Chpt. 11, Probability and Statistics Flashcards
Fundamental Counting Principle
in a sequence of selections, you can multiply the number of choices for each selection, and the product is the total number of possible overall outcomes
permutation
an arrangement of items in a particular order
the number of n objects taken r at a time is:
p = n!/(n - r)!
n factorial (!)
for any positive integer n, n factorial is n * n-1 * n-2, all the way down to zero
combination
any unordered selection of r objects from a set of n objects
the number of combinations of n objects taken r at a time is:
C = n!/r!(n-r)!
experimental probability
the ratio of the number of times something actually happens over the number of times the experiment has been done
simulation
a model that imitates one or more events
sample space
the set of all possible outcomes of an experiment
equally likely outcomes
events in a sample space that have the same chance of occurring
theoretical probability
if a sample space has n possible outcomes, and an event A occurs in m of these outcomes, then the theoretical probability of events a is P(A) = m/n
dependent events
when the outcome of one event determines the outcome of a second event
independent events
when the outcome of one event does not affect the probability of a second event
mutually exclusive events
when two events cannot happen at the same time
the probability of events A occurring and event B occurring also
P(A) * P(B)
conditional probability
conditional probability contains a condition that may limit the sample space for an event; for example:
(train arrives and departs on time) train departs on time)
measures of central tendency
mean, median, and mode
mean
the sum of the data divided by the number of data
median
the middle value in a set of data; if the data set contains an even number of values, this is the mean of the two middle values
mode
the most frequently occurring value (or values) in a set of data; a data set may have no mode, one mode, or more than one mode
bimodal
having multiple modes
outlier
a value substantially different from the rest of the data in the set
range (of a set of data)
the difference between the greatest and least values
quartile
values that separate a finite data set into four equal parts; the second quartile is the median of the data; the first and third quartiles are the medians of the upper and lower halves of the data, respectively
interquartile range
the difference between the third and first quartiles
box and whisker plot
a method of displaying data that uses quartiles to form the center box, and the maximum and minimum values to form the whiskers
percentile
a number from 0 to 100 that can be associated with a value x from a data set
measures of variance
measures (such as the range, interquartile range, or standard deviation) that describe how the data in a data set are spread out
variance
the square of the standard deviation
standard deviation
a measure of how much the values in a data set vary (deviate) from the mean, X; standard deviation:
- find the mean
- square the difference between each point and the mean
- find the mean of the squares
- take the square root of the mean of the squares
population
the members of a set
sample
a portion of a population
convenience sample
a sample in which all selected data points are those that are readily available (convenient)
self-selected sample
a sample of data points selected by the sampler
systematic sample
a sample in which the population is ordered in some way, then selected from at random intervals
random sample
a sample in which the data points are selected randomly
bias
a systematic error introduced by the sampling method
observational study
when the sample is interacted with in such a way that it is not affected
controlled experiment
an experiment with a “control”
survey
a sample in which every member is asked the same questions
