Fundamental Counting Principle
describes the method of using multiplication to count
permutation
an arrangement of items in a particular order
n factorial
n!=n(n-1)
...
3
2
1. 0!=1
combination
a selection in which order does not matter
experimental probability of event
P(event)=number of times the event occurs � number of trials
simulation
a model of the event
sample space
the set of all possible outcomes to an experiment or activity
equally likely outcomes
when each outcome in a sample space has the same chance of occurring
theoretical probability
If a sample space has n equally likely outcomes and an event A occurs in m of these outcomes where P(A)=m�n
dependent events
when the occurrence of one event affects how a second event can occur
independent events
when the occurrence of one event does not affect how a second event can occur
probability distribution
a function that gives the probability of each outcome in a sample space
uniform distribution
the theoretical probability of rolling each number on a standard number cube is the same
cumulative frequency
when you can assign numerical values to events
cumulative probability
the probability of events occurring with values that are less than or equal to a given value
conditional probability
the probability that an event, B, will occur given that another event, A, has already occurred
contingency table
two-way frequency table is a frequency table the contains data from two different categories
probability model
use this to assign probabilities to outcomes of a chance process
measure of central tendency
indicates the middle of the data set; the mean, median, and mode are the most common measures
mean
sum of the data values � number of data values
median
for a data set listed in order: the middle value for an odd number of data values; the mean of the two middle values for an even number of data values
mode
the most frequently occurring values
bimodal
two modes in a data set, in which case the modes are probably not statically useful
outlier
a value that is substantially different from the rest of the data in a set
range of a set of data
the difference between the greatest and least values
quartiles
the values that are separated into four parts. If you order data from least to greatest value, the median divides the data into two parts. The median of each part divides the data further and you have four parts in all.
box-and-whisker plot
a way to display data that uses quartile to bound the center box and the minimum and maximum values to form the whiskers
percentile
a number from 0 to 100 that you can associate with a value x from a data set
measure of variation
describes how the data in a data set are spread out
variance
in a data set, sum of the differences between each value x and the mean divided by the n values in the data set
standard deviation
in a data set, the square root of the sum of the differences between each value x and the mean divided by the n values in the data set
convenience sample
select any members of the population who are conveniently and readily available
self-selected sample
select only members of the population who volunteer for the sample
systematic sample
order the population in some way, and then select from it at regular intervals
random sample
all members of the population are equally likely to be chosen
bias
a systematic error introduced by the sampling method
observational study
you measure or observe members of a sample in such a way that they are not affected by the study
controlled experiment
you divide the sample into two groups. you impose a treatment on one group and not the other group. Then compare the effect on the treated group to the other group
survey
you ask every member of the sample a set of questions
binomial experiment
experiment has all these: fixed number of trials, each trial has two possible outcomes; the trials are independent; the probability of each outcome is constant throughout the trials
binomial probability
with n repeated independent trials (p+q=1). this probability of x successes in the nth trials can found by this formula
binomial theorem
discrete probability distribution
a finite number of possible events or values
continuous probability distribution
the events can be any value in an interval of real numbers
normal distribution
data that vary randomly from teh mean
margin of error
helps you find the interval in which the mean of the population is likely to be; based on the size of the sample and the confidence level desired
confidence interval
a range of values so defined that there is a specified probability that the value of a parameter lies within it
z-score
an important measure for normally distributed data which indicates the number of standard deviations a value lies above or below the mean of a population
interquartile range
the difference between the third and first quartiles
mutually exclusive events
two events that cannot happen at the same time where P(A and B)=0
sample
a part of population