BCOR 2200 Fall 2008
David M. Gross Ph. D.
Statistics and Normal Distribution Review
A way to estimate future events is to examine past events and assume that the pattern will be
repeated in the future.
We can use this technique to estimate possible ranges in annual returns
for investment classes.
The first step is to collect a sample of returns over a large number of years, then calculate the
mean and standard deviation of the sample of returns.
The mean and standard deviation of the
actual population are estimated using the sample.
•
Mean =
μ
≈
X
= (X
1
+ X
1
+ … + X
N
) / N
•
Standard Dev. =
σ
≈ S
X
={[(X
1
–
X
)
2
+ (X
2
–
X
)
2
+ … + (X
N
–
X
)
2
] / (N1)}
1/2
Note: Divide by N1 to calculate the standard deviation since we are using a "sample" of
past interest rate changes and not ALL past interest rate changes, in which case we would
divide by N. Dividing by N1 produces a larger standard deviation. When we use S
X
to
estimate probable future interest rate changes, we will get a larger estimate.
Other Statistics:
•
Median = value which divides the sample.
There are just as many observations greater than
the median as less than the median
•
Mode = value with the most observations.
For reasons of calculation simplicity, we will assume that interest rate changes are NORMALLY
distributed. This means that the frequency and probability of observations can be described by
what is often called the "bell shaped” curve. One of the reasons for making this "Normality
assumption” is that we know certain things about the area under the Normal curve, and can
therefore make statistical inferences by assuming normality.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 TOMNELSON
 Normal Distribution, Standard Deviation, 5%, 90%, Normal Distribution Review

Click to edit the document details