Stats

Statistics

the mathematical science that deals with the collection, analysis, and presentation of data, which can be then be used as a basis for inference and induction

infer a conclusion

Data and Information

Data	Information
values with no meaning (raw facts, measurements of interest)	once the data is processed it then is used for making a decision or can be used for a specific purpose.

Data Set and Database

Data Set	Database
collection of data points	row / columns

Sources of Data

Primary Data	Secondary Data
collected by self who is using the data	Collected by someone else
expensive, time consuming	quick, readily available
reliable	not reliable
sole control over the data	published on magazines, newspapers or any published data

Collection Methods (Primary Data)

Experiments	Direct Observation	Surveys /Questionnaires

Biased Surveys: Choose one from below (Forcing the user to take survey which can lead to ambiguous answer)

Two Types of Data

Within Quantitative Data:

Counted	Measured
Number of Children	Weight
Defects per hour (Counted items)	Voltage (Measured Characteristics)

Data by Level of Measurement

Level	Description	Example
Nominal	No ranking allowed	Postal Codes
Ordinal	Ranking Allowed but no measurable meaning to the number difference	Education Level (PHD, Masters, Bachelors)
Interval	Meaningful but no zero points	Calendar Year (2018, 2019)
Ratio	Has zero points to reference from	Income ($80,000)

Time Series vs. Cross-Sectional Data

Time Series	Cross-Sectional Data
Over the multiple years (2010-2020)	Within 2010 Data of (TX, AL, NY, CA, MN)
With time series we can observe trend	Compare data at one particular point of time

Population vs. Sample

Parameter vs Statistics

Inferential Statistics

Biased Samples
- a sample that does not represent the population

Ways to Misuse Statistics

Changing the graph scale
Choosing biased samples

Branches of Statistics:

Descriptive
- collecting, summarizing and displaying data
Inferential
- make conclusions/claims based on the sample data
Predictive
- take data from the past and predict the future values and make decisions

Chebyshev’s Theorem

not commonly used.
we work mostly with Normal Distributions

Average is the best way to represent the entire group if there are no outliers.

Probability

Numerical value ranging from 0 to 1.
0 being no chance of probability to 1 being 100% occurring of the event.

Experiment

Sample Space

All the possible outcomes.

Event

One of the outcome of an experiment.
Outcome is basically a subset of the sample space.

Simple Event

Single Outcome which the most basic form that cannot be further simplified.

Three Methods of Assigning Probability

Classical
Empirical
Subjective

Classical Probability

P(A) = Number of possible outcomes / Total number of possible outcomes

Experiment: Roll a die once Sample space = {1, 2, 3, 4, 5, 6}

P(A) = 1/6 = 0.167 or a 16.7% probability.

Empirical Probability

Conducting the experiment to observe the frequency with which an event occurs.

P(A) = Frequency in which Event A Occurs/Total number of observations

Law of Large Numbers Whenever the experiment is done more than

Subjective Probability

Used when classical and empirical probabilities are not available.
Example: The probability of inflation will be more than 4% next year.

Five Basic Properties of Probability

Event A must occur.
Even A will not occur.
Must range from 0 to 1.
The sum of all the probabilities for the simple events in the sample space must be equal to 1.
Complement to Event A is defined as all of the outcomes of

Formula for the complement rule: P(A) + P(A’) = 1

Baye’s Theorem

Qualitative and Quantitative

Nominal

deals with qualitative data

Ordinal