u4 c 1.2 dot plot and histogram 2 - ms fuentes math...

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


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


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)


(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

Page 1Page 2Page 3Page 4Attachments Page 1

u4 c 1.2 dot plot and histogram 2 - ms fuentes math...

Documents