Population vs Sample

The population includes all objects of interest whereas the sample is only a portion of the population. Parameters are associated with populations and statistics with samples. Parameters are usually denoted using Greek letters (mu, sigma) while statistics are usually denoted using Roman letters (x, s).

There are several reasons why we don't work with populations. They are usually large, and it is often impossible to get data for every object we're studying. Sampling does not usually occur without cost, and the more items surveyed, the larger the cost.

We compute statistics, and use them to estimate parameters. The computation is the first part of the statistics course (Descriptive Statistics) and the estimation is the second part (Inferential Statistics)

Discrete vs Continuous

Discrete variables are usually obtained by counting. There are a finite or countable number of choices available with discrete data. You can't have 2.63 people in the room.

Continuous variables are usually obtained by measuring. Length, weight, and time are all examples of continuous variables. Since continuous variables are real numbers, we usually round them. This implies a boundary depending on the number of decimal places. For example: 64 is really anything 63.5 <= x < 64.5. Likewise, if there are two decimal places, then 64.03 is really anything 63.025 <= x < 63.035. Boundaries always have one more decimal place than the data and end in a 5.

Levels of Measurement

There are four levels of measurement: Nominal, Ordinal, Interval, and Ratio. These go from lowest level to highest level. Data is classified according to the highest level which it fits. Each additional level adds something the previous level didn't have.

Types of Sampling

There are five types of sampling: Random, Systematic, Convenience, Cluster, and Stratified.

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James Jones