Week 1: Summary Statistics and Box Plots
ChE, BioE, EnvE 213
Prof. Milo Koretsky
I. Measures of Central Tendency
A. Mean (
x
).
Measure of
location
or central tendency.
Arithmetic mean is obtained by
adding up all the
samples
and dividing by the number of samples:
x
=
x
i
i
!
n
Also called the average.
B. Median.
Measure of
location
or central tendency.
Middle value in a set of data
which is arranged by value. If there is an even number of
samples
, the median is
the average of the two middle ones.
C. Mode.
Observation that occurs most frequently in a set of data. There may be more
than one mode in a frequency distribution, e.g., bimodal.
II. Measures of Dispersion
Standard Deviation of the sample
(s)
.
A descriptor of the dispersion or
variation
within a
sample.
Mathematically it is the square root of the average squared
deviation of the data about the mean.
s
=
x
i
!
x
(
)
2
i
"
n
!
1
Range
(
R
)
.
A descriptor of the dispersion or
variation
within a
sample.
Difference
between the largest (in value) and smallest member of the data set:
R
=
x
max
!
x
min
III. Box Plots
Box plots are useful graphical devices to compare and display sample statistical data. There are
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 Winter '08
 Staff
 Standard Deviation, Prof. Milo Koretsky

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