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math: add bias and types of data, expand descriptions

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@ -5,15 +5,54 @@ The course code for this page is **MHF4U7**.
## 4 - Statistics and probability
!!! note "Definition"
- **Statistics:** The techniques and procedures to analyse, interpret, display, and make decisions based on data.
- **Descriptive statistics:** The use of methods to organise, display, and describe data by using various charts and summary methods to reduce data to a manageable size.
- **Inferential statistics:** The use of samples to make judgements about a population.
- **Data set:** A collection of data with elements and observations, typically in the form of a table. It is similar to a map or dictionary in programming.
- **Element:** The name of an observation(s), similar to a key to a map/dictionary in programming.
- **Observation:** The collected data linked to an element, similar to a value to a map/dictionary in programming.
- **Raw data:** Data collected prior to processing or ranking.
- **Population**: A collection of all elements of interest within a data set.
- **Sample**: The selection of a few elements within a population to represent that population.
- **Raw data:** Data collected prior to processing or ranking.\
### Sampling
A good sample:
- represents the relevant features of the full population,
- is large enough so that it decently represents the full population,
- and is random.
The types of random sampling include:
- **Simple**: Choosing a sample completely randomly.
- **Convenience**: Choosing a sample based on ease of access to the data.
- **Systematic**: Choosing a random starting point, then choosing the rest of the sample at a consistent interval in a list.
- **Quota**: Choosing a sample whose members have specific characteristics.
- **Stratified**: Choosing a sample so that the proportion of specific characteristics matches that of the population.
??? example
- Simple: Using a random number generator to pick items from a list.
- Convenience: Asking the first 20 people met to answer a survey,
- Systematic: Rolling a die and getting a 6, so choosing the 6th element and every 10th element after that.
- Quota: Ensuring that all members of the sample all wear red jackets.
- Stratified: The population is 45% male and 55% female, so the proportion of the sample is also 45% male and 55% female.
### Types of data
!!! note "Definition"
- **Quantitative variable**: A variable that is numerical and can be sorted.
- **Discrete variable**: A quantitative variable that is countable.
- **Continuous variable**: A quantitative variable that can contain an infinite number of values between any two values.
- **Qualitative variable**: A variable that is not numerical and cannot be sorted.
- **Bias**: An unfair influence in data during the collection process, causing the data to be not truly representative of the population.
### Frequency distribution
A **frequency distribution** is a data set that lists ranges and the number of values in each range. It can be displayed using a frequency distribution table.
!!! note "Definition"
## Resources