Find 2 different data sets and compute summary statistics. For each data set try to answer the following questions:
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For each of the five data sets described, answer the following three questions and then use Figure 2.2 (on this page) to select an appropriate graphical display. Question 1: How many variables are in the data set? Question 2: Is the data set categorical or numerical? Question 3 : Would the purpose of a graphical display be to summarize the data distribution, to compare groups, or to investigate the relationship between two numerical variables? Data Set 1: To learn about the reason parents believe their child is heavier than the recommended weight for children of the same age, each person in a sample of parents of overweight children was asked what they thought was the most important contributing factor. Possible responses were lack of exercise, easy access to junk food, unhealthy diet, medical condition, and other. Data Set 2: To compare commute distances for full-time and part-time students at a large college, commute distance was determined for each student in a random sample of 50 full-time students and for each student in a random sample of 50 part-time students. Data Set 3: To learn about how number of years of education and income are related, each person in a random sample of 500 residents of a particular city was asked how many years of education he or she had completed and what his or her annual income was. Data Set 4: To see if there is a difference between faculty and students at a particular college with respect to how they commute to campus (drive, walk, bike, and so on), each person in a random sample of 50 faculty members and each person in a random sample of 100 students was asked how he or she usually commutes to campus. Data Set 5: To learn about how much money students at a particular college spend on textbooks, each student in a random sample of 200 students was asked how much he or she spent on textbooks for the current semester.
Graphical Methods for Describing Data Distributions
Selecting an Appropriate Graphical Display
Collecting, Analyzing and Comparing two Quantitative Data Sets 1. Decide on a question about quantitative data that compares two populations or groups. For example, suppose we want to find out whether part time Calstatela students or full time Calstatela student work more. Notice I would need two bits of information. If the student is a full or part time student and how many hours per week they work. You will then be analyzing the quantitative variable (hours of work) for each of the two groups. Be specific about the population and make the question address a quantitative variable. 2. Devise a method for taking a sample. The sample does not have to be large or randomly selected, but those are better. Part of your report will be to describe your sampling method and how well it applies to the population. For example, you may use a voluntary response survey, but in the report you will say that the sample data will not apply very well to the population. Also talk about the different kinds of bias if you write questions for people to answer, make sure to avoid question bias. 3. Collect your data. You should have two quantitative data sets each having at least 20 values. 4. Write a paragraph describing the method used to collect the data and if the data represents the population you are after. Also describe the various types of bias that could be present. 5. Use Statcrunch to analyze your data sets. Include, sample statistics for both data sets, dot plots, box plots and histograms for both data sets. There should be a total of 7 graphs. Also copy and paste the summary statistics from the computer program. There should be min, max, mean, standard deviation, mode, range, median, Q1, Q3, and IQR. Analyze all the sample statistics. Describe the shape, outliers, center and spread for each data set. Now compare the averages and typical values for the two groups. Which group had the higher average? Which group had more spread? Do the typical ranges of the groups overlap? Do you think
Sheryl E.
Consider the following four data sets. $$\begin{array}{cc|cc|cc|cc} \hline \text { Data } & \text { Set I } & \text { Data } & \text { Set II } & \text { Data } & \text { Set III } & \text { Data Set IV } \\ \hline 1 & 5 & 1 & 9 & 5 & 5 & 2 & 4 \\ 1 & 8 & 1 & 9 & 5 & 5 & 4 & 4 \\ 2 & 8 & 1 & 9 & 5 & 5 & 4 & 4 \\ 2 & 9 & 1 & 9 & 5 & 5 & 4 & 10 \\ 5 & 9 & 1 & 9 & 5 & 5 & 4 & 10 \\ \hline \end{array}$$ a. Compute the mean of each data set. b. Although the four data sets have the same means, in what respect are they quite different? c. Which data set appears to have the least variation? the greatest variation? d. Compute the range of each data set. e. Use the defining formula to compute the sample standard deviation of each data set. f. From your answers to parts (d) and (e), which measure of variation better distinguishes the spread in the four data sets: the range or the standard deviation? Explain your answer. g. Are your answers from parts (c) and (e) consistent?
Descriptive Measures
Measures of Variation
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