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Probability
The likelihood of an event occurring
Impossible
0% Probability
Unlikely
1% to 39% Probability
As Likely as Unlikely
40% to 60% Probability
Likely
61% to 99% Probability
Certain
100% Probability
Theoretical Probability
(Classical Probability) Computed by dividing the number of outcomes where the desired event occurs by the total number of outcomes. *Note that the outcomes must be equally likely
Empirical Probability
(Experimental Probability) A probability that is calculated by conducting trials or experiments and recording the results
Probability Model
A mathematical representation of a random phenomenon
Experiment
In probability, an experiment or trial is a procedure that can be done repeatedly, that has a well defined set of possible outcomes
Outcome
A single possible result of an experiment
Sample Space
The set of possible outcomes for an experiment *All the different outcomes
Event
An outcome or set of outcomes, whose chance of occurrence can be represented with a probability
Fair
In probability, this refers to a situation in which all outcomes are equally likely. It is the opposite of biased
Sample Size
In probability, this refers to the number of possible outcomes in a trial or experiment *The number of different outcomes
Fundamental Counting Principle
States that for one event with n outcomes and another, independent event with m outcomes, the sample size is n X m
*Used to find the total number of possible outcomes
Permutation
Order matters. The number of unique ordered possibilities for a certain situation
Sampling With Replacement
When an outcome can be selected more than once
Sampling Without Replacement
When an outcome cannot be selected more than once
Combination
Order does not matter. The number of unique unordered possibilities for a certain situation. *All of these problems will be without replacement
Mutually Exclusive
Two events that CANNOT occur at the same time
Intersection (AND)
Since the two events are mutually exclusive, it has no common intersection point. The probability of occurrence of such an event will be zero
Union (OR)
Addition rule of probability
Independent Events
Events where the occurrence of one does NOT affect the probability that the other event(s) will occur
Dependent Events
Events connected such that one event's occurrence IMPACTS the likelihood that the other event will take place
Independent Unions
The probability that either one or the other or both will occur
Independent Intersections
The probability that both event A and event B will occur
Data
A set of values of qualitative or quantitative variables; pieces of data are individual pieces of info
Categorical
This type of data consists of data values that can be sorted into groups or categories. Also called Qualitative Data
Quantitative
Numeric information based on some quantity or measured value. Also called Numerical Data
Categorical Graphs
- Pie Chart
- Bar Chart
- Pictograph
- Venn Diagram
Quantitative Graphs
- Line Graph
- Stem-and-Leaf Plot
- Box Plot
- Histogram
Intervals
A set of numbers between two specified values
Maximum
The greatest possible value available in a data set
Minimum
The lowest value available in a data set
Lower Quartile
A lower or left rectangle which shows the dividing point between the lower 25% of values and middle 25% of values
Upper Quartile
An upper or right rectangle which shows the dividing point between the middle value and the upper 75% of values
Five-Number Summary
The minimum, first quartile, median, third quartile, and maximum. Quartile and maximum. A box plot represents the five numbers in this summary
Scatterplot
A graph that uses dots on a coordinate plane to show the relationship between two quantitative variables
Correlation
An observed relationship between two quantitative variables, but not necessarily a casual relationship
Association
A pattern or relationship between two variables
Determining if Graphs are Skewed-Right or Left
Look for the highest point and determine left or right from there
U-Shaped
Occurs when symmetric distribution has a valley instead of a peak
Uniform
Gas similar frequency across its range
Spread (Range)
The difference between the minimum and maximum value in a given measurable set
Outlier
An observation point (number) that is significantly distant from the other observations in the data set
Causation
The relationship of cause and effect. *Can ONLY be determined from an experiment
Casual Relationship
A relationship between two variables that can be classified as cause-and-effect
Control Group
A group that does not undergo any change that can be compared to a treatment group
Regression Analysis
A statistical analysis tool that quantifies the relationship between a response variable and one or more explanatory variables
Explanatory Variable
The variable that may be the cause of some result or is presented as a variable that offers an explanation. Also called the independent variable
Response Variable
The variable that is obtained as a result or the response that gets measured or observed. Also called the dependent variable
Simple Linear
The predication of one response variable's value from one or more explanatory variables' value. When there is a linear relationship between the two variables
Regression Line
The line of best fit where the distance between the line and every point in the data set is minimized
Statistics
The science that deals with the interpretation of numerical facts or data through theories of probability
Measures of Central Tendency
A summary measure that is used to describe an entire set of data with one value that represents the middle or center of the data
Mean
Average. Calculated by adding a series of elements in a data set together then dividing the sum by the total numbers in the series
Median
The value/quantity lying at the midpoint of a frequency distribution
Mode
The most frequent value in a dataset
1 mode =
Unimodal
2 modes =
Bimodal
No Mode =
Uniform
Measures of Spread
A number of measures used to determine the distance of data from the center of the data set, such as range and standard
Range
The difference between the smallest (minimum) and the greatest (maximum) values of a data set
Normal Distribution
When data tends to occur around a central value with no bias right or left. All of these look like a symmetric, bell-shaped curve
Variance
A quantifiable deviation, departure, or divergence away from a known baseline or expected value
Standard Deviation
A measure of how far, on average, data points are from the mean
Probability
The likelihood of an event occurring
Impossible
0% Probability
Unlikely
1% to 39% Probability
As Likely as Unlikely
40% to 60% Probability
Likely
61% to 99% Probability
Certain
100% Probability
Theoretical Probability
(Classical Probability) Computed by dividing the number of outcomes where the desired event occurs by the total number of outcomes. *Note that the outcomes must be equally likely
Empirical Probability
(Experimental Probability) A probability that is calculated by conducting trials or experiments and recording the results
Probability Model
A mathematical representation of a random phenomenon
Experiment
In probability, an experiment or trial is a procedure that can be done repeatedly, that has a well defined set of possible outcomes
Outcome
A single possible result of an experiment
Sample Space
The set of possible outcomes for an experiment *All the different outcomes
Event
An outcome or set of outcomes, whose chance of occurrence can be represented with a probability
Fair
In probability, this refers to a situation in which all outcomes are equally likely. It is the opposite of biased
Sample Size
In probability, this refers to the number of possible outcomes in a trial or experiment *The number of different outcomes
Fundamental Counting Principle
States that for one event with n outcomes and another, independent event with m outcomes, the sample size is n X m
*Used to find the total number of possible outcomes
Permutation
Order matters. The number of unique ordered possibilities for a certain situation
Sampling With Replacement
When an outcome can be selected more than once
Sampling Without Replacement
When an outcome cannot be selected more than once
Combination
Order does not matter. The number of unique unordered possibilities for a certain situation. *All of these problems will be without replacement
Mutually Exclusive
Two events that CANNOT occur at the same time
Intersection (AND)
Since the two events are mutually exclusive, it has no common intersection point. The probability of occurrence of such an event will be zero
Union (OR)
Addition rule of probability
Independent Events
Events where the occurrence of one does NOT affect the probability that the other event(s) will occur
Dependent Events
Events connected such that one event's occurrence IMPACTS the likelihood that the other event will take place
Independent Unions
The probability that either one or the other or both will occur
Independent Intersections
The probability that both event A and event B will occur
Base Unit
A unit that serves as the foundation for other units within that measurement system
Time
A measurement of change, or a duration that orders events sequentially into past, present, and future
Temperature
A measurement of the heat inside an object
Celsius Scale
A scale with 0 degrees as the freezing point and 100 degrees as the boiling point. Is the metric unit of measurement for temperature
Fahrenehit Scale
Used in the U.S. 32 is the freezing point and 212 is the boiling point
Length
Is measured in two different systems: U.S. customary units and the metric system