Based on the scale of measurement for each variable listed below, which measure of central tendency is most appropriate for describing the data?
The time (in years) it takes a sample of students to graduate college
The blood type (e.g., Type A, B, AB, O) of a group of participants
The rankings of college undergraduate academic programs
3. An expert reviews a sample of 10 scientific articles (n = 10) and records the following numbers of error in each article: 0, 4, 2, 8, 2, 3, 1, 0, 5, and 7. Compute the SS, the variance, and the standard deviation for this sample using the definitional and computational formulas.
3. Radel and colleagues (2011) conducted a study of how feeling overly controlled makes you desire—even unconsciously—more freedom. In their study, 52 Canadian undergraduates played a video game in a laboratory and were randomly assigned to either:
a. an automony deprivation condition, in which they were told to follow instructions precisely, constantly given instructions over a loudspeaker, and carefully observed on everything they did.
b. a neutral condition, which was much more laid back.
After this activity, they were asked to do a “lexical decision task” (a standard approach for measuring unconscious responses) in which they were shown a series of words and nonwords in random order and had to press “C” if it was a real word or “N” if not. Half of the real words were related to autonomy (e.g., freedom, choice) and half were neutral (e.g., whisper, hammer). The key focus of the study was on how long it took people to press the button *(“response latency”) for each kind of real word, averaged over the many words of each type. The table below shows the mean and standard deviation across the participants of these four categories of results. Thus, for example, 782 milliseconds (thousandths of a second) is the average time it took participants in the autonomy-deprived condition to respond to the autonomy-related words, and 211 is the standard deviation across the 26 participants’ average response time in that condition. Explain the numbers in this table to a person who has never had a course in statistics. (Be sure to explain some specific numbers, as well as the general principle of the mean and standard deviation.) For your interest, the pattern of results shown here supported the researchers’ hypothesis: “Relative to a neutral instructional climate, a controlling climate thwarting the need for autonomy…enhanced accessibility for autonomy-related words.” (p.924)
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