# SL Math - Analysis and Approaches - A

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.
    - **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

 - [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf)
 - [IB Math Analysis and Approaches Formula Booklet](/resources/g11/ib-math-data-booklet.pdf)
 - [Calculus and Vectors 12 Textbook](/resources/g11/calculus-vectors-textbook.pdf)
 - [Course Pack Unit 1: Descriptive Statistics](/resources/g11/s1cp1.pdf)