QMM240
Descriptive Statistics - I
Statistical Methods for Business I - Lecture Notes
Page: 1
Descriptive Statistics I
Characteristic
Interpretation
Central tendency
Data concentration? Typical or
"middle values?
Dispersion
How variable? Unusual values?
Shape
Symmetric? Skewed? Flat? Peaked?
Multimodal?
Example:
PERatios.xls
I)
Measures of Central Tendency:
Can use dot plot, histogram and/or several statistics
1) Mean (or Average)
The average of the sample
n
X
X
n
i
i
1
The mean of the population
N
X
N
i
i
x
1
Pro
Con
Familiar
Sensitive to outliers
Uses all the data

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QMM240
Descriptive Statistics - I
Statistical Methods for Business I - Lecture Notes
Page: 2
Obs #
Value
1
0.2
2
0.1
3
4.8
4
2.7
5
25.6
Average
6.68
Notice how the mean falls
between data point 5 and the
rest of the data. No values
are very "close" to the mean.
Example:
JDPowers.xls
Use
=Average(
data range
)
in Excel
1
87
93
98
...
159
164
173
4639
125.38
37
37
n
i
i
x
x
n
Characteristics of the Mean
1
(
)
0
n
i
i
x
x
Sum of differences of
each data point from the
mean is ALWAYS = 0
1
(
)
n
i
i
x
x
= (42
–
65) + (60
–
65) + (70
–
65) + (75
–
65) + (78
–
65)
= (-23) + (-5) + (5) + (10) + (13) = -28 + 28 = 0
Mean is like a fulcrum. The
data is balanced at the mean.