Problem Set #2 Answer Key
Ch. 3
9) The answer to #9 is in the book.
18)
a) SX = mean * n = 12 * 8 = 96
b) 96 + 4 = 100
c) n = 9
d) mean = SX/n = 100/9 = 11.1
26)
a)
estimates
mean = 7.5
mdn = 7.5
computations
mean = (5 + 7 + 8 + 10)/4 = 7.5
mdn = (7 + 8)/2 = 7.5
b) If the highest score in the distribution changes from 10 to 14, the mean will go up but the median will stay the same. This is because (based on what the sketch would look like), the mean would have to shift right to accommodate the extra "weight" exerted by the new, more extreme score, but the median would stay put because it still has half of the scores to the right of it, and half to the left.
computations
mean = (5 + 7 + 8 + 14)/4 = 8.5
mdn = (7 + 8)/2 = 7.5
c) If the score X = 10 from the original distribution is changed to X = 6, the median will have to shift to the left, to between 6 and 7 (that is, 6.5). As scores get moved from one side of the median to the other, the median will move with the score.
28)
a) mean = 7.1875, mdn = 6.5
b) The mean score for the class is above the national norm.
c) The median score for the class is below the national norm.
Ponder this: Is the class above average or below average?
Ch 4
12)
a & b)
c)
SS = (8 – 5)2 + (7 – 5)2 + (6 – 5)2 + (5 – 5)2 + (4 – 5)2 + (4 – 5)2 + (3 – 5)2 + (3 – 5)2
SS = 9 + 4 + 1 + 0 + 1 + 1 + 4 + 4
SS = 24
s2 = SS/(n – 1)
s2 = 24/7
s2 = 3.43
s = 1.85 (see, 2 wasn't a bad guess at all!)
20)
a)
None of the scores is very extreme; they are all within one standard deviation of the mean. 65 is the most "extreme" at ¾ of a standard deviation away from the mean.
b)
In this case, all of the scores are at least 1½ standard deviations from the mean. 65 and 40 are so far from the mean that they're off the edges of the graph.
22)
a)
m = (2 + 0 + 8 + 2)/4 = 3
SS = (2 – 3)2 + (0 – 3)2 + (8 – 3)2 + (2 – 3)2
SS = 1 + 9 + 25 + 1
SS = 36
s2 = SS/N = 36/4 = 9
s = 3
b)
m = (5 + 3 + 11 + 5)/4 = 6
SS = (5 – 6)2 + (3 – 6)2 + (11 – 6)2 + (5 – 6)2
SS = 1 + 9 + 25 + 1
SS = 36
s2 = SS/N = 36/4 = 9
s = 3
c)
m = (4 + 0 + 16 + 4)/4 = 6
SS = (4 – 6)2 + (0 – 6)2 + (16 – 6)2 + (4 – 6)2
SS = 4 + 36 + 100 + 4
SS = 144
s2 = SS/N = 144/4 = 36
s = 6
d) When a constant is added to each score, deviation scores do not change, and therefore neither does the standard deviation.
e) When each score is multiplied by a constant, the deviation scores are multiplied by the same constant, and therefore so is the standard deviation.