Chapter 10 (Alg 2) Flashcards
Population
an entire group of people, animals, or objects that you want info. about
Sample
smaller part of the population
Unbiased sample
a sample that accurately represents a population
biased sample
over represents the population or under represents part of the population
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also watch for biased questions
Convenience sample
easy to reach members of a population are selected
self-selected sample
members of a population volunteer to be included
systematic sample
a rule or pattern is used to select memers of a populations
random sample
each member of a pupulation is equally likely to be chosen
Biased and unbiased ways of sample
a random sample is least likely to be biased, same or the systematic sample
Convenience and self-selected samples are likely to be biased
margin of error
a random sample can give a biased result just by chance
the margin of error is: M o E : + or - 1 /Sqrt.n
Central Tendency
the mean, median, and mode
measures of dispersion
Range and the difference between quartiles
Transformations of data
when you increase or decrease the data values by a constant amount or when you multiply them by a constant factor.
Comparing data after adding a constant
the mean, median and mode each increase
the range and the difference between the upper and lower quartiles remain the same
Comparing data after adding a constant (fraction, decimal)
The mean, median and mode each increases by 10%
the range and the difference between the upper and lower quartiles each increase by 10%
Graphing data after adding a constant and multiplying by a constant
adding a constant shifts the graph horizontally that number of units, but doesn’t change the graph’s shape
multiplying by a constant stretches the graph horizontal by the same factor, this moves the data’s middle and increase the date’s spread
Fundamental Counting Principle
if one event can occur in m ways and another event can occur in n ways, then the number of ways that both events can occur is m * n, this goes for 3, 4… so one events
permutation
an ordering of a set of objects
factorial
the number of permutations of n distinct objects in n!
n! = n * (n - 1) * (n - 2) * . . .
Permutations of n objects taken r at a time
The number of permutations of n objects taken r at a time is denoted by nPr and is given by the following formula: nPr = n! / (n - r)!
Combination
a selection of r objects from a group on n objects where their order is not important
Combinations of n objects taken r at a time
nCr = nPr / r! = n! / (n-r)! * r!
Pascal’s triangle
when you arronge the values of nCr in a triangular pattern in which each row corresponds to a value on n, you get a pattern called Pascal’s Triangle
Binomial Theorem
for any positive integer n, the expansion of (a + b)^n is:
(a + b)^n = nC0a^n b^0 + nC1 a^(n-1)b^1 + nC2 a^(n-2) b^2..
Probability
the probability of an event is a number from 0 to 1.
Theoretical Probability of an event
When all outcomes are equally likely, the theoretical probability that an event A will occur is:
P(A) = # of outcomes in event A
———————————-
total # of outcomes
often simply called its probability
Experimental Probability of an Event
For a given number o trials of an experiment, the experimental probability that an event A will occur is:
P(A) = Number of trials where A occurs
———————————————
Total number of trials
Geometric Probability
find probabilities based on ratios of two lengths, areas, or volumes.
Compound Event
The union or intersection of two events is called a compound event
overlapping events
Two events that have outcomes in common
Disjoint events or mutually exclusive
two events that have no outcomes in common
Probability of Compound Events (Overlapping events)
If A and B are overlapping events, then P(A and B) DNE, and the probability of A or B is:
P(A or B) = P(A) + P(B) - P(A and B)
Probability of Compound Events (Disjoint Events)
If A and B are disjoint events, P(A and B) = 0, and the probability of A or B is:
P(A or B) = P(A) + P(B)
Complement of an event
consists of all outcomes not in that event
Probability of the Complement of an Event
The sum of the probabilities of an event and its complement is .1
P(A) + P(not A) = 1, so P(not A) = 1 - P(A)
Independent (Two Events)
The two events are independent of each other if one event occurs and doesn’t effect the other
Dependent (Two Events)
The two events are dependent of each each other if one event occurs and effects the other
Conditional Probability
For two dependent events A and B, the probability that B will occur given that A has occurred is the Conditional Probability of B given A, written a P(B | A)
Probability of Independent and Dependent Events
Independent
If A nd B are independent events, then the probability that both A nd B occur is P(A and B) = P(A) * P(B)
and this could go one forever.
Probability of Independent and Dependent Events (Dependent)
If A and B are dependent events, then the probability that both A nd B occur is P(A and B) = P(A) * P(B | A)
