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..
