Algebra 2 Chapter 11: Probability and Statistics

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