Math 1029 final
all deviation sums should equal
zero
z-score
(data item - mean)/standard deviation
Because P(E) + P(not E)=1, then P(not E)=_______ and P(E)=______.
1 - P(E) 1- P(not E)
permutation
An arrangement, or listing, of objects in which order is important.
True or False: A data set can contain more than one median, or no median at all.
False change median to mode
decimal to percent
Move decimal 2 places to the right and add % sign
combination
a grouping of items in which order does not matter
Does it make sense? Assuming that it might rain tomorrow or that it might not rain at all, the probability of it not raining tomorrow is 0.5
The statement does not make sense because an event can have two outcomes with different chances of each occurring.
true or false A score in the 50th percentile on a standardized test is the median.
The statement is true because the median, or second quartile, is the 50th percentile.
Euler Circuit
a circuit that travels along each edge of a graph once and only once has NO odd vertices
Hamilton Circuit
a circuit that visits each vertex exactly once
If there is at least one edge connecting two vertices in a graph, the vertices are called _____. A sequence of such vertices and the edges connecting them is called a _____. If this sequence of vertices and connecting edges begins and ends at the same vertex, it is called a _____.
adjacent path circuit
deviation from the mean
data item-mean
The number of edges that connect to a vertex is called the _____ of the vertex.
degree
A path that passes through each vertex of a graph exactly once is called a/an _______ path. Such a path that begins and ends at the same vertex and passes through all other vertices exactly once is called a/an _______ circuit.
hamilton hamilton
P(E)=
outcomes of E/total outcomes n(E)/n(S)
If n% of the items in a distribution are less than particular data item, we say the data item is in the nth __________ of the distribution.
percentile
The set of all possible outcomes of an experiment is called the _______ of the experiment.
sample space
True or False: The sum of the deviations from the mean for a data set is always zero.
true
The probability of an event occurring at least once is equal to 1 minus the probability that _________.
the event does not occur
True or False if an event is certain to occur, its probability is 1.
true
True or False Every circuit is a path.
true a circuit is a path that begins and ends at the same vertex.
True or False: A graph can be drawn in many equivalent ways
true the placement of vertices and the shapes of the edges are unimportant.
The number of ways in which a series of successive things can occur is found by ______ the number of ways in which each thing can occur. This is called the _______ Principle.
multiplying Fundamental Counting
nPr=
n!/(n-r)!
nCr=
n!/(n-r)!r!
A graph that is connected and has no circuits is called a/an ____________. For such a graph, every edge is a/an ____________, and if there are n vertices, there must be ___________ edges.
tree bridge n-1
True or False: The mean, median, and mode of a normal distribution are all equal.
true
True or false: Measures of dispersion are used to describe the spread of data items in a data set.
true
True or false An edge can be a part of a path only once.
true a path is a sequence of adjacent vertices and the edges connecting them.
A connected graph has at least one Euler path, but no Euler circuit, if the graph has exactly _______ odd vertices/vertex.
two
Data can be displayed using a bar graph with bars that touch each other. This visual presentation of the data is called a/an _______. The heights of the bars represent the _______ of the data values.
histogram frequencies
score above the mean
mean + amount below mean • standard deviation
finding percent increase or decrease
1. Find multiplier with...Multiplier = (new/old) 2. Convert to percent
mutally exclusive events
P(A or B) = P(A) + P(B) - P(A and B)
True or False: The probability that an event happens at least once can be found by subtracting the probability that the event does not happen from 1.
true
True or False: The sum of the probabilities of all possible outcomes in an experiment is 1.
true
68-95-99.7
68-add/subtract standard deviation once 95-add/subtract standard deviation twice 99.7-add/subtract standard deviation three times
A connected graph has even vertices A, B, and C, and odd vertices, D and E. Each Euler path must begin at vertex D and end at vertex _______, or begin at vertex _______ and end at vertex _______.
E E D
A method that approximates the solution to the salesperson problem is called the ______ Method. This method involves continually choosing an edge with the smallest ______.
Nearest neighbor weight
Euler Path
a path that travels along each edge of a graph once and only once has EXACTLY two odd vetices
Hamilton Path
a path that visits all the vertices of a connected graph once and only once
Percent to Decimal
move decimal 2 places left and remove % sign
finding the circuits from vertices
(n-1)!
The probability of winning a lottery with one lottery ticket is the number of ways of winning, which is precisely ________, divided by the total number of possible ________.
1 combinations
A standard bridge deck has _______ cards with four suits: _______ and _______ are red, and _______ and _______ are black.
52 (26 of each color & 13 of each suit) hearts & diamonds clubs & spades
n a normal distribution, approximately __________% of the data items fall within 1 standard deviation of the mean, approximately __________% of the data items fall within 2 standard deviations of the mean, and approximately __________% of the data items fall within 3 standard deviations of the mean.
68 95 99.7
frequency distribution
A frequency distribution is a type of data presentation. The data values are listed in one column. The adjacent column indicates the number of times each value occurs.
A method that determines the solution to the traveling salesperson problem involves listing all Hamilton circuits and selecting the circuit with the minimum sum of weights. This method is called the _______ Method.
Brute Force
Explain the Fundamental Counting Priniple.
If you can choose one item from a group of M items and a second item from a group of N items, then the total number of two-item choices is Upper M x N.
True or False Every path is a circuit.
False not every path ends at the same vertex where it starts
True or False: A sample is the set of all the people or objects whose properties are to be described and analyzed by the data collector.
False. A population is the set of all the people or objects whose properties are to be described and analyzed by the data collector.
True or False: One disadvantage of a stem-and-leaf plot is that it does not display the data items.
False. One advantage of a stem-and-leaf plot is that it displays the data items.
true or false: Measures of dispersion get smaller as the spread of data items increases.
False. Measures of dispersion get smaller as the spread of data decreases.
Does it make sense? I would never choose the lottery numbers 1, 2, 3, 4, 5, 6 because the probability of winning with six numbers in a row is less than winning with six random numbers.
The statement does not make sense because every combination of six numbers is equally likely to be drawn.
A procedure that yields the minimum spanning tree of a graph is called ___________ Algorithm. The idea of the algorithm is to always pick the edge with the smallest available ___________, but avoid creating any ___________.
Kruskai's weight circuits
If you can choose one item from a group of M items and a second item from a group of N items, then the total number of two-item choices is _______.
M x N
combination or permutation: How many different 6-letter passwords can be formed from the letters H, I, J, K, L, M, and N if no repetition of letters is allowed
Permutation
Describe how to construct a stem-and-leaf plot from a set of data. Assume that the data consist of two-digit numerical values.
The plot is constructed by separating each data item into two parts. The first part is the stem. The stem consists of the tens digit. The second part is the leaf. The leaf consists of the units digit for a given value. Write all of the stems in the first column. Then, write each leaf in the second column, writing the leaf of each data item in the row corresponding to its associated stem.
Describe why the range might not be the best measure of dispersion.
The range is a quick but rough measure of dispersion. It is the difference between the highest and lowest data values in a data set. On the other hand, the standard deviation is a measure of dispersion that is dependent on all of the data items, and therefore is more accurate.
Does it make sense? When I toss a coin, the probability of getting heads or tails is 1, but the probability of getting heads and tails is 0.
This statement makes sense because when you toss a coin you can either get a head or a tail at a time. You cannot get head and tail both at the same time.
Does it make sense?When finding the probability of randomly selecting 2 men and 1 woman from a group of 10 men and 10 women, I used the formula for nCr 3 times.
This statement makes sense. The formula for nCr is used to find the number of combinations of 2 men out of the 10 men, the number of combinations of 1 woman out of the 10 women, and the number of combinations of 3 people out of the whole group.
True or False In a normal distribution, the z-score for the mean is 0.
True a z-score describes how many standard deviations a data item in a normal distribution lies above or below the mean.
True or False: A call-in poll on radio or television is not reliable because the sample is not chosen randomly from a larger population.
True because people choose to call in. They are not randomly selected.
True or False: Numbers representing what is average or typical about a data set are called measures of central tendency.
True because these numbers are generally located toward the center of a distribution.
If an edge is removed from a connected graph and leaves behind a disconnected graph, such an edge is called a _____.
bridge
combination or permutation: A medical researcher needs 37 people to test the effectiveness of an experimental drug. If 85 people have volunteered for the test, in how many ways can 37 people be selected?
combination
A graph that has an edge between each pair of its vertices is called a/an ________ graph. If such a graph has n vertices, the number of Hamilton circuits in the graph is given by the factorial expression ______.
complete (n-1)!
two events are__________________ if the occurrence of one of them has an effect on the probability of the other
dependent
Fraction to Percent
divide the top number by the bottom number. multiply the result by 100, add the "%" sign.
Degrees of a vertices
each edge connected to a vertex is 1 degree a loop is 2 degrees
Probability that is based on situations in which we observe how frequently an event occurs is called ______.
empirical
Two graphs that have the same number of vertices connected to each other in the same way are called _____.
equivalent
5!, called 5 _______ is the product of all positive integers from _______ down through _______. By definition, 0!=_______.
factorial 5 1 1
true or false: When finding the mean, it is necessary to arrange the data items in order.
false. change "mean" to "median".
True or False: If an event cannot occur, its probability is -1.
false. The true statement is "If an event cannot occur, its probability is 0."
If data values are listed in one column and the adjacent column indicates the number of times each value occurs, the data presentation is called a _______.
frequency distribution
If the midpoints of the tops of the bars of a histogram are connected with straight lines, the resulting line graph is a data presentation called a_______. To complete such a graph at both ends, the lines are drawn down to touch the _______.
frequency polygon horizontal axis
A finite set of points connected by line segments or curves is called ____. The points are called ____. The line segments or curves are called ____. Such a line segment or curve that starts and ends at the same point is called a ____.
graph vertices edges loop
Suppose a data presentation is given where data values are listed in one column and the adjacent column indicates the number of times each value occurs. If this data presentation is varied by organizing the data into classes, the data presentation is called a/an _______. If one class in such a distribution is 80-89, the lower class limit is _______ and the upper class limit is _______.
grouped frequency distribution 80 89
If the occurrence of one event has no effect on the probability of another event, the events are said to be _______. For such events, P(A and B)=_______.
independent P(A) x P(B)
A z-score describes how many standard deviations a data item in a normal distribution lies above or below the _____.
mean
thee sum of all the data items divided by the number of data items, is the measure of central tendency called the__________
mean
standard deviation
mean for each number subtract the mean and square the result mean of those squared differences. divide with n-1 (n is the number of items) Take the square root of that
score below the mean
mean - amount below mean • standard deviation
the measure of central tendency that is the data item in the middle of ranked, or ordered, data is called the _____.
median
The measure of central tendency that is found by adding the lowest and highest data values and dividing the sum by 2 is called the____________.
midrange
A data value that occurs most often in a data set is the measure of central tendency called the _____.
mode
A connected graph has at least one Euler circuit, which, by definition, is also an Euler path, if the graph has _______ odd vertices. An Euler circuit can start and end at _______ vertex.
no any
A connected graph has no Euler paths and no Euler circuits if the graph has more than two _______ vertices.
odd
Conditional Probability
the probability of an event ( A ), given that another ( B ) has already occurred. # of outcomes common the B and A/ # of outcomes in A
A sample obtained in such a way that every element in the population has an equal chance of being selected is called a/an _______ sample.
random
The difference between the highest and lowest data values in a data set is called the _______.
range
does it make sense? improperly worded questions can steer respondents towards answers that are not their own.
the statement makes sense because if a question is worded improperly, respondents might not know what is actually being asked.
A tree that is created from another connected graph and that contains all of the connected graph's vertices, is connected, and contains no circuits is called a/an ____________ tree.
spanning
A data presentation that separates each data item into two parts is called a _______.
stem-and-leaf plot
A graph whose edges have numbers attached to them is called a/an ______ graph. The numbers shown along the edges of such a graph are called the ______ of the edges. The problem of finding a Hamilton circuit for which the sum of these numbers is a minimum is called the ______ salesperson problem. Such a Hamilton circuit is called the ______ solution.
weighted weights traveling optimal
Does it make sense? When solving probability problems using the Fundamental Counting Principle, I find it easier to reduce the probability fraction if I leave the numerator and denominator as products of numbers.
yes