School

Quinnipiac University **We aren't endorsed by this school

Course

MA 585

Subject

Statistics

Date

Sep 18, 2023

Type

Other

Pages

5

Uploaded by JusticeRook30236 on coursehero.com

Application 1
Porcellini et. al. (A-8) studied 13 HIV positive patients who were treated with highly active antiretroviral therapy
(HAART) for at least 6 months. The CD4 T cell counts (
×
10
6
/
L
¿
at baseline for the 13 subjects are listed
below.
230
205
313
207
227
245
173
58
103
181
105
301
169
Compute (a) the mean, (b) the median, (c) the mode, (d) the range, (e) the variance, (f) the standard deviation,
(g) the coefficient of variation, (h) the interquartile range. Select the measure of central tendency that you think
would be most appropriate for describing the data.
58, 103, 105, 169, 173, 181, 205, 207, 227, 230, 245, 301, 313
a) mean = 2517/13 =
193.62
b) median = 13+1/2 = 14/2 = 7; therefore, the median is
205
c) there is
no mode
d) range = 313 - 58 =
255
e) variance =
[(58−193.62)
2
+(103−193.62)
2
+(105−193.62)
2
+(169−193.62)
2
+(173−193.62)
2
+(181−193.62)
2
+(205−193.62)
2
+(2
07−193.62)
2
+(227−193.62)
2
+(230−193.62)
2
+(245−193.62)
2
+(301−193.62)
2
+ (313−193.62)
2
] / (13-1) =
5568.09
f) standard deviation = √ (66817.08)/12=
74.62
g) coefficient of variation = 74.62/193.62 x 100% = 38.54%
h) interquartile range = 245 - 169 =
76
i) The measure of central tendency that would be most appropriate for describing the data is the median.
Application 2
Cardosi et. al. (A-12) performed a 4-year retrospective review of 102 women undergoing radical hysterectomy
for cervical or endometrial cancer. Catheter associated urinary tract infection was observed in 12 of the
subjects. Below is the number of postoperative days until diagnosis of the infection for each subject
experiencing an infection.
16
10
49
15
6
15
8
19
11
22 13
17
Compute (a) the mean, (b) the median, (c) the mode, (d) the range, (e) the variance, (f) the standard deviation,
(g) the coefficient of variation, (h) the interquartile range. Select the measure of central tendency that you think
would be most appropriate for describing the data.
6, 8, 10, 11, 13, 15, 15, 16, 17, 19, 22, 49
a) mean = 201/12 =
16.75
b) median = 12+1/2 = 6.5; therefore, the median is 15
c) the mode is
15
d) range = 49 - 6 =
43
e) variance = (6-16.75)
2
+ (8-16.75)
2
+ (10-16.75)
2
+ (11-16.75)
2
+ (13-16.75)
2
+ (15-16.75)
2
+ (15-16.75)
2
+
(16-16.75)
2
+ (17-16.75)
2
+ (19-16.75)
2
+ (22-16.75)
2
+ (49-16.75)
2
/ (12-1) =
124.02

f) standard deviation =
√
1364.22/11 = √124.02 =
11.14
g) coefficient of variation = 11.14/16.75 x 100 =
66.5%
h) Q1 = 10, Q3 = 19, IQR = 19-10 =
9
i) The measure of central tendency that would be most appropriate for describing the data would be median
since the set of data has such a large outlier, 49.
Application 3
Krieser et al. (A-17) examined glomerular filtration rate (GFR) in pediatric renal transplant recipients. GFR is an
important parameter of renal function assessed in renal transplant recipients. The following are measurements
from 19 subjects of GFR measured with diethylenetriamine pentacetic acid. (Note: some subjects were
measured more than once.)
18
42
21
43
21
43
23
48
27
48
27
51
30
55
32
58
32
60
32
62
36
67
37
68
41
88
42
63
Compute (a) the mean, (b) the median, (c) the variance, (d) the standard deviation, (e) the coefficient of
variation. (f) Select the measure of central tendency that you think would be most appropriate for describing the
data. (g) What percentage
of the measurements is within one standard deviation of the mean? Two standard
deviations of the mean? Three standard deviations of the mean?
18, 21, 21, 23, 27, 27, 30, 32, 32, 32, 36, 37, 41, 42, 42, 43, 43, 48, 48, 51, 55, 58, 60, 62, 63, 67, 68, 88
a) mean = 1215/28 =
43.39
b) the median is
42
c) variance = (18 - 43.39)
2
+ (21 - 43.39)
2
+ (21 - 43.39)
2
+ ... + (67 - 43.39)
2
+ (68 - 43.39)
2
+ (88 -
43.39)
2
=
291.95
28 - 1
d) standard deviation =
√
291.95
=
17.09
e) coefficient of variation = 17.09/43.39 x 100% =
39.4%
f) The measure of central tendency that would be most appropriate for describing the data would be the
median.
g) percent of measurements within one standard deviation of the mean: 68%
mean
±
1
standarddeviation

43.93 + 17.09 = 62.01
43.94 - 17.09 = 26.84
between (26.84, 62.01)
percent of measurements within two standard deviations of the mean: 96.4%
mean
±
2
standard deviation
43.93 + (17.09 + 17.09 )= 78.11
43.94 - (17.09 - 17.09) = 9.76
between (9.76, 78.11)
percent of measurements withing three standard deviations of the mean: 99.6%
43.93 + 17.09 + 17.09 + 17.09 = 95.2
43.94 - 17.09 - 17.09 - 17.09= -7.33
(28/28) · 100 = 100%
between (-7.33, 95.2)
Application 4
Spivack (A-18) investigated the severity of disease associated with C. difficile in pediatric inpatients. One of the
variables they examined was number of days patients experienced diarrhea. The data for the 22 subjects in the
study appear below.
3
11
3
4
14
2
4
5
3
11
2
2
3
2
1
1
7
2
1
1
3
2
Compute (a) the mean, (b) the median, (c) the variance, (d) the standard deviation, (e) the coefficient of
variation. (f) Select the measure of central tendency that you think would be most appropriate for describing the
data. (g) What percentage
of the measurements is within one standard deviation of the mean? Two standard
deviations of the mean? Three standard deviations of the mean?
1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 7, 11, 11, 14
a) mean = 87/22 =
3.95
b) median =
3
c) variance =
(
(
3
−
3.95
)
2
+
(
11
−
3.95
)
2
+
(
3
−
3.95
)
2
+
(
4
−
3.95
)
2
+
(
14
−
3.95
)
2
+
(
2
−
3.95
)
2
+
(
4
−
3.95
)
2
+
(
5
−
3.95
)
2
+
(
3
−
3.95
)
2
+
(
11
−