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.
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