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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”