Monday, March 18, 2013
Individual Text Assignment
11. For the following scores, find the (a) mean, (b) median, (c) sum of squared deviations, (d) variance, and (e) standard deviation:
2, 2, 0, 5, 1, 4, 1, 3, 0, 0, 1, 4, 4, 0, 1, 4, 3, 4, 2, 1, 0
(a) mean, 42/21 = 2 (b) median, 2 (c) sum of squared deviations, 46 (d) variance, 46/21 = 2.19 and (e) standard deviation, 1.47
12. For the following scores, find the (a) mean, (b) median, (c) sum of squared deviations, (d) variance, and (e) standard deviation:
1,112; 1,245; 1,361; 1,372; 1,472
(a) mean, 6,562/5 = 1,312 (b) median, 1,361 (c) sum of squared deviations, 76,090 (d) variance, 76,090/5 = 15,218 and (e) standard deviation, 123.361
13. For the following scores, find the (a) mean, (b) median, (c) sum of squared deviations, (d) variance, and (e) standard deviation:
3.0, 3.4, 2.6, 3.3, 3.5, 3.2
(a) mean, 19/6 = 3.166 (b) median, 3.25 (c) sum of squared deviations, 0.533 (d) variance, 0.533/6 = 0.088 and (e) standard deviation 0.296
16. A psychologist interested in political behavior measured the square footage of the desks in the official office of 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, and 36 square feet. (a) Figure the means and standard deviations for the governors and for the CEOs. (b) Explain, to a person who has never had a course in statistics, what you have done. (c) 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.
(a) Governors - mean = 43, standard deviations = 6.83; CEOs - mean = 44, standard deviations = 12.65
(b) To figure the mean add up all the scores and divide this sum by the number of scores, such as for the governors, 40 + 36 + 52 + 40 + = 172/4 the mean is 43, which is the same process for CEOs (Aron, Aron, & Coups, 2009). To figure the standard deviations figure the variance and take the square root. First figure the median, line up all the scores from lowest to highest, figure how many scores there are to the middle score by adding 1 to the number of scores and dividing by 2, and then count up to the middle score or scores, which is 42 (Aron, Aron, & Coups, 2009). Next locate the sum of squared deviation by subtracting the listed scores minus the means, and then square the result. Then add each end result and divide by the number of scores. Next find the variance by taking the SS, which is 140 and divide it by the numbers of scores, which is 4. The variance is 35. Now calculate the square root of the variance, which is the standard deviation.
(c) The mean is a measure when the distribution of data is continuous and symmetrical and it is the average. While standard deviation is the most used way of describing the spread of a group of scores and is the average amount that scores differ from the mean (Aron, Aron, & Coups, 2009). I would have to guess that individuals in a high power of authority such as CEOs and governors would have large desk which in a way represent then power they hold. With CEOs making more money and controlling powerful companies it would seem they would have larger desk.
21. Payne (2001) gave participants a computerized task in which they first see a face and then a picture of either a gun or a tool. The task was to press one button if it was a tool and a different one if it was a gun. Unknown to the participants while they were doing the study, the faces served as a “prime” (something that starts you thinking a particular way); half the time they were of a black person and half the time of a white person. Table 2–9 shows the means and standard deviations for reaction times (the time to decide if the picture is of a gun or a tool) after either a black or white prime. (In Experiment 2, participants were told to decide as fast as possible.) Explain the results 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.)
The mean is the measure when the distribution of data is continuous and symmetrical, while standard deviation is the most used way of describing the spread of a group of scores (Aron, Aron, & Coups, 2009). As for the gun the means of 423 and 441 were the best measures of central tendency from experiment 1 and the standard deviations were 64 and 73, which showed just how far apart or spread they were from the mean.
14. On a standard measure of hearing ability, the mean is 300 and the standard deviation is 20. Give the Z scores for persons who score (a) 340, (b) 310, and (c) 260. Give the raw scores for persons whose Z scores on this test are (d) 2.4, (e) 1.5, (f) 0, and (g) -4.5.
(a) 340, -2 (b) 310, -0.5 (c) 260, 2 (d) 2.4, 348 (e) 1.5, 330 (f) 0, 300 and (g) -4.5, 210
15. A person scores 81 on a test of verbal ability and 6.4 on a test of quantitative ability. For the verbal ability test, the mean for people in general is 50 and the standard deviation is 20. For the quantitative ability test, the mean for people in general is 0 and the standard deviation is 5. Which is this person’s stronger ability: verbal or quantitative? Explain your answer to a person who has never had a course in statistics.
To figure this out take the score of 81, which is 31 above the verbal ability test mean of 50, and divide by 20, which is (31/20) = 1.5. Therefore 81 is 1.5 standard deviations above the mean score for verbal ability. To figure the score of 6.4, which is 6.4 above the quantitative ability mean of 0 divide it by 5, which is 6.4/5 = 1.28 standard deviations above the mean of the quantitative ability test. Therefore with a Z score of 1.5 on verbal ability and a Z score of 2.8 on quantitative ability the person’s stronger ability is verbal ability.
22. Suppose you want to conduct a survey of the attitude of psychology graduate students studying clinical psychology toward psychoanalytic methods of psychotherapy. One approach would be to contact every psychology graduate student you know and ask them to fill out a questionnaire about it. (a) What kind of sampling method is this? (b) What is a major limitation of this kind of approach?
(a) This would be considered nonrandom sampling. (b) This type of sampling, only gives little guarantee that the sample will be representative of the entire population. This sampling is biased because it would not take into account for the psychology graduate students that are unknown.
25. You are conducting a survey at a college with 800 students, 50 faculty members, and 150 administrators. Each of these 1,000 individuals has a single listing in the campus phone directory. Suppose you were to cut up the directory and pull out one listing at random to contact. What is the probability it would be (a) a student, (b) a faculty member, (c) an administrator, (d) a faculty member or administrator, and (e) anyone except an administrator? (f) Explain your answers to someone who has never had a course in statistics.
(a) a student, 800/1000 or 8% probability (b) a faculty member, 50/1000 or 5% probability (c) an administrator, 150/1000 or 15% probability (d) a faculty member or administrator, 200/1000 or 20% probability (e) anyone except an administrator, 850/1000 or 85% probability (f) Probability is the measure or estimation of how likely that something will occur. To determine the probability one has to divide the number of a certain group to choose from (800 students) by the total number of the survey population (1000). Therefore, there is a 800/1000 or .08% or 8% probability.