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[latexpage]
At first, we sample $f(x)$ in the $N$ ($N$ is odd) equidistant points around $x^*$:

\[

f_k = f(x_k),\: x_k = x^*+kh,\: k=-\frac{N-1}{2},\dots,\frac{N-1}{2}
\]

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Not always right but...... Better than guessing, right?

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Science of Uncertainty
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from data
Technology of extracting information
from data
from samples and populations
Descriptive Statistics
Involve methods of organizing, picturing and summarizing information
from samples and populations
from a sample to draw conclusions about the population
Inferential Statistics
involves methods of using information
from a sample to draw conclusions about the population

Population ParametersSample Statistics

A population is a group of peple or objects
with a common theme
When every member of the group is considered
It is a population
A small portion of the population
is a sample
Can be a representative sample
or a biased sample
Data from every individual
is available in population data
Entire population
Census
Sample data is only available from
some of the individuals in the population

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2025