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VISUALIZING DATA
Section 2-3
Inthissection,wewilllearnhowtovisualize
datawithahistogram.Thegoalisnotsimply
toconstructthegraphs– butrathertolearn
somethingaboutthedataandunderstandthe
natureoftheirdistributions.
Histograms
HISTOGRAMS
Ahistogram isagraphconsistingofbarsof
equalwidthdrawnadjacenttoeachother
(unlesstherearegapsinthedata).The
horizontalscalerepresentsclassesof
quantitativedatavaluesandtheverticalscale
representsfrequencies.Theheightsofthebars
correspondtothefrequencyvalues.
QWERTY WORD RATING RELATIVE
FREQUENCY HISTOGRAM
QWERTY WORD RATING
FREQUENCY HISTOGRAM
Rating Frequency
0-2
20
3-5
14
6-8
15
9 - 11
2
12 - 14
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HISTOGRAM AND RELATIVE
FREQUENCY HISTOGRAM
Relative
Rating Frequency
0-2
38.5%
3-5
26.9%
6-8
28.8%
9 - 11
3.8%
12 - 14
1.9%
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DRAWING A FREQUENCY HISTOGRAM
FROM RAW DATA ON THE TI-83/84
1.
2.
3.
4.
5.
6.
7.
8.
PressSTAT;select1:Edit….
EnteryourdatavaluesinL1.(Note:Youcouldenter
theminadifferentlist.)
PressWINDOW.SetXmin tothelowerclassboundary
ofthefirstclass;setXmax totheupperclassboundary
ofthelastclass;andsetXscl totheclasswidth.(Note:
YoumayneedtosetYmin andYmax toseethe
histogram.)
Press2ND,Y= (forSTATPLOT).Select1:Plot1.
TurntheplotON.ForType,selectthehistogram(last
oneonfirstrow).
ForXlist,enterL1bypressing2ND,1.
ForFreq,enterthenumber1.
PressGRAPH.
DRAWING A FREQUENCY HISTOGRAM
FROM A FREQUENCY DISTRIBUTION ON
THE TI-83/84
1.
2.
3.
4.
5.
6.
7.
8.
9.
Computethemidpointofeachclass.
PressSTAT;select1:Edit….
EnterthemidpointsinL1 andthefrequencyfortheclass
inL2.
Press WINDOW.SetXmin tothelowerclassboundary
ofthefirstclass;setXmax totheupperclassboundary
ofthelastclass;andsetXscl totheclasswidth.(Note:
YoumayneedtosetYmin andYmax toseethe
histogram.)
Press2ND,Y= (forSTATPLOT).Select1:Plot1.
TurntheplotON.ForType,selectthehistogram(last
oneonfirstrow).
ForXlist,enterL1bypressing2ND,1.
ForFreq,enterL2bypressing2ND,2.
PressGRAPH.
CRITICALLY THINKING:
INTERPRETING HISTOGRAMS
COMMON DISTRIBUTION
SHAPES
Onekeycharacteristicofanormaldistribution
isthatithasa“bell”shape.Thehistogram
belowillustratesthis.
Inadditiontothebell‐shaped(normal
distribution),therearesomeothercommon
distributionshapes:
• Uniform
• Skewedtotheright
• Skewedtotheleft
BELL-SHAPED (NORMAL)
DISTRIBUTION
Inabell‐shaped(normal)distribution,(1)the
frequenciesincreasetoamaximumandthen
decrease,and(2)thegraphhassymmetry,withthe
lefthalfofthehistogrambeingroughlyamirror
imageoftherighthalf.
UNIFORM DISTRIBUTION
Withauniformdistribution,thedifferentpossible
valuesoccurwithapproximatelythesame
frequency,sotheheightsofthebarsonthe
histogramareapproximatelyuniform.
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SKEWED TO THE RIGHT
SKEWED TO THE LEFT
Dataskewedtotheright (alsocalled
positivelyskewed)havealongrighttail.
Dataskewedtotheleft (alsocalled
negativelyskewed)havealonglefttail.
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