25. Text: 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} 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 |
|---|---|---|
| X | A random variable | Time spent on website |
| x_1 | First observed value of the random variable X | 15 mins |
| \sum\limits_{i=1}^nx_i | Sum values beginning at the first observation and ending at the last | 5 + 2 + … + 3 |
| \frac{1}{n}\sum\limits_{i=1}^nx_i | Sum values beginning at the first observation and ending at the last and divide by the number of observations (the mean) | (5 + 2 + 3)/3 |
| \bar{x} | Exactly the same as the above - the mean of our data. | (5 + 2 + 3)/3 |
Notation for the Mean
We took our notation even farther 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}
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!