dispersion Assignment

MTF is an example of a social survey. The investigators selected a sample from the population of all high school seniors in the United States. This particular survey was conducted in 2017 and is a relatively large sample of a little more than 12,000 students. In a survey we ask respondents questions and use their answers as data for our analysis. The answers to these questions are used as measures of various concepts. In the language of survey research these measures are typically referred to as variables.

Run FREQUENCIES in SDA for the variable v2196. This variable is the number of miles per week that students drive. Here’s the question from the survey – “During an average week, how much do you usually drive a car, truck, or motorcycle?” To run the frequency distribution, enter the variable name, v2196, in the ROW box. The WEIGHT box is already filled in. Click on RUN THE TABLE to get the frequency distribution. Your screen should look like Figure 7-2.

This is the frequency distribution for v2196.

Figure 7-2

The responses to this question were divided into a set of six categories – none, 1 to 10, 11 to 50, 51 to 100, 101 to 200, and more than 200. This was done to make the question easier to answer. It’s difficult for respondents to remember the precise number of miles they drove per week. It’s a lot easier to select one of these categories. But this means that we don’t have the exact number of miles driven. Keep that in mind as we think about measures of central tendency.

Rerun the table but this time check the box for SUMMARY STATISTICS under TABLE OPTIONS and click on the drop-down arrow next to TYPE OF CHART and select BAR CHART. Below the frequency distribution you should see the statistics that SDA computes for you and the bar chart. The summary statistics should look like Figure 7-3.

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