Posted: September 20th, 2015

Finding the mean, median, and the mode.

 

Prepare a written response to the following questions.

 

Chapter 3

 

1. For the following scores, find the mean, median, and the mode. Which would be the most appropriate measure for this data set?

 

2, 2, 0, 5,1, 4,1, 3, 0, 0, 1, 4, 4, 0,1, 4, 3, 4, 2, 1

 

2. Based on the scale of measurement for each variable listed below, which measure of central tendency is most appropriate for describing the data?

 

1. The time (in years) it takes a sample of students to graduate college

 

1. The blood type (e.g., Type A, B, AB, O) of a group of participants

 

1. The rankings of college undergraduate academic programs

 

 

Chapter 4

 

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.

 

 

4. A psychologist interested in political behavior measured the square footage of the desks in the official office for four U.S. governors and of four chief executive officers (CEOs) of major U.S. corporations. The figures for the governors were 44, 36, 52, and 40 square feet. The figures for the CEOs were 32, 60, 48, 36 square feet.

 

1. Figure the means and standard deviations for the governors and CEOs.
2. Explain, to a person who has never had a course in statistics, what you have done.
3. Note the ways in which the means and standard deviations differ, and speculate on the possible meaning of these differences, presuming that they are representative of U.S. governors and large corporations’ CEOs in general.

 

5. 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:

 

1. 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.
2. 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).

 

Mean Latencies (in Milliseconds) in the Lexical Task Assessing Accessibility for Autonomy-Related Constructs (Experiment 1)
	Condition
	Autonomy Deprivation			Neutral
Construct	M	SD		M	SD
Autonomy-related words	782	211		857	243
Neutral words	835	258		841	301

 

 

Chapter 5

 

6. On a standard measure of hearing ability, the mean is 300 and the standard deviation is 20. Give the Z scores for persons whose raw scores are 340, 310, and 260. Give the raw scores for persons whose Z scores on this test are 2.4, 1.5, and -4.5.

 

7. Using the unit normal table, find the proportion under the standard normal curve that lies to the right of each of the following:
   1. z = 1.00
   2. z = -1.05
   3. z = 0
   4. z = 2.80
   5. z = 1.96

 

 

8. Suppose that the scores of architects on a particular creativity test are normally distributed. Using a normal curve table (page 477-480), what percentage of architects have Z scores:
9. Above .10?
10. Below .10?
11. Above .20?
12. Below .20?
13. Above 1.10?
14. Below 1.10?
15. Above -.10?
16. Below -.10?

 

Chapter 6

 

9. A statistics instructor wants to measure the effectiveness of his teaching skills in a class of 102 students (N =102). He selects students by waiting at the door to the classroom prior to his lecture and pulling aside every third student to give him/her a questionnaire.

 

1. Is this sample design an example of random sampling? Explain.
2. Assuming that all students attend his class that day, how many students will he select to complete his questionnaire?

 

 

1. Suppose that you were going to conduct a survey of visitors to your campus. You want the survey to be as representative as possible.

 

1. How would you select the people to survey?
2. Why would that be your best method?

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