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discrete data

box and whisker plot

Histogram

bar graph

A number is recorded for a discrete numerical variable.

Visual display of median, UQ,LQ, minimum value and maximum va…

Bars are joined together

Bars are separated

discrete data

A number is recorded for a discrete numerical variable.

box and whisker plot

Visual display of median, UQ,LQ, minimum value and maximum va…

Step 1

Step 2

Step 3

Step 4

A real world problem is observed.

A mathematical model is devised.

The mathematical model is used to make predictions about the…

Experimental data is collected from the real world.

Step 1

A real world problem is observed.

Step 2

A mathematical model is devised.

discrete data

box and whisker plot

Histogram

bar graph

A number is recorded for a discrete numerical variable.

Visual display of median, UQ,LQ, minimum value and maximum va…

Bars are joined together

Bars are separated

discrete data

A number is recorded for a discrete numerical variable.

box and whisker plot

Visual display of median, UQ,LQ, minimum value and maximum va…

Graphing

y = mx + c

mx

X and Y Intercepts

y/x = mx + c

y= Y-Intercept... x= X-intercept... m= Gradient... c= Constant

Gradient- Rate of change, unit cost of money

X-Intercept is when y=0... Y-Intercept is when x=0... Coordinates;…

Graphing

y/x = mx + c

y = mx + c

y= Y-Intercept... x= X-intercept... m= Gradient... c= Constant

Bernoulli

P probability of success

0,1,2...

Geometric pmf

Discrete distribution to model things like a coin toss or a w…

Parameters of bernoulli

Range of geometric

Px(k)=p(1-p)^k

Bernoulli

Discrete distribution to model things like a coin toss or a w…

P probability of success

Parameters of bernoulli

outliers

tally

distribution

mode

Numbers that are much greater or much less than the other num…

a method of counting where a single line represents one item…

the way data is spread out across a range

a measure of center-the value that occurs most frequently in…

outliers

Numbers that are much greater or much less than the other num…

tally

a method of counting where a single line represents one item…

How is the standard deviation found?

Formulas for Coefficient Variation?

Population/Deviation Symbol?

What is chebychevs Theorem?

Its the square root of standard deviation

Population δ÷µ×100% Sample S/x×100%

δ=Population Sx= Sample

1-1/k²

How is the standard deviation found?

Its the square root of standard deviation

Formulas for Coefficient Variation?

Population δ÷µ×100% Sample S/x×100%

average

class

class interval

data

a representative value; mode, mean and median are examples

a group of numbers or measurements

the width of a group or interval in a grouped frequency table

facts, numbers or measurements

average

a representative value; mode, mean and median are examples

class

a group of numbers or measurements

What is the domain for the following s…

What is the range of the following set…

In a function, what do you call the x…

What form is this line equation in: y=…

{0,2,3,4}

{-2,-1,2,6}

zeros

slope-intercept form

What is the domain for the following s…

{0,2,3,4}

What is the range of the following set…

{-2,-1,2,6}

Define the term 'Experiment'.

Define the term 'Event'.

Define the term 'Sample Space'.

Define the term 'Probability of an Eve…

A repeatable process that gives rise to a number of outcomes.

A collection of one or more outcomes.

A set of all possible outcomes of an experiment.

Number of outcomes / total possible outcomes.

Define the term 'Experiment'.

A repeatable process that gives rise to a number of outcomes.

Define the term 'Event'.

A collection of one or more outcomes.

Population

Census

Sample

Survey

Defined collection of individuals or objects about which we w…

Collection of information from the whole population.

Subset of the population which we want to collect information…

The collection of information from a sample.

Population

Defined collection of individuals or objects about which we w…

Census

Collection of information from the whole population.

Discrete Random Variable

Continuous Random Variable

Population Parameter

Estimator

Random variables whose values are finite or countably finite

Variable whose values are not finite or are countably infinite

A numerical value describing a characteristic of a population

Sample statistic that can be applied to the values in any sam…

Discrete Random Variable

Random variables whose values are finite or countably finite

Continuous Random Variable

Variable whose values are not finite or are countably infinite

census

data

discrete data

continuous data

A survey of a whole population.

The scores or information collected.

Data that is a measure of something restricted to certain lim…

Data that is a measure of something that can take on any valu…

census

A survey of a whole population.

data

The scores or information collected.

When using statistical term in a narra…

Statistical and Mathematical copy can…

3 or less numbers

20 or more numbers

Use the term not the symbol EX: ... *The medians were not ... *the…

tables figures and graphics

use a sentence

a graph is more useful than a table

When using statistical term in a narra…

Use the term not the symbol EX: ... *The medians were not ... *the…

Statistical and Mathematical copy can…

tables figures and graphics

Error Bars

Mean

Standard Deviation

T-Test

show the standard deviation (range) of data... Is the data signi…

average

indicates how far the data is spread from the mean

allows us to compare the means of two populations when ... 1) th…

Error Bars

show the standard deviation (range) of data... Is the data signi…

Mean

average

Expression

Equation

Term

Arithmetic operation

A mathematical statement that consists of one or more numbers…

A mathematical statement that says two expressions are equal.

A component of an expression and is analogous to a word in a…

Ways of meaningfully manipulating numbers or variables.

Expression

A mathematical statement that consists of one or more numbers…

Equation

A mathematical statement that says two expressions are equal.

What are the parameters for a binomial…

What are the parameters for a normal d…

What is the binomial equation?

What is the mean of a binomial distrib…

X~B(n,p)... (n = number, p = probability)

X~N(µ, σ²)... (µ = population mean, σ² = variance)

µ = np

What are the parameters for a binomial…

X~B(n,p)... (n = number, p = probability)

What are the parameters for a normal d…

X~N(µ, σ²)... (µ = population mean, σ² = variance)

cardinality

common

disjoint

proper subset

Is the number of elements in that set. You use the symbol n(A…

When an element of a set belongs to two or more sets, the set…

Mutually exclusive sets.

If every element in set B is in set A and the two sets are no…

cardinality

Is the number of elements in that set. You use the symbol n(A…

common

When an element of a set belongs to two or more sets, the set…

abductive reasoning

AND

axioms

case proof

Usually starts with an incomplete set of observations and adv…

Conjunction.

Self-evident beginnings.

Shows a statement is true by showing all the cases are true.

abductive reasoning

Usually starts with an incomplete set of observations and adv…

AND

Conjunction.

Alternative Hypothesis

Asymptotic Normality

Biased Estimator

Central Limit Theorem (CLT)

The hypothesis stating what the researcher is seeking evidenc…

the sampling distribution of a properly normalized estimator…

any sample statistic obtained from a randomly selected sample…

The theory that, as sample size increases, the distribution o…

Alternative Hypothesis

The hypothesis stating what the researcher is seeking evidenc…

Asymptotic Normality

the sampling distribution of a properly normalized estimator…

Tables

Quantitative Data

Categorical Data

Bar Graphs

A convenient way to present data clearly. The data is present…

Data having to do with quantities as the items being measured.

Data having to do with the categories as the items being meas…

Convey information using rectangular bars that do not touch e…

Tables

A convenient way to present data clearly. The data is present…

Quantitative Data

Data having to do with quantities as the items being measured.

Population

Census

Sample

Survey

Defined collection of individuals or objects about which we w…

Collection of information from the whole population.

Subset of the population which we want to collect information…

The collection of information from a sample.

Population

Defined collection of individuals or objects about which we w…

Census

Collection of information from the whole population.

What are the parameters for a binomial…

What are the parameters for a normal d…

What is the binomial equation?

What is the mean of a binomial distrib…

X~B(n,p)... (n = number, p = probability)

X~N(µ, σ²)... (µ = population mean, σ² = variance)

µ = np

What are the parameters for a binomial…

X~B(n,p)... (n = number, p = probability)

What are the parameters for a normal d…

X~N(µ, σ²)... (µ = population mean, σ² = variance)

abscissa

amphicrytic

antilogarithm

augend

\ab-ˈsi-sə, əb-\... the horizontal coordinate of a point in a pl…

\¦amfə¦sərtik\... having both sides convex — used of angles betw…

\ˌan-ˌtī-ˈlȯ-gə-ˌri-thəm, ˌan-ti-, -ˈlä-\... the number corres…

\ˈȯˌjend\... : the quantity to which an addend is added

abscissa

\ab-ˈsi-sə, əb-\... the horizontal coordinate of a point in a pl…

amphicrytic

\¦amfə¦sərtik\... having both sides convex — used of angles betw…

Population

Census

Sample

Survey

Is the complete group that statistical information would rela…

Obtains information from the whole population

Part of the population

Obtains data from a sample

Population

Is the complete group that statistical information would rela…

Census

Obtains information from the whole population

Quantitative Data

Categorical Data

Pie Chart

Line Graphs

Data having to do with quantities as the items being measured.

Data having to do with the categories as the items being meas…

Displays data as wedges in a circular shape. Also called circ…

Plot one variable against another. Similar to linear equation…

Quantitative Data

Data having to do with quantities as the items being measured.

Categorical Data

Data having to do with the categories as the items being meas…

Scientific Knowledge

Scientific Method ... (5 general steps)

Important Reminders... Scientific Method

Scientific Fact

- The sum of all scientific inquiries for truths about the na…

- identifying a problem or posing a question... - hypotheses or…

- use acceptable experimentation techniques... - objectivity... - p…

Objective & verifiable observation... ex: An object falls.

Scientific Knowledge

- The sum of all scientific inquiries for truths about the na…

Scientific Method ... (5 general steps)

- identifying a problem or posing a question... - hypotheses or…

Competency 005 (Probability and Statis…

Statistics

Statistical Methods

Probability

The teacher understands concepts... related to probability and s…

The science or study of data.

Methods used to describe, analyze, evaluate, and interpret in…

Gives a way to measure uncertainty and is essential for under…

Competency 005 (Probability and Statis…

The teacher understands concepts... related to probability and s…

Statistics

The science or study of data.

law

scientific theory

model

Anton van Leeuwenhoek (d. 1723)

an explanation of events that always lead to the same outcome

a greater body of accepted knowledge, principles, or relation…

-used to explain something on a smaller scale or in simpler t…

-used homemade magnifying glasses to become the first person…

law

an explanation of events that always lead to the same outcome

scientific theory

a greater body of accepted knowledge, principles, or relation…

What are the measures of central tende…

How does one find the mean?

How does one find the mode?

How does one find the median?

They are the mean, median, mode, and range?

The mean (also known as the arithmetic mean) of a set of data…

The mode of a set of data is the value repeated most often. I…

The median of a set of data is the value in the middle so tha…

What are the measures of central tende…

They are the mean, median, mode, and range?

How does one find the mean?

The mean (also known as the arithmetic mean) of a set of data…

Tables

Quantitative Data

Categorical Data

Bar Graphs

A convenient way to present data clearly. The data is present…

Data having to do with quantities as the items being measured.

Data having to do with the categories as the items being meas…

Convey information using rectangular bars that do not touch e…

Tables

A convenient way to present data clearly. The data is present…

Quantitative Data

Data having to do with quantities as the items being measured.

Advantages mathematical model

Disadvantages

1

2

Quick... Easy... Improve our understanding of the real world... enable…

only a partial description ... only work for a restricted range…

a real world problem is observed

a mathematical model is devised

Advantages mathematical model

Quick... Easy... Improve our understanding of the real world... enable…

Disadvantages

only a partial description ... only work for a restricted range…

Statistics

Range

Mean

Median

The science or study of data. Describe, analyze, evaluate, &…

Difference between highest & lowest number.

Average of the data values.

The middle value of all the numbers.

Statistics

The science or study of data. Describe, analyze, evaluate, &…

Range

Difference between highest & lowest number.

conditions for binomial

Highest value/point

population

sample

fixed number of trials... Two possible outcomes... Trials are Indep…

mode of continuous random variable

collection of individual items

selection of individual items from a population

conditions for binomial

fixed number of trials... Two possible outcomes... Trials are Indep…

Highest value/point

mode of continuous random variable

Null hypothesis

Alternative hypothesis

Significance level

Critical region

The condition assumed true under the condition of a hypothesi…

Believed to be correct if null is not true.

Probability of type I error (false positive) - Incorrectly re…

Range of values for test statistic where alt is more probable…

Null hypothesis

The condition assumed true under the condition of a hypothesi…

Alternative hypothesis

Believed to be correct if null is not true.

The Basic Principle of Counting

Tree Diagram

Permutations

Circular Permutations

If an operation consists of two steps, of which the first can…

Listing of all the possibilities within a sample space

A distinct arrangement of n different elements of a set

Permutations that occur when overs are arranged in a circle.

The Basic Principle of Counting

If an operation consists of two steps, of which the first can…

Tree Diagram

Listing of all the possibilities within a sample space

Net

Congruent Figures

Perimeter

Area

A two-dimensional figure that can be cut out and folded up to…

figures that have the same size and shape

the sum of lengths of the sides of a figure

the number of square units covered by the figure

Net

A two-dimensional figure that can be cut out and folded up to…

Congruent Figures

figures that have the same size and shape

Reasons for models

Advantages

Disadvantages

1st Step

-simplification... -used to make predictions of real world probl…

-quick and easy... -cheap and efficient models... -simplifies compl…

-Only gives a partial description of a real situation... -only w…

Real world problem found

Reasons for models

-simplification... -used to make predictions of real world probl…

Advantages

-quick and easy... -cheap and efficient models... -simplifies compl…

primary data

what does the collection of primary da…

secondary data

statistical tests

info observed or collected directly from fist hand. experienc…

designing the study, gaining ethical approval, piloting the s…

data info collected for a purpose other than the current one.…

designed to work out the probability of whether a particular…

primary data

info observed or collected directly from fist hand. experienc…

what does the collection of primary da…

designing the study, gaining ethical approval, piloting the s…

What does a correlation illustrate?

What is a positive correlation?

What is a negative correlation?

What is a zero correlation?

The strength and direction between 2 or more co variables

As one co variable increases, so does the other

As one co variable increases, the other decreases

When there is no relationship between the co-variables

What does a correlation illustrate?

The strength and direction between 2 or more co variables

What is a positive correlation?

As one co variable increases, so does the other

Bernoulli Random Variable

Indicator Random Variable

Binomial Distribution

Geometric Distribution

A Bernoulli random variable takes on only two values: 0 and 1…

If A is an event, then the indicator random variable, Ia, tak…

The probability of a particular sequence of k successes multi…

Is constructed from an infinite sequence of independent Berno…

Bernoulli Random Variable

A Bernoulli random variable takes on only two values: 0 and 1…

Indicator Random Variable

If A is an event, then the indicator random variable, Ia, tak…

Ω = {ccc,ccs,csc,css,scc,scs,ssc,sss}

A = {sss,ssc,scc,scs}... B = {sss,scs,ccs…

C = A∪B

C = A∩B

Sample Space - set of all possible outcomes of an experiment

Event - a subset of interest in the sample space... A = always s…

Union of two events - subset where either, or both occur.... C =…

Intersection of two events - subset where both A and B occur…

Ω = {ccc,ccs,csc,css,scc,scs,ssc,sss}

Sample Space - set of all possible outcomes of an experiment

A = {sss,ssc,scc,scs}... B = {sss,scs,ccs…

Event - a subset of interest in the sample space... A = always s…

P(A) = n/N = number of ways A can occu…

The multiplication principle

The extended multiplication principle

Combination

The probability of an event is equal to the total number of e…

If one experiment has m outcomes and another experiment has n…

If there are p experiments and the ﬁrst has n1 possible outco…

Unordered grouping of object. Their position does not matter,…

P(A) = n/N = number of ways A can occu…

The probability of an event is equal to the total number of e…

The multiplication principle

If one experiment has m outcomes and another experiment has n…

Arcsine Transform

Average Deviation

Bimodal Frequency Distribution

Central Tendency

When the data are proportions it is usually recommended that…

The average deviation, or the mean absolute deviation, measur…

A bimodal distribution is like a combination of two normal di…

In statistics, a central tendency (or more commonly, a measur…

Arcsine Transform

When the data are proportions it is usually recommended that…

Average Deviation

The average deviation, or the mean absolute deviation, measur…

Arcsine Transform

Average Deviation

Bimodal Frequency Distribution

Central Tendency

When the data are proportions it is usually recommended that…

the mean absolute deviation that measures the absolute differ…

A combination of two normal distributions -there are two peak…

In statistics, a __________________ (or more commonly, a meas…

Arcsine Transform

When the data are proportions it is usually recommended that…

Average Deviation

the mean absolute deviation that measures the absolute differ…