MATH 100 FINAL EXAM SPRING 2018

How do you find a Euler circuit?

if all vertices have an even number of valences, a euler circuit exists. If not, then must eulerize.

What is a Critical Path within an order requirement digraph?

it's the longest amount of time needed to complete a task path, which is also the shortest amount of time possible to complete the entire project.

A prospective study is?

like an experiment but not imposing any type of treatment.

How do you calculate the range?

max value minus min value.

statistical inference is?

methods for drawing conclusions about an entire population on the basis of data from a sample.

A town wants to supply water to all the houses on a new building development, which method is best to use?

minimum cost spanning tree.

What is the mode?

most commonly appearing value.

If regression line is y=4-3x, then the variables are positive or negative association?

negative because number before x is the slope and it negative.

How do you draw a box-plot with an outlier?

no clue.

Can a tree have two, disconnected parts?

no.

Must a spanning tree visit all cities?

no.

What is a valance?

number of edges connected to a vertex.

If the correlation between two variables (r) is 1, then the points of their scatterplot all lay where?

on the regression line.

For bitartite graphs, are Hamiltonian circuits possible?

only if each set has an equal number of vertices.

how do you calculate the frequency percentage?

part divided by whole.

If two variables are both positive, and tend to be linked so that growth of one variable tends to indicate growth in the other variable, then the variables are negatively or positively associated?

positively associated.

What are the rules for Kruskal's minimum cost spanning tree algorithm and what is the algorithm?

same as sorted edges algorithm, but rules of rejection are only to avoid circuits, not number of edges on a vertex.

Which is strongly affected by outlier, standard deviation and mean, or quartiles and medium?

standard deviation and MEAN.

How do you find the mean?

sum of all values (x) divided by number of values (n).

Describe a real-life scenario where a minimum cost spanning tree provides a good solution:

telephone company wants to install lines in new house development.

With a non-symmetric or non-normal distribution graph or skewed graph, which would describe the data more accurately, the five-number summary, or the mean and standard deviation?

the five number summary.

What is the sample proportion?

the part of the sample that agrees. The part divided by the whole to get the percentage.

If the variables have a negative association, then their correlation must be between what?

-1 and 0.

If the variables have a positive association, then their correlation must be between what?

0 and 1.

Algorithm for eurlerization?

1.label vertices and count valences. If even, creat euler circuit, if any odd, must eulerize. Start in upper left hand corner vertex. If valence even, pass over. If odd, create second path to next vertex and connect and update valance value. Continue until reach beginning. Chart out path with arrows and numbers. Record pathway.

Kris has 3 pairs of pants of different colors, 5 shirts, 2 pairs of shoes, how many outfits can Kris makes?

30 because 3x5x2=30.

A connected graph G has 32 vertices. How many vertices does a spanning tree of G have?

32.

What is a complete graph?

A graph that has an edge between every pair of vertices. Each vertex travels directly to each other.

Describe a real-life scenario where finding a Hamiltonian Circuit provides a good solution

A pizza boy wants to deliver 6 pizzas to houses in an area and return back to work.

Bias is?

A systematic error that tends to cause the observations to deviate in the same direction from the truth about the population whenever a sample or experiment is repeated.

A randomized comparative experiment is?

An experiment designed in order to compare two or more treatments, in which people, animals, or things are assigned to treatments be chance.

A the type of statistical study that can show cause and effect it?

An experimental study.

What is the Borda Count rule in voting?

Each voter ranks the candidates. If there are n candidates, then n points are assigned to the first choice for each voter with n-1 for the next choice and n-2 for next choice and so on. The points of each candidate are added and if one has more votes, they are declared the winner.

What is the difference between an experiment and an observational study?

Experiment has treatment that shows cause and effect. Observational study only observes.

Which is the explanatory variable, and which is the response variable? Time spent studying and Grades on Exam?

Explanatory is x, TIME spent studying, Response is y, GRADE on exam.

The nearest neighbor algorithm for solving the traveling salesman problem always produces the same result as the sorted-edges algorithm. True or False?

False

A spanning tree of a graph must contain every edge of the graph, true or false?

False.

How do you find the quartile values?

Find max, min, and range, mode, mean, and n. Find MEDIAN. This is the middle value. If n is odd, then it's n+1/2=M. Circle and don't use anymore. If even, then (n/2)+(n+1 and /2) then divide by 2=Median or Q2. Then calculate the quartiles (mid point of upper half and mid point of lower half usuing same technique. Label Q0=min. Q1=middle of bottom half, Q2 is Median, and Q3 is middle of top half and Q4= max value. Box plot has box of Q1-Q3 and legs that go to Q0 and Q4. IQR= Q3-Q1

What are the steps to make a histogram?

First, organize the data, then decide on intervals if needed, then use a tally scale to find frequency of value occurances. Next, draw an L with Fr. On left and xi on right. Plot out data. Draw to scale. Calculate frequency percentage. Add all together.

A pizza delivery guy takes pizzas to ten houses in a neighborhood and returns to work. Which method is best to use?

Hamiltonian circuit.

If two variables are negatively associated, then the regression line has a?

Negative slope.

Difference between sample and populations?

Population is complete number of things being studied, sample is part of the population that can be studied to gain information on the population as a whole.

What is preference table in voting? And how construct table?

Preference list ballots show first, second, and third place decisions for voters. If four candidates, number of possible combos is 4x3x2x1=24. Candidate who has highest number of first choice votes is winner.

What is an experiment?

Something that tests something and has a treatment.

What is the mean?

Sum of all values added together and divided by number of values (n).

What is majority rule voting?

The candidate that has more than 50% of the first place votes on the preference list ballots is the winner. If number of votes is n and n is even, then majority is n/2 +1. If n is odd, then majority is (n+1)/2. If no candidate has the majority, there is no winner and another rule must be used.

What is plurality voting?

The candidate with the most first place votes on the preference list ballots in the winner. We do not take into account the voters' preferences for the second, third, etc. places. If C has ten first place votes and B has nine, C is winner.

A heuristic algorithm may produce optimal results, true or false?

True.

What is the Condorcet criterion?

a candidate is declared the winner if she can defeat every other candidate in a one on one competition using majority rule. That is, the winner of each one on one competition will have over 50% of the votes.

What is a Euler Circuit?

a circuit that visits all vertices and travels all edges.

What is a connected graph?

a graph with all vertices connected to eachother, not two or more parts.

What is an edge?

a line.

How can an outlier affect the correlation?

a single outlier can change the value and the sign of the correlation.

what is an algorithm

an algorithm is a step by step process to find a solution to a problem. It is finite and is not solved until completed.

Describe a real-life scenario where a Euler circuit provides a good solution

an electric company needs to check the meter for every house in a neighborhood before returning to the office.//What is a Hamiltonian Circuit?//a circuit that is difficult to find and visits all vertices exactly once but does not need to travel all edges. Complete graphs always have them. Ways to find them are sorted edges, brute force, and nearest neighbor algorithms.

Nonresponse occurs when?

an individual selevted for sample cannot be contacted.

suppose an architect needs to design an intercom system for a large office building. The technique most likely to be useful in solving this problem is

applying Kruskal's algorithm for finding a minimum cost spanning tree for a graph.

Suppose a maintenance worker needs to empty garbage dumpsters from five locations on the grounds of a park in the most efficient way possible. The technique most likely to be useful in solving this is

applying the nearest-neighbor algorithm for the traveling salesman problem.

How do you find the mediun (M)?

arrange all values. Count n. If odd, then n+1 divided by 2 = middle value= M. If n=even, then( n/2) +(n/2 +1)/2.

Sampling bias is

built in error in a sample that will lean results one way or another.

How do you find the critical path in an order requirement digraph?

calculate paths of each possibility and add their weight. Find highest weight. This is critical path.

An outlier is an individual value that?

deviates from the pattern.

What is a vertex/vertices?

dot, or city.

An employee of a power company reads the electricity meters outside each house along the streets in a residential area, which method is best to use?

euler circuit.

What is brute force approach (Hamiltonian Circuit)

extensive and accurate method of testing every possible combination of pathways to find lowest cost. To find number of possibilities for a graph with 6 cities, you must times 5x4x3x2x1. If you don't want to repeat any combinations (backwards ones,) divide the answer by two.

The path produced by the sorted-edges algorithm when solving the traveling salesman problem may be depended on the starting city, true or false?

false

What is the 68, 95, 99.7 Rule? How do you find it?

first draw normal distribution slope. X in center. Draw three sd to left and three to right. Title in order from left to right x-3sd (700), x-2sd (800), x-sd (900), x (1000), x+sd (1100), x+2sd (1200), x+3sd (1300). Then draw middle two into 68%, middle four into 95%, and middle 6 is 99.7%. This shows the percentage distribution. If you want 100%, then remember to add value of 1.5% on each side. To find middle 50%, x-.67/SD and x+.67/SD.

What is the algorithm for a random digits random selection?

first label the things that will be randomly selected with numbers. If more 2 digit amount, start first number 01. IF three digit amount, begin with 001. Then, find line on random digits table to begin with. Observe 2 or 3 digit pairs (depending on number of items to randomly select) and throw them out if they are not found in the list of numbers you made. If they are present, then record the order they can be found in.

How do you use the sorted edges algorithm to find a Hamiltonian circuit?

first make a chart. Sort edges pairs from lowest weight to highest. Accept the first two. Rejection requirements are 1-closes an imcomplete circuit. 2---3 edges on a vertex. Go all the way down the list and keep ones that don't meet rejection criteria. Add all weight together and then chart out pathway. Record.

How do you create a stem plot?

first, organize data. Find max, min, and range, mode, mean, and n. Find MEDIAN. This is the middle value. If n is odd, then it's n+1/2=M. Circle and don't use anymore. If even, then (n/2)+(n+1 and /2) then divide by 2=Median or Q2. Then calculate the quartiles (mid point of upper half and mid point of lower half usuing same technique. Label Q0=min. Q1=middle of bottom half, Q2 is Median, and Q3 is middle of top half and Q4= max value. Box plot has box of Q1-Q3 and legs that go to Q0 and Q4. IQR= Q3-Q1.

What is a minimum cost spanning Tree?

graph used to calculate easiest way to reach all vertices but with no circuits.

With a symmetric graph with normal distribution, which would describe the data more accurately, the five-number summary, or the mean and standard deviation?

the standard deviation and mean.

How do you tell which direction a histogram is skewed toward?

the tail side is the side you mention.

The minimum-cost spanning tree produced by applying Kruskal's algorithm may contain the most expensive edge of the graph, true or false?

true.

What is a circuit?

visits all vertices and returns to start.

What is nearest neighbor algorithm (Hamiltonian Circuit)?

when you start at beginning and select shortest distance to each vertex until all are visited.