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2000 we 026 300-< 350 1 0.02
800-400 12, Oe 350-< 400 1 0.02
400- < 500 4 0.04 6 406 i aD
500- < 600 3 0.03 0 00
600- < 700 1 0.01 a
700- < 800 0 0.00
800- < 900 1 0.01
100 1.00
The distribution is skewed to the right, or positively
skewed. There is a gap in the histogram, and what
appears to be an outlier in the “500-550” interval.
The histogram is skewed right, with a majority of
observations between 0 and 300 cycles. The class
holding the most observations is between 100 and 200
cycles.
--- Trang 829 ---
816 Chapter 1
———-_. owas decreased to any value at least 370 without changing
b. Class interval Freq. Rel. Freq. the median.
ee d. 6.18 min; 6.16 min
2.25 < 2.75 2 0.04
2.75 < 3.25 2 O04 = Bia 12
goseenas n 008 b. If 127.6 is reported as 130, then the median is 130, a
lee 4 6i6 substantial change. When there is rounding or grouping,
the median can be highly sensitive to a small change.
4.25 < 415 18 0.36
4.75 < 5.25 10 0.20 37. ¥ = 92, Xu(2s) = 95.07, Xu(10) = 102.23, ¥ = 119.3
5.25 < 5.75 4 0.08 Positive skewness causes the mean to be larger than the
575 < 625 3 006 median. Trimming moves the mean closer to the median.
9. 8 F=8 te, faite
The distribution of the natural logs of the original data b. yer pack
is much more symmetric than the original.
41. 2.25.8 b.49.31 €.7.02 4.49.31
¢. 56,14.
43. a. 2887.6, 2888 b. 7060.3
29. d. The frequency distribution is:
45. 24.36
Relative Relative 47. $1,961,160
Class frequency Class frequency yy 3.5.13, 19, 9.0,23,-25
0< 150.193 900 < 1050 019 SL. a. 1,6,5
150 < 300.183 1050 < 1200 029 b. The box plot shows positive skewness. The two
300< 450.251 1200 < 1350 005 longest runs are extreme outliers.
450 < 600.148, 1350 < 1500 004 ¢. outlier: greater than 13.5 or less than —6.5
600< 750 097 «1500 < 1650 001 extreme outlier: greater than 21 or less than ~14
750<900 066. +1650 < 1800-002 e woe equidtinpeatiecreased £0: &
1800 < 1950 .002 ‘
53. a. The mean is 27.82, the median is 26, and the 5%
The relative frequency distribution is almost unimodal trimmed mean is 27.38. The mean exceeds the
and exhibits a large positive skew. The typical middle median, in accord with positive skewness. The
value is somewhere between 400 and 450, although the trimmed mean is between the mean and median, as
skewness makes it difficult to pinpoint more exactly than you would expect.
this. b. There are two outliers at the high end and one at the
e. 775, 014 low end, but there are no extreme outliers. Because
f. 211 the median is in the lower half of the box, the upper
whisker is longer than the lower whisker, and there are
BL. a. 5.24 two high outliers compared to just one low outlier, the
b. The median, 2, is much lower because of positive plot suggests positive skewness.
skewness, =
¢. Trimming the largest and smallest observations yields 55+ The two distributions are centered in about the same
the 5:9% trimmed mean, 44, which is between the place, but one machine is much more variable than the
isin and Wiedian. other. The more precise machine produced one outlier,
but this part would not be an outlier if judged by the
33. a. A stem-and leaf display: distribution of the other machine.
32 | 55 Stem: ones 57. All of the Indian salaries are below the first quartile of
33 | 49 Leaf: tenths Yankee salaries, There is much more variability in the
34 Yankee salaries. Neither team has any outliers.
35 | 6699
| es 61. The three flow rates yield similar uniformities, but the
values for the 160 flow rate are a little higher.
37 | 03345,
38 | 9 63. a. 9.59, 59.41. The standard deviations are large, so it is
30 | 2347 certainly not true that repeated measurements are
40 | 33 identical.
Hi b. 396, .323. In terms of the coefficient of variation, the
HC emissions are more variable.
4214
65. 10.65
The display is reasonably symmetric, so the mean and 67g, yar th, =ars?,
median will be close. b. 100.78, 572
b. 370.7, 369.50.
¢. The largest value (currently 424) could be increased
by any amount without changing the median. It can be
--- Trang 830 ---
Chapter2 817
69. The mean is .93 and the standard deviation is O81. The 7. a. (111, 112, 113, 121, 122, 123, 131, 132, 133, 211,
distribution is fairly symmetric with a central peak, as 212, 213, 221, 222, 223, 231, 232, 233, 311, 312, 313,
shown by the stem and leaf display: 321, 322, 323, 331, 332, 333}
. b. (111, 222, 333}
Leaf unit = 0.010 ce. (123, 132, 213, 231, 312, 321)
7 7 (111, 113, 131, 133, 311, 313, 331, 333}
8 Be 8
S pee 9. a. S=(BBBAAAA, BBABAAA, — BBAABAA,
4 SSaaseay BBAAABA, BBAAAAB, BABBAAA, BABABAA,
BABAABA, BABAAAB, BAABBAA, BAABABA,
3 a3 BAABAAB, BAAABBA, BAAABAB, BAAAABB,
10 O48 ABBBAAA, ABBABAA, ABBAABA, ABBAAAB,