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Summary On Notation

Notation is a crucial tool for conveying mathematical concepts, with capital letters representing random variables and lowercase letters with subscripts denoting specific observations. The document explains how to use notation for random variables, including examples for summation and calculating the mean. Understanding notation is essential for both mathematical communication and programming, laying the groundwork for future data analysis.

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5 views2 pages

Summary On Notation

Notation is a crucial tool for conveying mathematical concepts, with capital letters representing random variables and lowercase letters with subscripts denoting specific observations. The document explains how to use notation for random variables, including examples for summation and calculating the mean. Understanding notation is essential for both mathematical communication and programming, laying the groundwork for future data analysis.

Uploaded by

Kassa getawey
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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Summary on Notation

Notation Recap
Notation is an essential tool for communicating mathematical ideas. We have
introduced the fundamentals of notation in this lesson that will allow you to
read, write, and communicate with others using your new skills!

Notation and Random Variables


As a quick recap, capital letters signify random variables. When we look
at individual instances of a particular random variable, we identify these
as lowercase letters with subscripts attach themselves to each specific
observation.

For example, we might have X be the amount of time an individual spends on


our website. Our first visitor arrives and spends 10 minutes on our website,
and we would say \bold{x_1}x1 is 10 minutes.

We might imagine the random variables as columns in our dataset, while a


particular value would be notated with the lower case letters.

Notation English Example


Time spent
X A random variable
on website
First observed value of the random
x_1x1 variable X
15 mins
Sum values beginning at the first 5 + 2 + ... +
\sum\limits_{i=1}^nx_i i=1∑nxi observation and ending at the last 3
Sum values beginning at the first
\frac{1}{n}\sum\ observation and ending at the last (5 + 2 +
limits_{i=1}^nx_in1i=1∑nxi and divide by the number of 3)/3
observations (the mean)
Exactly the same as the above - the (5 + 2 +
\bar{x}xˉ mean of our data. 3)/3

Notation for the Mean


We took our notation even further by introducing the notation for summation \
sum∑. Using this we were able to calculate the mean as:

\bold{\frac{1}{n}\sum\limits_{i=1}^nx_i} n1i=1∑nxi

In the next section, you will see this notation used to assist in your
understanding of calculating various measures of spread. Notation can take
time to fully grasp. Understanding notation not only helps in conveying
mathematical ideas but also in writing computer programs - if you decide you
want to learn that too! Soon you will analyze data using spreadsheets. When
that happens, many of these operations will be hidden by the functions you
will be using. But until we get to spreadsheets, it is important to understand
how mathematical ideas are commonly communicated. This isn't easy, but
you can do it!

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