math: add bias and types of data, expand descriptions

docs/mhf4u7.md

@@ -5,16 +5,55 @@ 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