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Communicating Quantitative Information

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Title: Communicating Quantitative Information


1
Communicating Quantitative Information
  • Detroit bailout request
  • Recession
  • Uninsured children
  • Precision.
  • Decision making optimization
  • Spreadsheet Reprise future value, mortgage
    paymentsNew VLOOPUP
  • Homework Project II

2
Detroit request
  • Detroit General Motors, Ford, Chrysler
    automakers
  • http//www.nytimes.com/imagepages/2008/12/03/busin
    ess/1203-biz-auto.graphic.html
  • Context first request came without a plan, so
    this is an improvement
  • Extra credit look up Chrysler bailout in 1979.

3
Recession
  • Business Cycle Dating Committee of the National
    Bureau of Economic Research declared that the USA
    is 'in recession' and it started December 2007!
  • This doesn't mean it is close to being over.
  • Recessions are defined looking backwards at
    several factors including Gross Domestic Product,
    employment, demand

4
Think about each of these claims
  • 8.6 Million Children Are Uninsured
  • One in nine American children (11.1 percent) is
    uninsured.
  • The five states with the largest number of
    uninsured children are Texas, California,
    Florida, New York, and Georgia. Together, the
    uninsured children in these five states account
    for nearly half of all uninsured children in the
    country (48.3 percent).
  • The five states with the highest rates of
    uninsured children are Texas, Florida, New
    Mexico, Arizona, and Nevada. More than 15 percent
    of children in each of these states are
    uninsured, compared to a national median of 9.2
    percent.

5
  • 8.6 Million Children Are Uninsured
  • One in nine American children (11.1 percent) is
    uninsured.This is saying there are
    (approximately) 8.6 times 9 children.
  • The five states with the largest number of
    uninsured children are Texas, California,
    Florida, New York, and Georgia.
  • TX, CA, FL, NY have the largest population, so
    this isn't too surprising..
  • Together, the uninsured children in these five
    states account for nearly half of all uninsured
    children in the country (48.3 percent).
  • The five states with the highest rates of
    uninsured children are Texas, Florida, New
    Mexico, Arizona, and Nevada. Rate is uninsured /
    all children.
  • More than 15 percent of children in each of these
    states are uninsured, compared to a national
    median of 9.2 percent. Order all the states by
    rate. The median of these numbers is 9.2. Half
    greater than or equal. Half less than or equal.

6
Voting in USA 2008 update?
  • What percentage of eligible citizens voted in
    2008?
  • Note be careful there are 3 measurements/percent
    ages/proportions of interest
  • Percentage of eligible voters who register
  • Percentage of registered voters who vote in
    specific election
  • Percentage of eligible voters who vote in
    specific election. This last is the product of
    the first two.

7
Retirement exercise
  • Exercise in dealing with quantities
  • Requires patience
  • Probably need to look up definitions
  • Some calculators have better interfaces than
    others
  • Negative savings is not the best way to deliver a
    positive message.
  • Provide understanding to comments People look at
    their 401K statements and feel bad

8
Transition
  • Calculators are estimates. May be more precise
    than accurate

9
Precision vs Accuracy
  • Accurate means "capable of providing a correct
    reading or measurement." In physical science it
    means 'correct'. A measurement is accurate if it
    correctly reflects the size of the thing being
    measured.
  • Precise means "exact, as in performance,
    execution, or amount. "In physical science it
    means "repeatable, reliable, getting the same
    measurement each time."
  • http//honolulu.hawaii.edu/distance/sci122/SciLab/
    L5/accprec.html

10
Precision
  • significant digits more is more precise.
  • 61.58 is more precise than 61.6
  • Use of mathematical notation makes it easier to
    compare
  • Number times 10 raised to a power
  • 8 103 is 8000. 1 significant digit
  • 8.0 103 is 8000. 2 significant digits
  • 8.00 103 is 8000. 3 significant digits

11
Precision
  • Repeatibility
  • Get same answer when test/measurement is repeated
  • Reproducibility
  • Get same answer when using different tools
  • This includes different graders. Would different
    graders assign the same grade to an essay?

12
Related story
  • Philipstown Highway superintendent it is not in
    people's interest to report the
    Latitude/Longitude given by their GPS system
  • The Highway Department can only work within a
    fixed area in terms of the report.
  • Don't want to be too precise

13
Optimization
  • Way of thinking about decisions
  • Mathematical field but
  • Can be useful informally

14
Optimization Problem
  • Make a decision choose value or values (setting)
    for one or more quantities to get the best result
  • Some problems/situations can be expressed in
    (relatively) simple equations so that it is easy
    to compute a maximum or minimum point
  • Maximum or minimum within an interval

15
Example
  • Company is putting on a play and needs to set the
    price of a ticket.
  • Income number of tickets sold price of a
    ticket
  • Number of tickets sold goes down as price of
    ticket goes up
  • within some limits, and not counting family
    members!
  • Notion of price elasticity

16
Example, cont.
  • Say estimate is number of tickets sold 400
    20 price
  • Let p stand for the price
  • Income p (400-20p)
  • If you graphed this, it would be a parabola

Max. at p 10, No. of tickets sold 200 Income
2000
17
Example, cont.
  • This is a standard word problem in calculus
    classes, since the min. or max. is reached at an
    end point OR a point where the derivative is
    zero.
  • Derivative is the slope of the curve
  • Can balance a line at the max. or min.

18
Similar problem
  • Shoot a projectile (rocket, arrow, bullet) into
    the air, when and where does it reach the highest
    point.
  • http//newmedia.purchase.edu/Jeanine/games/cannon
    ballflashbasic.html
  • very simple simulation of ballistic motion
  • Cannonball coming out of cannon at angle
  • Horizontal component of vector remains constant
  • Vertical component is changed because of gravity

19
General Optimization problems
  • Have more than one quantity that needs to be set
  • x1, x2, .
  • Have conditions that must be met. These are
    called the constraints
  • There is what is called an objective function
    that you want to minimize or maximize.
  • What are the values of the xs that
  • Satisfy the constraints AND
  • provide the optimal value (biggest or smallest,
    depends on the problem) of the objective
    function?

20
Terms
  • Predates computer programming.
  • Mathematical programming
  • Linear programming
  • Integer programming used
  • Also, operations research
  • Management science
  • other

21
Examples
  • Deciding on inventory in store
  • Satisfy customers constraint
  • Fit on the shelves constraint
  • Bring in most revenue want to maximize
  • Traveling salesman problem determine best route
  • Visit all stops constraint
  • Minimize length of path
  • Variant minimize travel time. May not be the
    same thing

22
Aside
  • Article regarding Obama versus Clinton on
    experience
  • Referred to Nixon versus Kennedy in 1960
  • Nixon had experience being VP under Eisenhower
  • Claim (with hindsight) Kennedy side changed the
    argument from comparing who had most experience
    to 'threshold test', did Kennedy have enough.
    This may characterize what Obama did.
  • This is changing an aspect of a problem
  • from something to optimize
  • to something to satisfy a condition

23
Example
  • Farmer has A acres of land to plant.
  • Crop 1 (soy beans) cost C1 per acre to plant and
    brings in P1 per acre yield at the market.
  • Crop 2 (corn) costs C2 per acre to plant and
    brings in P2 per acre yield at the market.
  • Let x1 be the amount of soy beans and x2 be the
    amount of corn.

24
Example, cont.
  • Constraint
  • x1 x2 lt A
  • x1 gt 0, x2 gt 0
  • Income is the objective function
  • x1 (p1 c1) x2 (p2-c2)
  • Answer see which is greater (p1-c1) versus
    (p2-c2) and plant all A acres with one crop!

25
Linear programming
  • This is an example of a linear programming (LP)
    problem, actually an IP (integer) programming.
  • Many problems fall into this class
  • and dont have obvious solutions.
  • There are software packages that produce
    solutions, or, at least pretty good solutions.

26
Example from Wiki
  • Farmer has more complex situation.
  • Crop 1 requires F1 fertilizer and D1 pesticides
  • Crop 2 requires F2 fertilizer and D2 pesticides
  • There is a limit on the amount of fertilizer and
    a limit on the amount of pesticide.
  • So

27
Example, cont.
  • Constraints
  • x1 x2 lt A
  • x1f1 x2f2 lt F fertilizer limit
  • x1d1x2d2 lt D insecticide limit
  • x1gt0, x2gt0
  • Objective function (same as before). Want to
    maximize income
  • x1p1 x2p2

28
Future?
  • Companies may have constraints on generation of
    carbon
  • May be in the form of taxes (extra costs) OR
  • Carbon credits (which can be traded)OR
  • Fixed limit(s)
  • ???

29
Lessons
  • These problems/situations exist and people do
    attempt to solve them!
  • Personal lesson when doing your own decision
    making, even if you cannot quantify all issues,
    think about
  • Constraints --- must dos
  • versus
  • Objective function --- what you want to be
    biggest or smallest

30
Stochastic problems
  • Element of chance
  • How to invest money
  • Investment A has 30 chance of losing AL percent,
    40 chance of gaining AG percent, and (1-(ALAG))
    chance of remaining the same. Same for
    investments B, C, D
  • Planning a program in figure skating!
  • Certain moves/steps have bigger point potential
    but also carry risks

31
Extra credit
  • Formulate a decision making situation for you or
    someone else or a businessin terms of
    constraints and objectives. This is termed
    defining a model of the problem.
  • Post (proofread) in General Forum or
  • Turn in privately (proofread!!!!!)

32
Spreadsheet
  • Demonstrate using Google Documents
  • Reprise certain things
  • Do new VLOOKUP

33
General terminology
  • Mathematics and computer programming
  • A function has inputs and produces a value
  • Syntax (name for punctuation)
  • F (a1, a2, a3, )
  • Area of a rectangular yard is length
    widtharea(length, width) is a function from R x
    R to R
  • The a1, a2, a3 are arguments aka parameters
  • In spreadsheets,
  • you need to use an equal sign FV()
  • There can be optional values that if omitted,
    take a default value. Can be omitted only if
    they are the last ones

34
Google Spreadsheet
  • FV future value of steady investment
  • PV what input or output in future is valued now
  • PMT calculates how much payment will be for a
    loan
  • Use Formulas / more / pick category / select one
    you want

35
Google Spreadsheet
  • Name cell or range
  • Formulas Range Names Define New
  • Conditional formatting
  • Select cell or range
  • Edit Text or Background
  • Click on Rules
  • Write rule
  • Select Text and/or Background colors

36
VLOOKUP
  • Make an array with the first column the start of
    the ranges and the second column the grades

37
VLOOKUP, continued
  • vlookup(value,reference to array, column to be
    used for return value)
  • Name 2 column array grades
  • vlookup(e2, grades , 2)
  • Use Help
  • Note Excel and Google have different meanings
    for an optional 4th parameter

38
Compare with frequency
  • frequency(data_array, bins_array) ? array
  • vlookup (value this probably is reference,
  • array probably 2 columns
  • column)
  • So vlookup (value, array, column) ? value
  • Note hlookup uses information organized in rows.

39
Class/group projects
  • I do give C-, C, B-, B, A-
  • I do give A
  • SO.
  • What should the columns be
  • What should the vlookup be

40
Google spreadsheet
  • Formulas more google
  • ImportHtml(URL, "list" "table", index)
  • Need to have site that uses lists and tables
    relatively simply
  • Example url
  • http//en.wikipedia.org/wiki/List_of_capitals_in_t
    he_United_States
  • ImportHTML(url,"table",2)

41
Try something else?
  • Formulas more pick category .
  • ????

42
Google documents
  • Also have sharing option
  • Keep track of revisions by author
  • Look at my documents Alumni
  • Note Excel does have more formatting options.
    Maybe more useable

43
Homework
  • Project II!
  • Remember definitions, denominators, context,
    comparisons, relevant statistics, trends, .
  • PROOFREAD
  • This includes PowerPoint charts!
  • Use automatic feature
  • Re-read yourself
  • (ask a friend, relative)
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