1.7 – Notation
Finally, it is important to start discussing the different symbols we will use in this book. Learning statistics is a lot like learning a language. You have already started to learn some of that language with the different concepts and phrases we have discussed thus far. And the quicker you memorize those concepts and become “fluent” with them, the easier your learning will go.
To aid that learning, it can be helpful to expose you to some of the types of symbols and notations we will use in this book. These symbols are short-hand for many of the concepts will run into as we progress, and there are some patterns in terms of the choice of symbols.
One of the most important distinctions we will need to make is whether a concept comes from the population or from the sample. You will find that in many cases we will use upper-case letters to denote concepts that come from the population, while we will use lower-case letters to denote concepts that come from the sample:
| Population (Upper-Case) |
Sample (Lower-Case) |
|
| Individual’s Score | X | x |
| Number of Individuals in the Group |
N | n |
You can see above that the letter “x” is used to describe an individual’s measurement or score, and whether the individual score came from the population or sample is depicted by being upper or lower case. Likewise, the letter “n” is used to describe the total number of people that we measured, and whether we are talking about the total number of people in our population or our sample depends on the case. So if we saw, “X = 3,” we would know that an individual from the population scored 3 on whatever we were measuring.
Another way that we will distinguish between populations and samples is by using Greek letters when we are denoting a concept from the population, and Roman letters when we are denoting a concept from the sample:
| Population (Greek) |
Sample (Roman) |
|
| Mean (average) | μ | M |
| Standard Deviation | σ | s |
The symbol for the population mean, 𝜇, is the upper-case Greek letter M or “mu” (pronounced, “myoo”). The symbol for the sample mean is the Roman letter M. Likewise, the symbol for the population standard deviation, 𝜎, is the lower-case Greek letter s or “sigma,” while the symbol for sample standard deviation is the lower-case Roman letter s.
You may not know what a mean or standard deviation is yet (we will cover them in Chapter 3), but think of this as priming you for the system that will be used for the symbols. You will find that your learning will go much smoother if you memorize what each symbol means quickly.
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