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U4C1.2DotplotandHistogram2 January1516,2015
U4:C1.1DotPlotsandHistograms
Objective: Wewillbeabletorepresentdatawithplotsontherealnumberline,using: DotPlots Histogramsandcomparetwosetsofdataonthesamegraphtomakeadecision.
CCSS.912.SID.1
Vocabulary
Histogramsisaspecialtypeofbargraph.Thehorizontalaxisrepresentsarangeofvalues,calledaninterval,instead ofa
singlevalueorcategory.Theverticalaxis representsthefrequencyofdatavaluesinaequal interval.
DotPlotIncludesallvaluesfromtherangeofthedataandplotsapointfor eachoccurrenceofan
observedvalueonanumberline.
WhichofthefollowingtwographisaDotPlotandHistogram?Howdoyouknow?
Vocabulary
OutlierAdatapointoranobservationthatiswelloutsideoftheexpectedrangeofvalues.
equalintervalsofnumericaldataHorizontalAxis
VerticalAxis
frequency
MinimumThesmallestnumberinafinitesetofnumbers.Avalueofafunctionthatislessthananyothervalueofthefunctionovera specific
interval.
Vocabulary
Maximumisthelargestorthegreatestvalue,quantityinasetofdata.Theperiodofhighest,greatest,overaspecificinterval.
FrequencyHowoftensomethinghappens(usuallyduringaperiodoftime).
Intervalsspacebetweentwounits,setofnumbersconsistingofallnumbersbetweenthem.
(upperextreme)
(lowerextreme)
Waystodescribepatternofdistributionare:
Spreaddatathedegreetowhichdataarespreadoutaroundtheircenter.
MeasuresofCenter(Location) ShapeSpread(variation)
Mean Median Mode
Range Variance StandardDeviation
SkewnessPositively/RightskewedNegative/LeftSkewed
http://bobhall.tamu.edu/FiniteMath/Module8/Introduction.html
U4C1.2DotplotandHistogram2 January1516,2015
Vocabulary
MeanThemostcommonnumberinthedistribution.Tocalculateit,addupthevaluesofalltermsandthendividebythenumberofterms.
MedianIfthenumberoftermsisodd,thenthemedianisthenumberinthemiddlefromanorderedset.Ifthenumberoftermsiseven,thenthemedianistheaverageofthetwonumbersinthemiddle.
Centerislocatedatthemedianofthedistribution.Thisisthepointinagraphicdisplaywhereabouthalfoftheobservationsareoneitherside.Inthecharttobelowthe
observationsarecenteredover4.
Mode
VocabularySpreadreferstothedistributionofthedata.Iftheobservationcoverawiderage,the
spreadislarge.Iftheobservationareclusteredaroundasinglevalue,thespreadissmaller.
Rangethegreatestvaluessubtractedfromtheleastvaluesinthedistribution.
VariationTheextenttowhichdatapointsaredistributionordatasetdivergefromthemeanvalue.Variabilityalsoreferstotheextenttowhichthesedatapointsdifferfromeachother(alot,littleornone).
StandardDeviation
ShapedistributionisdescribedbythefollowingcharacteristicsSymmetry,Skewness,Uniform.
Vocabulary
Mostmeasurementsfallinthemiddle,andfewerfallatpointsfartherawayfromthemiddle.
Symmetry.Asymmetricdistributioncanbedividedatthecentersothateachhalfisamirrorimageoftheother.
Skewness.Tails:Thethinnerendsofadistributionarecalledtails.Ifonetailstretchesoutfartherthantheotherthehistogramissaidtobeskewedtothesideofthelongertail.
Vocabulary
Tail Tail
UniformWhentheobservationsinasetofdataareequallyspreadacrosstherangeofthedistributionitiscalledauniformdistribution.Auniformdistributionhasnoclearpeaks.
VocabularyDOTPLOTS
Step1:Labelyouraxisandtitleyour
graph.Drawahorizontallineandlabelit
withthevariable.Titleyourgraph
Step2:Scaletheaxisbasedonthe
valuesofthevariable
Step3:Markadotabovethenumberon
thehorizontalaxiscorrespondingtoeach
datavalue.Numberofrescueddogs
DogsrescuedbyASPCAShelters
0 5 1015202530
U4C1.2DotplotandHistogram2 January1516,2015
Datawascollectedontheaveragerestingheartrateofthestudentstakingathletics.Createadotplotfortheheartbeatdata:
1)Drawanumberlinethatspansthedata2)Placeadotforeachofthedataentries3)Titlethegraph.
67 65 71 63 64 58 100100 73 63 70 72 72 48969864
686562
74
7363
576957
757054
637562Describetheoverallpatternofthedata.
Watch&Listen#1
ThenumberofgoalsscoredbyeachteaminthefirstroundoftheCaliforniaSouthernSectionDivisionVhighschoolsoccerplayoffsisshowninthefollowingtable.
5 0 1 0 7 2 1 0 4
0 3 0 2 0 3 1 5 0
3 0 1 0 1 0 2 0 3
wedoExample2
Createadotplotfortheabovedataanddescribetheoverallpatternofdata.
ThistableshowsapproximatelyhowlongittookmembersofAlicia'smathclasstocompleteacrossnumberpuzzle.a)Showthisdataonadotplot.b)Whatistherangeofthedata?
UdoExample3
Thestudentsinonesocialstudiesclasswereaskedhowmanybrothersandsisters(siblings)theyeachhave.Thedotplothereshowstheresults.a)Howmanyofthestudentshavesixsiblings?
b)Howmanyofthestudentshavenosiblings?
c)Howmanyofthestudentshavethreeormoresiblings?
#ofSiblings
SocialStudiesClass(Siblings)
UdoExample4
Step1. Draw the axes. Label the vertical axis. Choose an appropriate scale and mark equal intervals.
Step2. Label horizontal axis and list the age intervals.
Step3. Draw a bar for each age interval. Do not leave spaces between the bars.
Step4. Give the graph a title.
20181614121086420
09 1019
2029
3039
4049
505
960
69
Ahistogramislikeabargraphbutwithnospacesbetweenthebars.
Histogram
HowtofindtheIntervalwidth?
Howtofind#Interval?
(howmany#'sinthedataset)#ofintervals=#ofintervals=
(howmany#'sinthedataset) (Roundtheanswerup)
Range#ofintervals
Intervalwidth= (Roundtheanswerup)
U4C1.2DotplotandHistogram2 January1516,2015
(howmany#'sinthedataset)#ofintervals=
Range#ofintervals
Intervalwidth =
ExampleManycommunitiesaddfluoridetowatertopreventtoothdecay.Ina25dayperiod,theselevelsoffluorideweremeasured:
75,86,84,85,97,94,89,84,83,89,88,78,77,76,82,72,92,105,94,83,81,85,97,93,79
Findtheintervalwidthfortheabovedataandfrequency.
levelsoffluoride
Count,frequency
#ofHeartbeats
Count,frequency
4554556465747584859495104
21113204
Describethehistogram'sshape,spread,andcenter.Howdoesthehistogramcomparetothedotplotdrawnbefore?
Histograms:Watch&Listen#5
The20062007LivingstonHighSchoolVarsityBoysbasketballteamhadanexcellentseason,compilingarecordof155(15winsand5losses).Thetotalpointsscoredbytheteamforeachofthe20gamesarelistedbelowintheorderinwhichthegameswereplayed:
76,55,76,64,46,91,65,46,45,53,56,53,57,67,62,64,67,52,58,62
(a)Completethefrequencytablebelow.(b)Onthegraphgridprovided,createahistogramusingthefrequencytablefrom(a)above.
wedoExample6
Thefollowingsetofdatarepresentsthescoresonamathematicsquiz:
58,79,81,99,68,92,76,84,53,57,81,91,77,50,65,57,51,72,84,89
Completethefrequencytablebelowand,ontheaccompanyinggrid,drawandlabelafrequencyhistogramofthesescores.
(a)Inwhatintervaldoesthemedianofthisdatasetlie?
(b)Describethehistogram.
UdoExample7
Attachments
U4C1.1DotPlotsandHistogramswks.docx
Unit4VocabularyforDotplotandHistogram.docx
U4:C 1.1 Dot Plot & HistogramsName:_______________________________ Per______
Assignment #20
1) Suppose the property taxes for 12 families are given below:
$800$1150 $100 $1000 $950 $800 $1050 $1050 $500 $800 $1050 $ 1150
a) Make a dot plot of the data.
b) Find the Median.
c) Find the range.
d) Find the interquartile range.
e) Are there any outliers, how do you know?
2) Create a histogram for the set of data. The frame is set up for you.
Chocolate candies per bag of trail mix:
504211945683267111613175
39626449555133117966482
Frequency table:
Interval
# of value
3) The following data consists of the weights, in pounds, of 30 Algebra 1 students:
195, 206, 100, 98, 150, 210, 195, 106, 195,168, 180, 212, 104, 195, 100, 216, 195, 209,112, 99, 206, 116, 195, 100, 142, 100, 135,98, 160, 155
Using the data, complete the frequency table and construct histogram on the grid below.
Interval
Frequency
4) Make a dot plot and histogram for theses 32 observations on the number of customers to use a downtown CitiBank ATM during the noon hours on 32 consecutive workdays. Describe its appearance.
SMART Notebook
Unit 4: Dot Plots and Histogram Vocabulary
VOCABULARY
Dot Plot-
Includes all values from the range of the data and plots a point for each occurrence of an observed value on a number line.
Histograms
is a special type of bar graph. The horizontal axis represents a range of values, called an interval, instead of a single value or category. The vertical axis represents the frequency of data values in an equal interval.
Horizontal
Axis
equal intervals of numerical data
Vertical
Axis
frequency
Outlier
A data point or an observation that is well outside of the expected range of values.
Intervals
space between two units, set of numbers consisting of all numbers between them.
Mximum
(upper extreme)
is the largest or the greatest value, quantity in a set of data. The period of highest, greatest, over a specific interval.
Minimum
(lower extreme)
The smallest number in a finite set of numbers. A value of a function that is less than any other value of the function over a specific interval.
Frequency
How often something happens (usually during a period of time).
Center
is located at the median of the distribution. This is the point in a graphic display where about half of the observations are on either side. In the chart to below the observations are centered over 4.
Mean
The most common number in the distribution. To calculate it, add up the values of all terms and then divide by the number of terms.
Median
If the number of terms is odd, then the median is the number in the middle from an ordered set. If the number of terms is even, then the median is the average of the two numbers in the middle.
Spread
refers to the distribution of the data. If the observation cover a wide rage, the spread is large. If the observation are clustered around a single value, the spread is smaller.
Range
the greatest values subtracted from the least values in the distribution.
Variation
The extent to which data points are distribution or data set diverge from the mean value. Variability also refers to the extent to which these data points differ from each other (a lot, little or none).
Standard Deviation
Shape
distribution is described by the following characteristics
Symmetry, Skewness, Uniform.
Symmetry.
A symmetric distribution can be divided at the center so that each half is a mirror image of the other.
Skewness.
Tails: The thinner ends of a distribution are called tails. If one tail stretches out farther than the other the histogram is said to be skewed to the side of the longer tail.
Uniform
When the observations in a set of data are equally spread across the range of the distribution it is called a uniform distribution. A uniform distribution has no clear peaks.
SMART Notebook
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