GRAPHICAL METHODS FOR QUANTITATIVE DATA
Chapter 4Displaying and Summarizing Quantitative DataCHAPTER
OBJECTIVESAt the conclusion of this chapter you should be able to:
1)Construct graphs that appropriately describe quantitative data
2)Calculate and interpret numerical summaries of quantitative data.
3)Combine numerical methods with graphical methods to analyze a
data set. 4)Apply graphical methods of summarizing data to choose
appropriate numerical summaries. 5)Apply software and/or
calculators to automate graphical and numerical summary
procedures.
Displaying Quantitative DataHistogramsStem and Leaf
DisplaysRelative Frequency Histogram of Exam
Grades0.05.10.15.20.25.30405060708090GradeRelative
frequency1006Sample histogram;
Do not confuse with bar chartFrequency Histogram
HistogramsA histogram shows three general types of
information:It provides visual indication of where the approximate
center of the data is.We can gain an understanding of the degree of
spread, or variation, in the data.We can observe the shape of the
distribution.Center, spread, shapeAll 200 m Races 20.2 secs or
lessHistograms Showing Different Centers
Histograms Showing DifferentCenters(football head coach
salaries)
Histograms - Same Center, Different Spread(football head coach
salaries)
Excel Example: 2012-13 NFL SalariesStatcrunch Example: 2012-13
NFL Salaries
Grades on a statistics examData:75 66 77 66 64 73 91 65 59 86 61
86 6158 70 77 80 58 94 78 62 79 83 54 52 4582 48 67 55Frequency
Distribution of Grades Class Limits Frequency40 up to 5050 up to
6060 up to 7070 up to 8080 up to 9090 up to 100Total 2 6 8 7 5
2304Relative Frequency Distribution of Grades Class Limits Relative
Frequency40 up to 5050 up to 6060 up to 7070 up to 8080 up to 9090
up to 100 2/30 = .067 6/30 = .200 8/30 = .267 7/30 = .233 5/30 =
.167 2/30 = .0675Relative Frequency Histogram of
Grades0.05.10.15.20.25.30405060708090GradeRelative
frequency1006Frequency and relative frequency histogram of same
data will have the same shape.Based on the histo-gram, about what
percent of the values are between 47.5 and 52.5?
50%5%17%30%
Countdown10Stem and leaf displaysHave the following general
appearancestemleaf 18 9 21 2 8 9 9 32 3 8 9 40 1 56 7 64
Probably havent seen one before now; heres what one looks
like.Stem and Leaf DisplaysPartition each no. in data into a stem
and leafConstructing stem and leaf display1) deter. stem and leaf
partition (5-20 stems)2) write stems in column with smallest stem
at top; include all stems in range of data3) only 1 digit in
leaves; drop digits or round off4) record leaf for each no. in
corresponding stem row; ordering the leaves in each row
helpsExample: employee ages at a small company18 21 22 19 32 33 40
41 56 57 64 28 29 29 38 39; stem: 10s digit; leaf: 1s digit18:
stem=1; leaf=8; 18 = 1 | 8stemleaf 18 9 21 2 8 9 9 32 3 8 9 40 1 56
7 64Constructing display;
Order the leaves in each stem rowSuppose a 95 yr. old is
hiredstemleaf 18 9 21 2 8 9 9 32 3 8 9 40 1 56 7 64 7 8 95Include
all stems in the range of dataNumber of TD passes by NFL teams:
2012-2013 season(stems are 10s
digit)stemleaf43032472667778920122223344411346788908Smallest
number? Largest number?Pulse Rates n = 138
Ignore the circles showing in the graphic;
*Stem rows have leaves o through 4
Note that leaves in each row are orderedAdvantages/Disadvantages
of Stem-and-Leaf DisplaysAdvantages1) each measurement displayed2)
ascending order in each stem row3) relatively simple (data set not
too large)Disadvantagesdisplay becomes unwieldy for large data
setsPopulation of 185 US cities with between 100,000 and
500,000Multiply stems by 100,000
Each leaf should be just 1 digit to keep display simple;
sometimes data has to be rounded or truncated
Note four rows for each stem value so display is not too
wide.
3|6 = 360,000Back-to-back stem-and-leaf displays. TD passes by
NFL teams: 1999-2000, 2012-13multiply stems by
101999-20002012-1324036372324665526677789433222211002012222334449998887666167889421113408Below
is a stem-and-leaf display for the pulse rates of 24 women at a
health clinic. How many pulses are between 67 and 77?
Stems are 10s digits
4681012
Countdown10Interpreting Graphical Displays: ShapeA distribution
is symmetric if the right and left sides of the histogram are
approximately mirror images of each other.
Symmetric distribution
Complex, multimodal distributionNot all distributions have a
simple overall shape, especially when there are few
observations.
Skewed distributionA distribution is skewed to the right if the
right side of the histogram (side with larger values) extends much
farther out than the left side. It is skewed to the left if the
left side of the histogram extends much farther out than the right
side.Heights of Students in Recent Stats Class
Shape (cont.)Female heart attack patients in New York stateAge:
left-skewedCost: right-skewed
AlaskaFloridaShape (cont.): OutliersAn important kind of
deviation is an outlier. Outliers are observations that lie outside
the overall pattern of a distribution. Always look for outliers and
try to explain them.The overall pattern is fairly symmetrical
except for 2 states clearly not belonging to the main trend. Alaska
and Florida have unusual representation of the elderly in their
population.
A large gap in the distribution is typically a sign of an
outlier.
30This is from the book. Imagine you are doing a study of health
care in the 50 US states, and need to know how they differ in terms
of their elderly population.This is a histogram of the number of
states grouped by the percentage of their residents that are 65 or
over.You can see there is one very small number and one very large
number, with a gap between them and the rest of the
distribution.Values that fall outside of the overall pattern are
called outliers. They might be interesting, they might be mistakes
- I get those in my data from typos in entering RNA sequence data
into the computer. They might only indicate that you need more
samples. Will be paying a lot of attention to them throughout class
both for what we can learn about biology and also because they can
cause trouble with your statistics.
Guess which states they are (florida and alaska).Center: typical
value of frozen personal pizza? ~$2.65
Spread: fuel efficiency 4, 8 cylinders4 cylinders: more spread8
cylinders: less spread
Other Graphical Methods for Economic DataTime plotsplot
observations in time order, with time on the horizontal axis and
the vari-able on the vertical axis** Time seriesmeasurements are
taken at regular intervals (monthly unemployment, quarterly GDP,
weather records, electricity demand, etc.)Heat Maps
Unemployment Rate, by Educational Attainment
Water Use During Super Bowl
Winning Times 100 M Dash
Numerical Summaries of Quantitative DataNumerical and More
Graphical Methods to Describe Univariate Data2 characteristics of a
data set to measurecentermeasures where the middle of the data is
locatedvariabilitymeasures how spread out the data isThe median: a
measure of centerGiven a set of n measurements arranged in order of
magnitude,Median=middle valuen oddmean of 2 middle values,n evenEx.
2, 4, 6, 8, 10; n=5; median=6Ex. 2, 4, 6, 8; n=4; median=(4+6)/2=5
Student Pulse Rates (n=62)38, 59, 60, 60, 62, 62, 63, 63, 64, 64,
65, 67, 68, 70, 70, 70, 70, 70, 70, 70, 71, 71, 72, 72, 73, 74, 74,
75, 75, 75, 75, 76, 77, 77, 77, 77, 78, 78, 79, 79, 80, 80, 80, 84,
84, 85, 85, 87, 90, 90, 91, 92, 93, 94, 94, 95, 96, 96, 96, 98, 98,
103Median = (75+76)/2 = 75.5Medians are used oftenYear 2014
baseball salariesMedian $1,450,000 (max=$28,000,000 Zack Greinke;
min=$500,000)Median fan age: MLB 45; NFL 43; NBA 41; NHL 39Median
existing home sales price: May 2011 $166,500; May 2010
$174,600Median household income (2008 dollars) 2009 $50,221; 2008
$52,029The median splits the histogram into 2 halves of equal
area
ExamplesExample: n = 717.5 2.8 3.2 13.9 14.1 25.3 45.8Example n
= 7 (ordered):2.8 3.2 13.9 14.1 17.5 25.3 45.8Example: n = 817.5
2.8 3.2 13.9 14.1 25.3 35.7 45.8Example n =8 (ordered)2.8 3.2 13.9
14.1 17.5 25.3 35.7 45.8
m = 14.1m = (14.1+17.5)/2 = 15.8Below are the annual tuition
charges at 7 public universities. What is the median tuition?
442949604960497152455546758652454965.549604971
Countdown10Below are the annual tuition charges at 7 public
universities. What is the median tuition?
442949605245554649715587758652454965.555464971
Countdown10Measures of SpreadThe range and interquartile
range
Ways to measure variabilityrange=largest-smallestOK sometimes;
in general, too crude; sensitive to one large or small data
valueThe range measures spread by examining the ends of the dataA
better way to measure spread is to examine the middle portion of
the data
m = median = 3.4Q1= first quartile = 2.3Q3= third quartile =
4.2
Quartiles: Measuring spread by examining the middleThe first
quartile, Q1, is the value in the sample that has 25% of the data
at or below it (Q1 is the median of the lower half of the sorted
data).
The third quartile, Q3, is the value in the sample that has 75%
of the data at or below it (Q3 is the median of the upper half of
the sorted data).49We are going to start out with a very general
way to describe the spread that doesnt matter whether it is
symmetric or not - quartiles. Just as the word suggests - quartiles
is like quarters or quartets, it involves dividing up the
distribution into 4 parts.Now, to get the median, we divided it up
into two parts. To get the quartiles we do the exact same thing to
the two halves.Use same rules as for median if you have even or odd
number of observations.Now, what an we do with these that helps us
understand the biology of these diseases?Quartiles and median
divide data into 4 pieces
Q1 M Q31/41/41/41/4Quartiles are common measures of
spreadhttp://oirp.ncsu.edu/ir/admit
http://oirp.ncsu.edu/univ/peer
University of Southern California
Economic Value of College Majors
Rules for Calculating QuartilesStep 1: find the median of all
the data (the median divides the data in half)
Step 2a: find the median of the lower half; this median is
Q1;Step 2b: find the median of the upper half; this median is
Q3.
Important:when n is odd include the overall median in both
halves;when n is even do not include the overall median in either
half.Example 2 4 6 8 10 12 14 16 18 20 n = 10
Median m = (10+12)/2 = 22/2 = 11
Q1 : median of lower half 2 4 6 8 10Q1 = 6
Q3 : median of upper half 12 14 16 18 20Q3 = 1611Quartile
example: odd no. of data valuesHRs hit by Babe Ruth in each season
as a Yankee54 59 35 41 46 25 47 60 54 46 49 46 41 34 22Ordered
values:22 25 34 35 41 41 46 46 46 47 49 54 54 59 60Median: value in
ordered position 8. median = 46
Lower half (including overall median):22 25 34 35 41 41 46
46
Upper half (including overall median):46 46 47 49 54 54 59
60
Pulse Rates n = 138
Median: mean of pulses in locations 69 & 70: median=
(70+70)/2=70Q1: median of lower half (lower half = 69 smallest
pulses); Q1 = pulse in ordered position 35;Q1 = 63Q3 median of
upper half (upper half = 69 largest pulses); Q3= pulse in position
35 from the high end; Q3=78Below are the weights of 31 linemen on
the NCSU football team. What is the value of the first quartile
Q1?#stemleaf22255423576242672571026257122759(4)28156715293559910303337314553215523361340
287257.5263.5262.5
Countdown10Interquartile rangelower quartile Q1middle quartile:
medianupper quartile Q3interquartile range (IQR)IQR = Q3 Q1measures
spread of middle 50% of the dataExample: beginning pulse ratesQ3 =
78; Q1 = 63
IQR = 78 63 = 15Below are the weights of 31 linemen on the NCSU
football team. The first quartile Q1 is 263.5. What is the value of
the
IQR?#stemleaf22255423576242672571026257122759(4)28156715293559910303337314553215523361340
23.539.54669.5
Countdown105-number summary of dataMinimum Q1 median Q3
maximum
Pulse data 45 63 70 78 111m = median = 3.4Q3= third quartile =
4.2Q1= first quartile = 2.3
Largest = max = 6.1Smallest = min = 0.6
Five-number summary:min Q1 m Q3 maxBoxplot: display of 5-number
summaryBOXPLOT61Add in a one other thing we know - the spread - the
largest and smallest values, and make a box plot.Now, why would you
want to make one of these? Boxplot: display of 5-number
summaryExample: age of 66 crush victims at rock concerts 1999-2000.
5-number summary:13 17 19 22 47
Boxplot construction1) construct box with ends located at Q1 and
Q3; in the box mark the location of median (usually with a line or
a +)2) fences are determined by moving a distance 1.5(IQR) from
each end of the box;2a) upper fence is 1.5*IQR above the upper
quartile2b) lower fence is 1.5*IQR below the lower quartileNote:
the fences only help with constructing the boxplot; they do not
appear in the final boxplot displayBox plot construction (cont.)3)
whiskers: draw lines from the ends of the box left and right to the
most extreme data values found within the fences; 4) outliers:
special symbols represent each data value beyond the fences;4a)
sometimes a different symbol is used for far outliers that are more
than 3 IQRs from the quartilesQ3= third quartile = 4.2Q1= first
quartile = 2.3
Largest = max = 7.9Boxplot: display of 5-number
summaryBOXPLOT
8Interquartile rangeQ3 Q1=4.2 2.3 = 1.9Distance to Q37.9 4.2 =
3.71.5 * IQR = 1.5*1.9=2.85. Individual #25 has a value of 7.9
years, which is 3.7 years above the third quartile. This is more
than 2.85 = 1.5*IQR above Q3. Thus, individual #25 is a suspected
outlier.65Add in a one other thing we know - the spread - the
largest and smallest values, and make a box plot.Now, why would you
want to make one of these? ATM Withdrawals by Day, Month,
Holidays
Beg. of class pulses (n=138)Q1 = 63, Q3 = 78IQR=78 63=15
1.5(IQR)=1.5(15)=22.5
Q1 - 1.5(IQR): 63 22.5=40.5
Q3 + 1.5(IQR): 78 + 22.5=100.570637840.5100.545Below is a box
plot of the yards gained in a recent season by the 136 NFL
receivers who gained at least 50 yards. What is the approximate
value of Q3 ?
0136273410547684821958109512321369Pass Catching Yards by
Receivers450750215545
Countdown10Rock concert deaths: histogram and boxplot
Automating Boxplot ConstructionExcel out of the box does not
draw boxplots.Many add-ins are available on the internet that give
Excel the capability to draw box plots.Statcrunch
(http://statcrunch.stat.ncsu.edu) draws box plots.Q3= third
quartile = 4.2Q1= first quartile = 2.3
Largest = max = 7.9Statcrunch Boxplot
72Add in a one other thing we know - the spread - the largest
and smallest values, and make a box plot.Now, why would you want to
make one of these? Tuition 4-yr Colleges
Statcrunch: 2012-13 NFL Salaries by Position
College Football Head Coach Salaries by Conference
2013 Major League Baseball Salaries by Team
End of General Numerical Summaries.Next: Numerical Summaries of
Symmetric Data
#StemLeaves
4*
34.588
95*001233444
105.5556788899
236*00011111122233333344444
236.55556666667777788888888
167*00000112222334444
237.55555666666777888888999
108*0000112224
108.5555667789
49*0012
29.58
410*0223
10.
111*1
Ht,flowersheightbinclassFrequencystemleavesheightheightwomanheightwomanheight58.264.04
big outliersFrequencyNumberNamePOSFeetInchesTotalBinUCI
womenClassUCI
mentotal=allflowerscompressNamefeetinchestotalinchesweightMenFrequencyMenAloneFrequencyclass,women,
men, no
outliersBinFrequencyBinwhitepinkred58.25757058258.258.264.0158.21464.059.564.55701Lisa
FaulknerG55655901012Jesse
Obrand627418557074158.25705910059.55858059559.559.564.5259.51564.560.764.15803Ashley
BigginsC64766001014Jerry
Green637519058075459.55806010060.759591607960.760.764.1360.71664.160.964.85914Katie
SturgeonF62746102028Jeff
Gloger637517559076260.75916120060.960601619960.960.964.8460.91764.861.965.260110Lisa
WoznickG511716202028DeVaughn
Peace637518060077260.96016220061.96161262224961.961.965.2561.91865.261.965.761211Jana
CiperovaG60726304045Aras
Baskauskas637518761078061.96126340061.9626226319961.961.965.7661.91965.762.266.262212Wendy
GabbeF511716404043Mike
Hood647619062079161.96226440062.26363464015862.262.266.2762.22066.262.266.763413Courtney
FergusonG56666513047Jeff
Hufford647617563080062.26346531062.264644652762.262.266.7862.22166.762.467.164414Kristen
GreenG58686622043Jordan
Harris657721764081162.26446622062.465653662762.462.467.1962.42267.162.967.865320Kimberly
MartinF60726702027Ross
Schraeder657718565082162.46546720062.966662671862.962.967.81062.92367.863.968.966221Erin
TomlinsonG59696812036Matt
Okoro677922266083162.96646821063.16767268963.163.968.91163.92468.963.169.667222Chanda
McLeodF511716911021J.R.
Christ698124567084163.16726911063.96868269663.963.169.61263.12569.663.974.068224Nina
HanG56667001012Stanislav
Zuzak6108222068085063.96837010063.96969163.963.91363.9n=2569134Brandy
HudsonF61737140042Ryan
Codi6118321069086163.96927104064.07070164.070142Cindy
OparahF511717230031Adam
Parada7084240mean700More064.07017203064.171More064.171044Christina
CallawayF607270.4666666667731001Dave
Korfman728627578.3333333333710this is for red
plants64.17147301064.57264.5720741012median72064.57237401164.87364.87307500447773064.87317500465.27465.274076102374165.27427601265.77565.775077002275465.77547700266.27666.276078040476266.27637800066.77766.777079001177266.77727900167.1median7867.178480000078067.17808000067.863.97967.8More081001179167.87918100168.9mean8068.982001180068.98008200169.663.98169.683001181169.68118300178.0821598.3sum840011821658218400178.08363.9average850000831768318500078.0mean
c out84860011841748418600178.065.98563.985071850median with
out868617286164.1More071More06668average69.672697166737172747575757576767777798182838486
Ht,flowers
FrequencyHeight in InchesNumber of WomenWomen's Height
birthweight
FrequencyHeight in InchesNumber of WomenWomen's Height + 4
myeloma
FrequencyBinFrequencyHeight of women on on UCI basketball
team
Sheet1
UCI womenClassUCI menHeight in inchesNumber of IndividualsHeight
of Class, Women's and Men's Teams
UCI womenClassHeight in inchesNumber of WomenWomen's Height:
Class and Team
FrequencyHeight in centimetersNumber of PlantsSize of
Red-flowered Plants
FrequencyHeight in centimetersNumber of PlantsHeight of All
Plants
whitepinkredHeight in centimetersNumber of PlantsHeight of
Plants by Color
lowerlimitupperlimitNpercentdiepercent
deadhttp://www.dhs.vic.gov.au/phb/hce/peri/pn/tables/t20.html5009993250.517854.77147100014993840.65113.28333150019997551.2567.426992000249924333.8572.34237625002999983215.2620.639770300034992373936.7540.2323685350039991973630.5350.18197014000449963209.8140.2263064500499910561.650.4710515000up1090.210.92108total64689
YrSinceDiagnosisPercentDeadThisYearOf25NMMyelomabinBinFrequencyNMdisease
xbinBinFrequencydisease x+outginBinFrequencytables
altered110.610.6110.610.6110.6110.21298110.2117110.61110.6111to
show221.221.2221.221.2221.2220.72164220.7225221.22241.2224even and
odd331.631.6331.631.6331.6330.83123330.8333331.63361.6336441.941.9441.941.9441.9440.9492440.9443441.94461.9446551.551.5551.551.5551.5551.0582551552551.55551.5555662.162.1662.162.1662.1661.0661661662662.16622.1662772.372.3772.372.3772.3771.0751771771772.3More12.3771882.382.3882.382.3862.3881.1830881.1880882.32.3880992.592.5992.592.5952.5991.2931991.2990992.52.599010102.8102.810102.8102.81042.810101.5102010101.51010110102.8average3.42916666672.81010011112.9112.911112.9112.91132.911111.6111111111.61111011112.9median3.42.91111012123.3123.3123.3123.31223.312121.8121112121.81212012123.43.412122133.4133.4133.4133.41313.4132.51310132.513130133.43.4More01413.6143.61413.6143.61423.61412.814101412.8141411413.63.61523.7153.71523.7153.71533.71522.815101522.815More01523.73.7average3.95925925931633.8163.81633.8163.81643.81633.516111633.51633.83.8median3.61743.9173.91743.9173.91753.91743.817101743.81743.93.91854.1184.11854.1184.11864.11854.02518541854.14.11964.2194.21964.2194.21974.21965.01965average3.3521964.24.22074.5204.52074.5204.52064.52075.02075median2.52074.54.52184.7214.72184.7214.72154.72185.12185.12184.74.72294.9224.92294.9224.92244.92295.52295.52294.94.923105.3235.323105.3235.32335.323107.02310723105.35.324115.6245.624115.6245.62425.6241110.024111024115.65.625126.1256.12516.1251214.025121425126.16.11212
IndividualsYears until deathYears until death after diagnosis
with disease X
IndividualsYears until deathYears until death after diagnosis
with disease X
FrequencyYears until deathNumber of IndividualsYears until death
after diagnosis with disease X
FrequencyYears until deathNumber of IndividualsYears until death
after diagnosis with disease X
FrequencyYears until deathNumber of IndividualsYears until death
after diagnosis with multiple myeloma
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&APage &P
normpdf000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
&APage &Pgeneralstandard
tpdfxstandard(df+1)/2ln[G((n+1)/2)]G((n+1)/2)df/2ln[G(n/2)]G(n/2)sqrt(np)1+x^2/n(1+x^2/n)^(-(n+1)/2)xstandardt
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&APage &P
tpdf000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
&APage &Pstandardt diststandard normal and t dist
normpdf
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&APage &P
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&APage &P
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&APage &P
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&APage &P
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&APage &P
#StemLeaves
4*
34.588
95*001233444
105.5556788899
236*00011111122233333344444
236.55556666667777788888888
167*00000112222334444
237.55555666666777888888999
108*0000112224
108.5555667789
49*0012
29.58
410*0223
10.
111*1
Ht,flowersheightbinclassFrequencystemleavesheightheightwomanheightwomanheight58.264.04
big outliersFrequencyNumberNamePOSFeetInchesTotalBinUCI
womenClassUCI
mentotal=allflowerscompressNamefeetinchestotalinchesweightMenFrequencyMenAloneFrequencyclass,women,
men, no
outliersBinFrequencyBinwhitepinkred58.25757058258.258.264.0158.21464.059.564.55701Lisa
FaulknerG55655901012Jesse
Obrand627418557074158.25705910059.55858059559.559.564.5259.51564.560.764.15803Ashley
BigginsC64766001014Jerry
Green637519058075459.55806010060.759591607960.760.764.1360.71664.160.964.85914Katie
SturgeonF62746102028Jeff
Gloger637517559076260.75916120060.960601619960.960.964.8460.91764.861.965.260110Lisa
WoznickG511716202028DeVaughn
Peace637518060077260.96016220061.96161262224961.961.965.2561.91865.261.965.761211Jana
CiperovaG60726304045Aras
Baskauskas637518761078061.96126340061.9626226319961.961.965.7661.91965.762.266.262212Wendy
GabbeF511716404043Mike
Hood647619062079161.96226440062.26363464015862.262.266.2762.22066.262.266.763413Courtney
FergusonG56666513047Jeff
Hufford647617563080062.26346531062.264644652762.262.266.7862.22166.762.467.164414Kristen
GreenG58686622043Jordan
Harris657721764081162.26446622062.465653662762.462.467.1962.42267.162.967.865320Kimberly
MartinF60726702027Ross
Schraeder657718565082162.46546720062.966662671862.962.967.81062.92367.863.968.966221Erin
TomlinsonG59696812036Matt
Okoro677922266083162.96646821063.16767268963.163.968.91163.92468.963.169.667222Chanda
McLeodF511716911021J.R.
Christ698124567084163.16726911063.96868269663.963.169.61263.12569.663.974.068224Nina
HanG56667001012Stanislav
Zuzak6108222068085063.96837010063.96969163.963.91363.9n=2569134Brandy
HudsonF61737140042Ryan
Codi6118321069086163.96927104064.07070164.070142Cindy
OparahF511717230031Adam
Parada7084240mean700More064.07017203064.171More064.171044Christina
CallawayF607270.4666666667731001Dave
Korfman728627578.3333333333710this is for red
plants64.17147301064.57264.5720741012median72064.57237401164.87364.87307500447773064.87317500465.27465.274076102374165.27427601265.77565.775077002275465.77547700266.27666.276078040476266.27637800066.77766.777079001177266.77727900167.1median7867.178480000078067.17808000067.863.97967.8More081001179167.87918100168.9mean8068.982001180068.98008200169.663.98169.683001181169.68118300178.0821598.3sum840011821658218400178.08363.9average850000831768318500078.0mean
c out84860011841748418600178.065.98563.985071850median with
out868617286164.1More071More06668average69.672697166737172747575757576767777798182838486
Ht,flowers
FrequencyHeight in InchesNumber of WomenWomen's Height
birthweight
FrequencyHeight in InchesNumber of WomenWomen's Height + 4
myeloma
FrequencyBinFrequencyHeight of women on on UCI basketball
team
Sheet1
UCI womenClassUCI menHeight in inchesNumber of IndividualsHeight
of Class, Women's and Men's Teams
UCI womenClassHeight in inchesNumber of WomenWomen's Height:
Class and Team
FrequencyHeight in centimetersNumber of PlantsSize of
Red-flowered Plants
FrequencyHeight in centimetersNumber of PlantsHeight of All
Plants
whitepinkredHeight in centimetersNumber of PlantsHeight of
Plants by Color
lowerlimitupperlimitNpercentdiepercent
deadhttp://www.dhs.vic.gov.au/phb/hce/peri/pn/tables/t20.html5009993250.517854.77147100014993840.65113.28333150019997551.2567.426992000249924333.8572.34237625002999983215.2620.639770300034992373936.7540.2323685350039991973630.5350.18197014000449963209.8140.2263064500499910561.650.4710515000up1090.210.92108total64689
YrSinceDiagnosisPercentDeadThisYearOf25NMMyelomabinBinFrequencyNMdisease
xbinBinFrequencydisease x+outginBinFrequencytables
altered110.610.6110.610.62516.1110.21298110.2117110.61110.6111to
show221.221.2221.221.22425.6220.72164220.7225221.22241.2224even and
odd331.631.6331.631.62335.3330.83123330.8333331.63361.6336441.941.9441.941.92244.9440.9492440.9443441.94461.9446551.551.5551.551.52154.7551.0582551552551.55551.5555662.162.1662.162.12064.5661.0661661662662.16622.1662772.372.3772.372.31974.2771.0751771771772.3More12.3771882.382.3882.382.31864.1881.1830881.1880882.32.3880992.592.5992.592.51753.9991.2931991.2990992.52.599010102.8102.810102.8102.81643.810101.5102010101.51010110102.8average3.42916666672.81010011112.9112.911112.9112.91533.711111.6111111111.61111011112.9median3.42.91111012123.3123.3123.3123.31423.612121.8121112121.81212012123.43.412122133.4133.4133.4133.41313.4132.51310132.513130133.43.4More01413.6143.61413.6143.61223.31412.814101412.8141411413.63.61523.7153.71523.7153.71132.91522.815101522.815More01523.73.7average3.95925925931633.8163.81633.8163.81042.81633.516111633.51633.83.8median3.61743.9173.91743.9173.9952.51743.817101743.81743.93.91854.1184.11854.1184.1862.31854.02518541854.14.11964.2194.21964.2194.2772.31965.01965average3.3521964.24.22074.5204.52074.5204.5662.12075.02075median2.52074.54.52184.7214.72184.7214.7551.52185.12185.12184.74.72294.9224.92294.9224.9441.92295.52295.52294.94.923105.3235.323105.3235.3331.623107.02310723105.35.324115.6245.624115.6245.6221.2241110.024111024115.65.625126.1256.1110.6251214.025121425126.16.11212
IndividualsYears until deathYears until death after diagnosis
with disease X
IndividualsYears until deathYears until death after diagnosis
with disease X
FrequencyYears until deathNumber of IndividualsYears until death
after diagnosis with disease X
FrequencyYears until deathNumber of IndividualsYears until death
after diagnosis with disease X
FrequencyYears until deathNumber of IndividualsYears until death
after diagnosis with multiple myeloma
Ht,flowersheightbinclassFrequencystemleavesheightheightwomanheightwomanheight58.264.04
big outliersFrequencyNumberNamePOSFeetInchesTotalBinUCI
womenClassUCI
mentotal=allflowerscompressNamefeetinchestotalinchesweightMenFrequencyMenAloneFrequencyclass,women,
men, no
outliersBinFrequencyBinwhitepinkred58.25757058258.258.264.0158.21464.059.564.55701Lisa
FaulknerG55655901012Jesse
Obrand627418557074158.25705910059.55858059559.559.564.5259.51564.560.764.15803Ashley
BigginsC64766001014Jerry
Green637519058075459.55806010060.759591607960.760.764.1360.71664.160.964.85914Katie
SturgeonF62746102028Jeff
Gloger637517559076260.75916120060.960601619960.960.964.8460.91764.861.965.260110Lisa
WoznickG511716202028DeVaughn
Peace637518060077260.96016220061.96161262224961.961.965.2561.91865.261.965.761211Jana
CiperovaG60726304045Aras
Baskauskas637518761078061.96126340061.9626226319961.961.965.7661.91965.762.266.262212Wendy
GabbeF511716404043Mike
Hood647619062079161.96226440062.26363464015862.262.266.2762.22066.262.266.763413Courtney
FergusonG56666513047Jeff
Hufford647617563080062.26346531062.264644652762.262.266.7862.22166.762.467.164414Kristen
GreenG58686622043Jordan
Harris657721764081162.26446622062.465653662762.462.467.1962.42267.162.967.865320Kimberly
MartinF60726702027Ross
Schraeder657718565082162.46546720062.966662671862.962.967.81062.92367.863.968.966221Erin
TomlinsonG59696812036Matt
Okoro677922266083162.96646821063.16767268963.163.968.91163.92468.963.169.667222Chanda
McLeodF511716911021J.R.
Christ698124567084163.16726911063.96868269663.963.169.61263.12569.663.974.068224Nina
HanG56667001012Stanislav
Zuzak6108222068085063.96837010063.96969163.963.91363.9n=2569134Brandy
HudsonF61737140042Ryan
Codi6118321069086163.96927104064.07070164.070142Cindy
OparahF511717230031Adam
Parada7084240mean700More064.07017203064.171More064.171044Christina
CallawayF607270.4666666667731001Dave
Korfman728627578.3333333333710this is for red
plants64.17147301064.57264.5720741012median72064.57237401164.87364.87307500447773064.87317500465.27465.274076102374165.27427601265.77565.775077002275465.77547700266.27666.276078040476266.27637800066.77766.777079001177266.77727900167.1median7867.178480000078067.17808000067.863.97967.8More081001179167.87918100168.9mean8068.982001180068.98008200169.663.98169.683001181169.68118300178.0821598.3sum840011821658218400178.08363.9average850000831768318500078.0mean
c out84860011841748418600178.065.98563.985071850median with
out868617286164.1More071More06668average69.672697166737172747575757576767777798182838486
Ht,flowers
FrequencyHeight in InchesNumber of WomenWomen's Height
birthweight
FrequencyHeight in InchesNumber of WomenWomen's Height + 4
myeloma
FrequencyBinFrequencyHeight of women on on UCI basketball
team
Sheet1
UCI womenClassUCI menHeight in inchesNumber of IndividualsHeight
of Class, Women's and Men's Teams
UCI womenClassHeight in inchesNumber of WomenWomen's Height:
Class and Team
FrequencyHeight in centimetersNumber of PlantsSize of
Red-flowered Plants
FrequencyHeight in centimetersNumber of PlantsHeight of All
Plants
whitepinkredHeight in centimetersNumber of PlantsHeight of
Plants by Color
lowerlimitupperlimitNpercentdiepercent
deadhttp://www.dhs.vic.gov.au/phb/hce/peri/pn/tables/t20.html5009993250.517854.77147100014993840.65113.28333150019997551.2567.426992000249924333.8572.34237625002999983215.2620.639770300034992373936.7540.2323685350039991973630.5350.18197014000449963209.8140.2263064500499910561.650.4710515000up1090.210.92108total64689
YrSinceDiagnosisPercentDeadThisYearOf25NMMyelomabinBinFrequencyNMdisease
xbinBinFrequencydisease x+outginBinFrequencytables
altered110.610.6110.610.62517.9110.21298110.2117110.61110.6111to
show221.221.2221.221.22426.1220.72164220.7225221.22241.2224even and
odd331.631.6331.631.62335.3330.83123330.8333331.63361.6336441.941.9441.941.92244.9440.9492440.9443441.94461.9446551.551.5551.551.52154.7551.0582551552551.55551.5555662.162.1662.162.12064.5661.0661661662662.16622.1662772.372.3772.372.31974.2771.0751771771772.3More12.3771882.382.3882.382.31864.1881.1830881.1880882.32.3880992.592.5992.592.51753.9991.2931991.2990992.52.599010102.8102.810102.8102.81643.810101.5102010101.51010110102.8average3.42916666672.81010011112.9112.911112.9112.91533.711111.6111111111.61111011112.9median3.42.91111012123.3123.3123.3123.31423.612121.8121112121.81212012123.43.412122133.4133.4133.4133.41313.4132.51310132.513130133.43.4More01413.6143.61413.6143.61223.31412.814101412.8141411413.63.61523.7153.71523.7153.71132.91522.815101522.815More01523.73.7average3.95925925931633.8163.81633.8163.81042.81633.516111633.51633.83.8median3.61743.9173.91743.9173.9952.51743.817101743.81743.93.91854.1184.11854.1184.1862.31854.02518541854.14.11964.2194.21964.2194.2772.31965.01965average3.3521964.24.22074.5204.52074.5204.5662.12075.02075median2.52074.54.52184.7214.72184.7214.7551.52185.12185.12184.74.72294.9224.92294.9224.9441.92295.52295.52294.94.923105.3235.323105.3235.3331.623107.02310723105.35.324115.6245.624115.6245.6221.2241110.024111024115.65.625126.1256.1110.6251214.025121425126.16.11212
IndividualsYears until deathYears until death after diagnosis
with disease X
IndividualsYears until deathYears until death after diagnosis
with disease X
FrequencyYears until deathNumber of IndividualsYears until death
after diagnosis with disease X
FrequencyYears until deathNumber of IndividualsYears until death
after diagnosis with disease X
FrequencyYears until deathNumber of IndividualsYears until death
after diagnosis with multiple myeloma
Ht,flowersheightbinclassFrequencystemleavesheightheightwomanheightwomanheight58.264.04
big outliersFrequencyNumberNamePOSFeetInchesTotalBinUCI
womenClassUCI
mentotal=allflowerscompressNamefeetinchestotalinchesweightMenFrequencyMenAloneFrequencyclass,women,
men, no
outliersBinFrequencyBinwhitepinkred58.25757058258.258.264.0158.21464.059.564.55701Lisa
FaulknerG55655901012Jesse
Obrand627418557074158.25705910059.55858059559.559.564.5259.51564.560.764.15803Ashley
BigginsC64766001014Jerry
Green637519058075459.55806010060.759591607960.760.764.1360.71664.160.964.85914Katie
SturgeonF62746102028Jeff
Gloger637517559076260.75916120060.960601619960.960.964.8460.91764.861.965.260110Lisa
WoznickG511716202028DeVaughn
Peace637518060077260.96016220061.96161262224961.961.965.2561.91865.261.965.761211Jana
CiperovaG60726304045Aras
Baskauskas637518761078061.96126340061.9626226319961.961.965.7661.91965.762.266.262212Wendy
GabbeF511716404043Mike
Hood647619062079161.96226440062.26363464015862.262.266.2762.22066.262.266.763413Courtney
FergusonG56666513047Jeff
Hufford647617563080062.26346531062.264644652762.262.266.7862.22166.762.467.164414Kristen
GreenG58686622043Jordan
Harris657721764081162.26446622062.465653662762.462.467.1962.42267.162.967.865320Kimberly
MartinF60726702027Ross
Schraeder657718565082162.46546720062.966662671862.962.967.81062.92367.863.968.966221Erin
TomlinsonG59696812036Matt
Okoro677922266083162.96646821063.16767268963.163.968.91163.92468.963.169.667222Chanda
McLeodF511716911021J.R.
Christ698124567084163.16726911063.96868269663.963.169.61263.12569.663.974.068224Nina
HanG56667001012Stanislav
Zuzak6108222068085063.96837010063.96969163.963.91363.9n=2569134Brandy
HudsonF61737140042Ryan
Codi6118321069086163.96927104064.07070164.070142Cindy
OparahF511717230031Adam
Parada7084240mean700More064.07017203064.171More064.171044Christina
CallawayF607270.4666666667731001Dave
Korfman728627578.3333333333710this is for red
plants64.17147301064.57264.5720741012median72064.57237401164.87364.87307500447773064.87317500465.27465.274076102374165.27427601265.77565.775077002275465.77547700266.27666.276078040476266.27637800066.77766.777079001177266.77727900167.1median7867.178480000078067.17808000067.863.97967.8More081001179167.87918100168.9mean8068.982001180068.98008200169.663.98169.683001181169.68118300178.0821598.3sum840011821658218400178.08363.9average850000831768318500078.0mean
c out84860011841748418600178.065.98563.985071850median with
out868617286164.1More071More06668average69.672697166737172747575757576767777798182838486
Ht,flowers
FrequencyHeight in InchesNumber of WomenWomen's Height
birthweight
FrequencyHeight in InchesNumber of WomenWomen's Height + 4
myeloma
FrequencyBinFrequencyHeight of women on on UCI basketball
team
Sheet1
UCI womenClassUCI menHeight in inchesNumber of IndividualsHeight
of Class, Women's and Men's Teams
UCI womenClassHeight in inchesNumber of WomenWomen's Height:
Class and Team
FrequencyHeight in centimetersNumber of PlantsSize of
Red-flowered Plants
FrequencyHeight in centimetersNumber of PlantsHeight of All
Plants
whitepinkredHeight in centimetersNumber of PlantsHeight of
Plants by Color
lowerlimitupperlimitNpercentdiepercent
deadhttp://www.dhs.vic.gov.au/phb/hce/peri/pn/tables/t20.html5009993250.517854.77147100014993840.65113.28333150019997551.2567.426992000249924333.8572.34237625002999983215.2620.639770300034992373936.7540.2323685350039991973630.5350.18197014000449963209.8140.2263064500499910561.650.4710515000up1090.210.92108total64689
YrSinceDiagnosisPercentDeadThisYearOf25NMMyelomabinBinFrequencyNMdisease
xbinBinFrequencydisease x+outginBinFrequencytables
altered110.610.6110.610.62517.9110.21298110.2117110.61110.6111to
show221.221.2221.221.22426.1220.72164220.7225221.22241.2224even and
odd331.631.6331.631.62335.3330.83123330.8333331.63361.6336441.941.9441.941.92244.9440.9492440.9443441.94461.9446551.551.5551.551.52154.7551.0582551552551.55551.5555662.162.1662.162.12064.5661.0661661662662.16622.1662772.372.3772.372.31974.2771.0751771771772.3More12.3771882.382.3882.382.31864.1881.1830881.1880882.32.3880992.592.5992.592.51753.9991.2931991.2990992.52.599010102.8102.810102.8102.81643.810101.5102010101.51010110102.8average3.42916666672.81010011112.9112.911112.9112.91533.711111.6111111111.61111011112.9median3.42.91111012123.3123.3123.3123.31423.612121.8121112121.81212012123.43.412122133.4133.4133.4133.41313.4132.51310132.513130133.43.4More01413.6143.61413.6143.61223.31412.814101412.8141411413.63.61523.7153.71523.7153.71132.91522.815101522.815More01523.73.7average3.95925925931633.8163.81633.8163.81042.81633.516111633.51633.83.8median3.61743.9173.91743.9173.9952.51743.817101743.81743.93.91854.1184.11854.1184.1862.31854.02518541854.14.11964.2194.21964.2194.2772.31965.01965average3.3521964.24.22074.5204.52074.5204.5662.12075.02075median2.52074.54.52184.7214.72184.7214.7551.52185.12185.12184.74.72294.9224.92294.9224.9441.92295.52295.52294.94.923105.3235.323105.3235.3331.623107.02310723105.35.324115.6245.624115.6245.6221.2241110.024111024115.65.625126.1256.1110.6251214.025121425126.16.11212
IndividualsYears until deathYears until death after diagnosis
with disease X
IndividualsYears until deathYears until death after diagnosis
with disease X
FrequencyYears until deathNumber of IndividualsYears until death
after diagnosis with disease X
FrequencyYears until deathNumber of IndividualsYears until death
after diagnosis with disease X
FrequencyYears until deathNumber of IndividualsYears until death
after diagnosis with multiple myeloma