gender

brand of car

employment status

eye color

etc. 

Discrete

assumes values that can be counted.

children in a family

successful pitches

Continuous

assumes infinite # of values in an interval between 2 boundaries, obtained by measuring. rounded to the nearest unit.

weight, height, time, temperature 

measurement scales:

nominal

e.g. zip code, gender, eye color, nationality

no ranking or order 

measurement scales:

ordinal

e.g. judging, grade, rating scale, preference

no precise differences but ranking 

measurement scales:

interval

e.g. temperature, year/date on calendar

precise differences, ranking, but no "true" zero

zero is arbitrary 

measurement scales:

ratio-level

i.e. height, weight, time, salary, age

there is a "true" zero 

sampling techniques:

random sampling

sampling techniques:

systematic sampling

sampling techniques:

stratified sampling

sampling techniques:

cluster sampling

unrepresentative samples (small, convenience samples)

misleading representations of data (1% of pop. vs. 2,000,000 ppl)

detached statistics (y brand has twice as much x)

implied connections (studies suggest that using this will....)

framing questions

should be 5-20 classes

class width preferably odd #

classes must be mutually exclusive (non overlapping class limits)

must be continuous 

must accommodate all data

must be equal in width 

• design does not change inappropriately--shows data variation (not design)
• irregular use of scale is not used to misrepresent
• must not quote data out of context
• clear, detailed, and thorough labeling
• w/ money in a time series, deflated or standardized units of measurement better

most commonplace value/occurs the most in the data set

usually for categorical data 

for normal distributions

• 68% of data values will fall w/n 1 s.d. of the mean
• 95% of data values will fall w/n 2 s.d. of the mean
• 99.7% of data values will fall w/n 3 s.d. of the mean

divide the distribution into 4 groups separated by Q1 (corresponding to 25th percentile), Q2 (50th percentile--the median), Q3 (75th percentile)

• interquartile range- difference between Q1 and Q3 and is the range of the middle 50% of the data 

the chance of an event occurring.

can be expressed as fractions, decimals, or percentages. 

consists of a set of outcomes of a probability experiment.

• simple event-event w/ 1 outcome
• compound event- an event that consists of more than one outcome

uses sample spaces to determine the numerical probability that an event will happen and it assumes that all outcomes in the sample space are equally likely to occur (have the same prob of ocurring)

• 0<p(E)<1
• if event can't occur, P(E)=0
• if event is certain, P(E)=1
• sum of all probabilities of the outcomes = 1 

the set of outcomes in the sample space that are not included in the outcomes of the event E.

1- P(E) 

personal or subjective definitions of probability assert probabilities on the basis of personal beliefs concerning the particular situation.

if logically consistent, it provides a functional basis for prob. theory

of an event B in relationship to an event A is the probability of that event B occurs after event A has already occurred.

P(B/A) 

in a sequence of n events in which the first one has k1 possibilities of outcomes, and the second event has k2 possibilities, and the third has k3 possibilities, and so forth, the total number of possibilities of the sequence will be

k1 . k2 . k3.....kn 

for any counting n

n!= n(n-1)(n-2)....1

0!=1 

an arrangement of n objects in a specific order. the arrangement of n objects in a specific order using r objects at a time is written nPr

nPr=(n!)/(n-r)! 

a selection of distinct objects from n objects without regard to order. the number of combinations of r objects selected from n objects is denoted by nCr

nCr=(n!)/(n-r)!r! 

a probability experiment whose outcomes are two or could be reduced to two. used to analyze categorical (ordinal or nominal) data. appropriate w/ sampling w/ replacement and w/o

4 requirements:

• must be an n number of (bernoulli) trials
• each trial has 2 categories of outcomes, not necessarily equally likely; success or failure
• prob of success p is same for each trial
• trials are independent. 

in n binomial trials with the probability of p of success in each trial , the prob of exactly x successes is

P(x successes) = (n!/x!(n-x)!) . p^x . q^n-x

• bell-shaped; mean, median, and mode are all equal and located at center of distribution
• symmetrical about the mean
• curve is continuous w/ no gaps or holes, for each x there is a y
• falls smoothly from mean in either direction. it is asymptotic (curve gets closer and closer to x-axis but never touches it)
• location of normal distribution is determined by the mean. the dispersion is determined by the standard deviation.
• empirical normal rule applies
• the prob that the value of x will be in a specified interval is shown by the corresponding aread under a probability density curve (total area=1)