L7-12

mathematical logic

• or symbolic logic

• branch of mathematics that studies logic

formal reasoning

science or study of how to evaluate arguments & reasoning

aristotle

father of logic

statement

declarative statement which is either true or false

propositional variable

variable which used to represent a statement

conjunction

and (^)

disjunction

or (v)

negation

not (~)

implication or conditional

if then (➡️)

biconditional

if and only if (⬅➡)

exclusive or

XOR (⊕)

p^q = same, then false

p^q = opposite, then true

predicate

• or open statements

• statement whose truth depends on the value of one or more variables

propositional function

a sentence P(x) becomes a statement only when variable x is given particular value

universal quantifiers

reversed A symbol

a logical statement that applies to all objects in a collection

existential quantifiers

applies to some objects in a collection

mathematical knowledge

often expressed with quantified statements

statistics

branch of mathematics that deal with collecting, classifying, presenting, analyzing, and interpreting data

descriptive statistics

includes collection, classification, presentation, and description of numerical data

inferential statistics

refers to techniques of interpreting the values

population

denoted as N, collection, or set of individuals, objects or measurement whose properties are to be analyzed

sample

denoted as n, is a subset of a population

marginal error

probability of committing a mistake

confidence level

probability of getting the correct result

random sampling

also called lottery sampling or raffle sampling

systematic sampling

elements are numbered for identification and samples are selected at regular intervals

interval = N/n

stratified sampling

set of interests is divided into groups

convenience sampling

samples are those chosen to respond

purposive sampling

samples are chosen based on specific objective

categorical data

qualitative

numerical data

quantitative

discrete data

data expressed as counts

continuous data

data expressed as measurements

nominal data

values that represent discrete units and are used to label variables

ordinal data

values that represent discrete units and ordered units

interval data

represent ordered values that have the same difference

ratio data

represent ordered values that have the same difference and HAS AN ABSOLUTE ZERO VALUE

response variable

a characteristic of interest about each individual element (e.g personal details form)

datum

a value of response associated with one element of a population or sample

data

set of values collected from the response variable from each of the elements belonging to the sample

parameter

a numerical characteristic that describes the entire population

statistic

a numerical characteristic of a sample, also called “estimate”

central tendency

commonly referred to as average, is a single value that represents a data set

arithmetic mean

all values play an equal role

xbar for sample, mu for population

median

middle value in a dataset

x~

mode

the most frequent item in a set

x^