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STAT E50  Introduction to Statistics
The Normal Model
1. Researchers have investigated lead absorption in children of parents who worked in
a factory where lead is used to make batteries.
Shown below are the levels of lead in
the children’s blood (in
μ
g/dl of whole blood):
38
23
41
18
37
36
23
62
31
34
24
14
21
17
16
20
15
10
45
39
22
35
49
48
44
35
43
39
34
13
73
25
27
Source:
D. Morton, et al., “Lead Absorption in Children of Employees in a LeadRelated Industry,”
American Journal of Epidemiology
155 (1982).
30
20
10
0
10
20
30
40
50
60
0
5
minus 30
Frequency
a) Construct the histogram, using classes of 10  20, 20  30, etc:
Page 1
0 1
02
03
04
05
06
07
08
09
0
0
5
lead level
b) What would the data look like if we
shift
the data by subtracting 30 from each value?
What happens to center of the data?
What happens to the spread?
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0
0
5
10
div by 15
Frequency
c)
What would the data look like if we
rescale
the data by dividing each of the original
values by 15?
What happens to center of the data?
What happens to the spread?
2. Here are the descriptive statistics for the original data and the shifted data:
Descriptive Statistics: lead level
Variable
N
Mean
SE Mean
StDev
Minimum
Q1
Median
Q3
Maximum
lead level
33
31.85
2.51
14.41
10.00
20.50
34.00
40.00
73.00
Descriptive Statistics: minus 30
Variable
N
Mean
SE Mean
StDev
Minimum
Q1
Median
Q3
Maximum
minus 30
33
1.85
2.51
14.41
20.00
9.50
4.00
10.00
43.00
a) Which results changed when the data was shifted?
By how much?
b) Which results did not change?
Page 2
Page 3
3. Here are the descriptive statistics for the original data and the rescaled data:
Descriptive Statistics: lead level
Variable
N
Mean
SE Mean
StDev
Minimum
Q1
Median
Q3
Maximum
lead level
33
31.85
2.51
14.41
10.00
20.50
34.00
40.00
73.00
Descriptive Statistics: div by 15
Variable
N
Mean
SE Mean
StDev
Minimum
Q1
Median
Q3
Maximum
div by 15
33
2.123
0.167
0.960
0.667
1.367
2.267
2.667
4.867
a) Which results changed when the data was rescaled?
By how much?
b) Which results did not change?
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4. Here are the results when the data was shifted by subtracting the mean, and when
the data was rescaled by dividing by the standard deviation:
Descriptive Statistics: lead level
Variable
N
Mean
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This note was uploaded on 05/20/2008 for the course STAT 50 taught by Professor Weinstein during the Spring '08 term at Harvard.
 Spring '08
 WEINSTEIN
 Statistics

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