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1
Introduction to Business Statistics
Lecture 2
Descriptive Statistics
II:
Numerical Methods
Example:
A large manufacturing company in Michigan has about 5000
assembly line workers. For training purposes, management needs to
know skill level of these workers. A sample of 296 workers has been
randomly selected and given an aptitude test with 25 multiple choice
questions. The 296 test scores have been arranged in ascending order.
What can we say about these 290 observations of scores?
Mean:
5777
.
19
296
5795
n
X
f
X
i
i
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Scores (
i
X
)
Frequency (
i
f
) Relative Frequency(%)
0
0.00
1
2
3
4
5
1
0.34
6
7
8
9
0.68
10
1.01
11
12
2.03
13
2.36
14
9
3.04
15
16
18
6.08
17
21
7.09
20
6.76
19
35
11.82
25
8.45
32
10.81
22
30
10.14
23
39
13.18
24
4.05
3
Scores
Frequency
24
21
18
15
12
9
6
40
30
20
10
0
Histogram of Scores
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20
2
20
20
2
score
149th
score
148th
n
observatio
ranked
th
2
1
Median
n
Explanation
:
Suppose we have 4 observations 1, 4, 6, 9. Then median
is at (4+1)/2 = 2.5
th
position – in the middle of
2
nd
and 3
rd
observations.
That is,
(4+6)/2 = 5
Mode:
The value in a data set that appears most frequently = 23.
20
5
25
Range
smallest
largest
X
X
First quartile:
n
observatio
ordered
th
4
1
1
n
Q
= 17
5
Explanation
:
If we have 8 observations 1, 1.5, 3.5, 5, 5.2, 7.5, 8, 10, then
1
Q
is at (8+1)/4=2.25
th
position, which is between 2
nd
and 3
rd
observations
and closer to the 2
.
In this case, we let
5
.
1
1
Q
, the 2
observation.
Third quartile:
n
observatio
ordered
th
4
)
1
(
3
3
n
Q
= 23
6
17
23
range
ile
Interquart
1
3
Q
Q
※
How would you describe the distribution of scores
?
Location Measures
of the frequency distribution of scores:
Mean, Median (resistance to outliers), Mode
Example
: Let data be 1, 4, 6, 9. If we change 9 to 1,000,000, what will
happen to the mean and median?
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Variability Measures
of the frequency distribution of scores:
Range, Interquartile range, Sample variance, Standard deviation
MAD (Mean Absolute Deviation)
n
X
X
X
X
X
X
n






MAD
2
1
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This note was uploaded on 11/23/2010 for the course BBA ISOM111 taught by Professor Hu during the Fall '08 term at HKUST.
 Fall '08
 HU
 Management

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