Chapter2:FrequencyDistributionandGraphsSection1:OrganizingDataWorksheet

1. Thefollowingareclassesforagroupedfrequencydistribution.Findthelowerandupperclasslimitofthenextclassthatwouldfollow.Findtheclassboundariesandclasswidth.

a. 32–38Noticethatthelimits(lowerlimitis32,upperlimitis38)areinwholenumbers.

b. 86–104

c. 895–905

32.0 38-0.5+0.531.5–38.5

Limitsarewhole#s,soboundariesshouldbeonemoreadd’lplacevalue(tenths)andendin5.

Findingtheboundaries:Sincelimitisinwhole#,wesubtract/add0.5(5tenths)from/tothelimits.

32–3839-45

Findingthelimitsforthenextclass:

Addtheclasswidthtothelimitsoftheclasstogetthelimitsforthenextclass.Noticethatthelimitsareinwhole#s.andthenextwhole#after38(upperlimitoftheclass)is39(lowerlimitofthenextclass).

Findingtheclasswidth:

38.5-31.57

Subtractthelowerboundaryfromtheupperboundary.Noticetthewidthisalsoawhole#.

Youcanalsofindtheclasswidthbysubtractingthelower/upperlimitsfromtwoadjacentclasses.

39-327

45-387

or

Noticethatthelimits(lowerlimitis86,upperlimitis104)areinwholenumbers

Findingtheboundaries:

86 104-0.5+0.585.5–104.5

Sincelimitisinwhole#,wesubtract/add0.5(5tenths)from/tothelimits.

Limitsarewhole#s,soboundariesshouldbeonemoreadd’lplacevalue(tenths)andendin5.

Findingtheclasswidth:

104.5-86.519

Subtractthelowerboundaryfromtheupperboundary.

Youcanalsofindtheclasswidthbysubtractingthelower/upperlimitsfromtwoadjacentclasses.

105-8619

or123-10419

Addtheclasswidthtothelimitsoftheclasstogetthelimitsforthenextclass.Noticethatthelimitsareinwhole#s.andthenextwhole#after104(upperlimitoftheclass)is105(lowerlimitofthenextclass).

86–104105-123

Findingthelimitsforthenextclass:

Noticethatthelimits(lowerlimitis895,upperlimitis905)areinwholenumbers

Findingtheboundaries:

895 905-0.5+0.5894.5–905.5

Sincelimitisinwhole#,wesubtract/add0.5(5tenths)from/tothelimits.

Limitsarewhole#s,soboundariesshouldbeonemoreadd’lplacevalue(tenths)andendin5.

Findingtheclasswidth:

905.5-894.511

Subtractthelowerboundaryfromtheupperboundary.

Youcanalsofindtheclasswidthbysubtractingthelower/upperlimitsfromtwoadjacentclasses.

906-89511

or916-90511

Addtheclasswidthtothelimitsoftheclasstogetthelimitsforthenextclass.Noticethatthelimitsareinwhole#s.andthenextwhole#after905(upperlimitoftheclass)is906(lowerlimitofthenextclass).

895–905906-916

Findingthelimitsforthenextclass:

d. 12.3–13.5

e. 32.4–40.0

f. 67.8–78.9

g. 8.67–15.39

Noticethatthelimits(lowerlimitis12.3,upperlimitis13.5)haveonedecimalplacevalue(tenths).

Findingtheboundaries:

12.3 13.5-0.05+0.0512.25–13.55

Sincelimithasonedecimalplacevalue(tenths),wesubtract/add0.05(5hundredths)from/tothelimits.

Limitshavedecimalplacevalue(tenths),soboundariesshouldbeonemoreadd’lplacevalue(hundredths)andendin5.

Findingtheclasswidth:

13.55-12.251.3

Subtractthelowerboundaryfromtheupperboundary.

Youcanalsofindtheclasswidthbysubtractingthelower/upperlimitsfromtwoadjacentclasses.

13.6-12.31.3

or14.8-13.51.3

Addtheclasswidthtothelimitsoftheclasstogetthelimitsforthenextclass.Noticethatthelimitsareinthetenths.Andthenexttenthsafter13.5(upperlimitoftheclass)is13.6(lowerlimitofthenextclass).

12.3–13.513.6–14.8

Findingthelimitsforthenextclass:

Noticethatthelimits(lowerlimitis67.8,upperlimitis78.9)haveonedecimalplacevalue(tenths).

Findingtheboundaries:

67.878.9-0.05+0.0567.75-78.95

Sincelimithasonedecimalplacevalue(tenths),wesubtract/add0.05(5hundredths)from/tothelimits.

Limitshavedecimalplacevalue(tenths),soboundariesshouldbeonemoreadd’lplacevalue(hundredths)andendin5.

Findingtheclasswidth:

78.95-67.7511.2

Subtractthelowerboundaryfromtheupperboundary.

Youcanalsofindtheclasswidthbysubtractingthelower/upperlimitsfromtwoadjacentclasses.

79.0-67.811.2

or90.1-78.911.2

Addtheclasswidthtothelimitsoftheclasstogetthelimitsforthenextclass.Noticethatthelimitsareinthetenths.Andthenexttenthsafter78.9(upperlimitoftheclass)is79.0(lowerlimitofthenextclass).

67.8–78.979.0–90.1

Findingthelimitsforthenextclass:

Noticethatthelimits(lowerlimitis32.4,upperlimitis40.0)haveonedecimalplacevalue(tenths).

Findingtheboundaries:

32.4 40.0-0.05+0.0532.35-40.05

Sincelimithasonedecimalplacevalue(tenths),wesubtract/add0.05(5hundredths)from/tothelimits.

Limitshavedecimalplacevalue(tenths),soboundariesshouldbeonemoreadd’lplacevalue(hundredths)andendin5.

Findingtheclasswidth:

40.05-32.357.7

Subtractthelowerboundaryfromtheupperboundary.

Youcanalsofindtheclasswidthbysubtractingthelower/upperlimitsfromtwoadjacentclasses.

40.1-32.47.7

or47.7-40.07.7

Addtheclasswidthtothelimitsoftheclasstogetthelimitsforthenextclass.Noticethatthelimitsareinthetenths.Andthenexttenthsafter40.0(upperlimitoftheclass)is40.1(lowerlimitofthenextclass).

32.4–40.040.1–47.7

Findingthelimitsforthenextclass:

Noticethatthelimits(lowerlimitis8.67,upperlimitis15.39)havetwodecimalplacevaluesandendinthehundredths.(tenths).

Findingtheboundaries:

8.6715.39-0.005+0.0058.665–15.395

Sincelimithastwodecimalplacevalue(hundredths),wesubtract/add0.005(5thousandths)from/tothelimits.

Limitshavetwodecimalplacevalue(hundredths),soboundariesshouldbeonemoreadd’lplacevalue(thousandths)andendin5.

Findingtheclasswidth:

15.395-8.6656.73

Subtractthelowerboundaryfromtheupperboundary.

Youcanalsofindtheclasswidthbysubtractingthelower/upperlimitsfromtwoadjacentclasses.

15.40-8.676.73

or22.12-15.396.73

Addtheclasswidthtothelimitsoftheclasstogetthelimitsforthenextclass.Noticethatthelimitsareinthehundredths.Andthenexthundredthsafter15.39(upperlimitoftheclass)is15.40(lowerlimitofthenextclass).

8.67–15.3915.40–22.12

Findingthelimitsforthenextclass:

h. 4.65–5.20

i. 3.18–4.96

2. Shownherearethreefrequencydistributions.Eachisincorrectlyconstructed.Statethereason(s)why.

a. Class Frequency 27–32 1

33–38 0

39–44 6

45–49 4

50–55 2

b.

Class Frequency 5–9 1

9–13 2

13–17 5

17–20 6

20–24 3

Noticethatthelimits(lowerlimitis4.65,upperlimitis5.20)havetwodecimalplacevaluesandendinthehundredths.(tenths).

Findingtheboundaries:

4.655.20-0.005+0.0054.645–5.205

Sincelimithastwodecimalplacevalue(hundredths),wesubtract/add0.005(5thousandths)from/tothelimits.

Limitshavetwodecimalplacevalue(hundredths),soboundariesshouldbeonemoreadd’lplacevalue(thousandths)andendin5.

Findingtheclasswidth:

5.205-4.6450.56

Subtractthelowerboundaryfromtheupperboundary.

Youcanalsofindtheclasswidthbysubtractingthelower/upperlimitsfromtwoadjacentclasses.

5.21-4.650.56

or5.76-5.200.56

Addtheclasswidthtothelimitsoftheclasstogetthelimitsforthenextclass.Noticethatthelimitsareinthehundredths.Andthenexthundredthsafter5.20(upperlimitoftheclass)is5.21(lowerlimitofthenextclass).

4.65–5.205.21–5.76

Findingthelimitsforthenextclass:

Noticethatthelimits(lowerlimitis3.18,upperlimitis4.96)havetwodecimalplacevaluesandendinthehundredths.(tenths).

Findingtheboundaries:

3.184.96-0.005+0.0053.175-4.965

Sincelimithastwodecimalplacevalue(hundredths),wesubtract/add0.005(5thousandths)from/tothelimits.

Limitshavetwodecimalplacevalue(hundredths),soboundariesshouldbeonemoreadd’lplacevalue(thousandths)andendin5.

Findingtheclasswidth:

4.965-3.1751.79

Subtractthelowerboundaryfromtheupperboundary.

Youcanalsofindtheclasswidthbysubtractingthelower/upperlimitsfromtwoadjacentclasses.

4.97-3.181.79

or6.75-4.961.79

Addtheclasswidthtothelimitsoftheclasstogetthelimitsforthenextclass.Noticethatthelimitsareinthehundredths.Andthenexthundredthsafter4.96(upperlimitoftheclass)is4.97(lowerlimitofthenextclass).

3.18–4.964.97–6.75

Findingthelimitsforthenextclass:

Classwidthisnotuniformthroughout.Wehavedifferentclasswidths.Therulesstatethattheclasswidthshouldbeequalthroughoutthedistribution.Exceptionisopen-endeddistributions.Pleasenotethatthe2ndclasscannotberemovedevenifthereisafrequencyof0(zero),sinceitisnotthefirstorthelastclass.

Classwidth:6

665

6

5

6

6

Classwidthisnotuniformthroughout.Wehavedifferentclasswidths.Therulesstatethattheclasswidthshouldbeequalthroughoutthedistribution.Exceptionisopen-endeddistributions.Overlappingclasslimits(9,13,17,20).Ifwehadadatavalue9,whichclassdoweputthedatain?Samegoesfor13,17,and20.

Classwidth:4

464635

46

35

46

46

c. Class Frequency 123–127 3

128–132 7

138–142 2

143–147 19

3. Thedatashownarethenumberofgramsperservingof16selectedbrandsofcakes.Constructa

groupedfrequencydistributionusing5classes.32 47 51 41 46 30 46 3852 48 48 38 43 41 21 24a. Range

b. ClassWidth

Classwidth:5

10

5

5

1010

5Classesarenotcontinuous.Aclassismissingafterthe2ndclass(128–132).Thereisabiggapbetweenthe2ndand3rdclass.Noticethe2ndclassendsat132thenthe3rdclassstartswith138.Theclass133–137ismissingandshouldbebetweenthe2ndand3rdclass.Aclasscannotberemovedfromthedistributionunlessithasafrequencyof0(zero)ANDitisthefirstorthelastclass.Pleasenotethatonceweplacethemissingclassbackintothefrequencydistribution,theclasswidthwillbesamethroughoutthedistribution.

Range=highestvalue–lowestvalue. 52–21=31

𝑐𝑙𝑎𝑠𝑠 𝑤𝑖𝑑𝑡ℎ ≈𝑟𝑎𝑛𝑔𝑒

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑙𝑎𝑠𝑠𝑒𝑠 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 31

5= 6.2 → 𝟕

GramsPerServingforSelectedCakes

(Thisistheclassusinglimits)Gramsperserving

(Thisistheclassusingboundaries)Gramsperserving

Tally

(Thisisthefrequency)Numberofcakes

21–27 20.5–27.5 II 228–34 27.5–34.5 II 235–41 34.5–41.5 IIII 442–48 41.5–48.5 IIIII-I 649–55 48.5–55.5 II 2

16Afrequencydistributionismadeupofclassesandfrequencies.

Theclassisgramsperserving(datavaluesrepresentgramsperserving).Weusedthelimitsandtheboundariesfortheclasses.Withagroupedfrequencydistribution,youdonotneedtohaveboththelimitsandtheboundaries;oneortheotherwillbefine.Imayspecifyinaproblemtohaveboth.

Noticethattheonlyseparationbetweentheclassesisonewhole#(sincethedatavaluesareinwhole#s).Classboundariesfillinthosegaps,soONLYtheclassboundariesoverlap.Again,classlimitscannotoverlap.

Thelowerclasslimitforthe1stclasswillbesmallestdatavalue(21).Togetthelowerlimitforthenextclass,weaddtheclasswidth(7)tothelowerclasslimitofthe1stclass.Werepeatthisuntilwehavethelowerlimitsforthe5classes.

Togettheupperclasslimitofthe1stclass,wesubtractonewhole#(sincethedataisinwhole#s)fromthelowerlimitofthe2ndclass.Togettheupperlimitforthenextclass,weaddtheclasswidthtotheupperlimitofthe1stclass.Wecontinuetoaddtheclasswidthuntilwehavetheupperlimitsforallthe5classes.

Youdonotneedtohaveacolumnforthetally.Thisisjustusedtotallyupthedataasyouplacethemintotheclasses.

Thefrequencytellsushowmanydatavaluesareinaclass.Inthiscase,thefrequencytellsushowmanycakeshavecertain#ofgramsperserving.

Forinstance,2cakesis21to27gramsperserving.

Pleasenotethatthetotalfrequencyis16,thetotalnumberofdatavalueswehave.Youshouldalwaysmakesurethatthetotalfrequencyisthesameasthetotalnumberofdatavalueyouhave.Ifthetotalfrequencyisless,thenyoudidnotplaceone/someofthedatavaluesintoaclass.Ifthetotalfrequencyisgreater,thenyouplacesone/somedatavaluesintomorethanoneclass.

Alwayshaveatitletoletusknowwhatthefrequencydistributionispresenting.

Alwaysrounduptothenext#withthesame#ofplacevaluesasthedata.Sincethedataareinwhole#s,werounduptheclasswidthtothenextwhole#.So7isnowourclasswidth.

4. Theamountwon(inmillionsofdollars)for16winninglotteryticketsisshown.Constructagroupedfrequencydistributionforthedatausing5classes.28.5 51.7 19 5 2 1.2 14 14.60.8 11.6 3.5 30.1 1.7 1.3 13 14

a. Range

b. ClassWidth

Range=highestvalue–lowestvalue. 51.7–0.8=50.9

𝑐𝑙𝑎𝑠𝑠 𝑤𝑖𝑑𝑡ℎ ≈𝑟𝑎𝑛𝑔𝑒

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑙𝑎𝑠𝑠𝑒𝑠 𝑑𝑒𝑠𝑖𝑟𝑒𝑑

50.95

= 10.18 → 𝟏𝟎. 𝟐

Alwaysrounduptothenext#withthesame#ofplacevaluesasthedata.Sincethedatahasatmostonedecimalplacevalue(tenths),werounduptheclasswidthtothenext#(inthetenths).So10.2isnowourclasswidth.

LotteryWinnings

(Thisistheclassusinglimits)AmountWon(inMillionsof$)

(Thisistheclassusingboundaries)AmountWon(inMillionsof$)

Tally

(Thisisthefrequency)NumberofLotteryTickets

0.8–10.9 0.75–10.95 IIIII-II 711.0–21.1 10.95–21.15 IIIII-I 621.2–31.3 21.15–31.35 II 231.4–41.5 31.35–41.55 041.6–51.7 41.55–51.75 I 1

16

Alwayshaveatitletoletusknowwhatthefrequencydistributionispresenting.

Afrequencydistributionismadeupofclassesandfrequencies.

TheclassisAmountWon(datavaluesrepresenttheamountwoninmillionsofdollars).Weusedthelimitsandtheboundariesfortheclasses.Withagroupedfrequencydistribution,youdonotneedtohaveboththelimitsandtheboundaries;oneortheotherwillbefine.Imayspecifyinaproblemtohaveboth.

Noticethattheonlyseparationbetweentheclassesisonetenths(0.1)sincethedatavalueshaveatmostonedecimalplacevalue(tenths).Classboundariesfillinthosegaps,soONLYtheclassboundariesoverlap.Again,classlimitscannotoverlap.

Thelowerclasslimitforthe1stclasswillbesmallestdatavalue(0.8).Togetthelowerlimitforthenextclass,weaddtheclasswidth(10.2)tothelowerclasslimitofthe1stclass.Werepeatthisuntilwehavethelowerlimitsforthe5classes.

Togettheupperclasslimitofthe1stclass,wesubtractonetenths(0.1)(sincethedatahasatmostonedecimalplacevalue)fromthelowerlimitofthe2ndclass.Togettheupperlimitforthenextclass,weaddtheclasswidthtotheupperlimitofthe1stclass.Werepeatthisuntilwehavetheupperlimitsforthe5classes.

Youdonotneedtohaveacolumnforthetally.Thisisjustusedtotallyupthedataasyouplacethemintotheclasses.

Thefrequencytellsushowmanydatavaluesareinaclass.Inthiscase,thefrequencytellsushowmanylotteryticketswonacertainamountofdollars(inmillions).

Forinstance,7lotteryticketshadwinningamountsof0.8to10.9milliondollars.

Pleasenotethatthetotalfrequencyis16,thetotalnumberofdatavalueswehave.Youshouldalwaysmakesurethatthetotalfrequencyisthesameasthetotalnumberofdatavalueyouhave.Ifthetotalfrequencyisless,thenyoudidnotplaceone/someofthedatavaluesintoaclass.Ifthetotalfrequencyisgreater,thenyouplacedone/somedatavaluesintomorethanoneclass.

5. Thenumberofstoriesineachoftheworld’s20tallestbuildingsfollows.Constructagroupedfrequencydistributionwith7classes.88 88 110 88 80 69 102 78 70 5579 85 89 199 69 89 77 55 75 55a. Range

b. ClassWidth

Range=highestvalue–lowestvalue. 199–55=144

𝑐𝑙𝑎𝑠𝑠 𝑤𝑖𝑑𝑡ℎ ≈𝑟𝑎𝑛𝑔𝑒

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑙𝑎𝑠𝑠𝑒𝑠 𝑑𝑒𝑠𝑖𝑟𝑒𝑑

1447

≈ 20.571429… → 𝟐𝟏

Alwaysrounduptothenext#withthesame#ofplacevaluesasthedata.Sincethedataarewhole#s,werounduptheclasswidthtothenextwhole#.So21isnowourclasswidth.

StoriesforWorld’s20TallestBuildings

(Thisistheclassusinglimits)NumberofStories

(Thisistheclassusingboundaries)NumberofStories

Tally

(Thisisthefrequency)NumberofBuildings

55–75 54.5–75.5 IIIII-II 776–96 75.5–96.5 IIIII-IIIII 1097–117 96.5–117.5 II 2118–138 117.5–138.5 0139–159 138.5–159.5 0160–180 159.5–180.5 0181-201 180.5–201.5 I 1

20

TheclassisNumberofStories(datavaluesrepresentthenumberofstoriesintheworld’stallestbuildings).

Noticethattheonlyseparationbetweentheclassesisonewhole#sincethedatavaluesareinwhole#s.

Alwayshaveatitletoletusknowwhatthefrequencydistributionispresenting.

Thefrequencytellsushowmanydatavaluesareinaclass.Inthiscase,thefrequencytellsushowmanybuildingshaveacertainnumberofstories.

Forinstance,0buildingshave160to180stories.Or0buildingshave159.5to180.5stories.

Pleasenotethatthetotalfrequencyis20,thetotalnumberofdatavalueswehave.Youshouldalwaysmakesurethatthetotalfrequencyisthesameasthetotalnumberofdatavalueyouhave

6. Thefollowingarecholesterolreadings(mg/deciliterofblood)oftwentypatients.Constructagroupedfrequencydistributionwith7classes.184 230 195 186 240 190 238 254 225 237210 224 214 197 203 233 198 215 216 205a. Range

b. ClassWidth

Range=highestvalue–lowestvalue. 254-184=70

𝑐𝑙𝑎𝑠𝑠 𝑤𝑖𝑑𝑡ℎ ≈𝑟𝑎𝑛𝑔𝑒

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑙𝑎𝑠𝑠𝑒𝑠 𝑑𝑒𝑠𝑖𝑟𝑒𝑑

707= 10 → 𝟏𝟏

Alwaysrounduptothenext#withthesame#ofplacevaluesasthedata.Sincethedataarewhole#s,werounduptheclasswidthtothenextwhole#.So11isnowourclasswidth.

WagesforFactoryWorkers

(Thisistheclassusinglimits)

Hourly(InDollars)

(Thisistheclassusingboundaries)

HourlyWages(inDollars)

(Thisisthefrequency)NumberofWorkers

184–194 183.5–194.5 3195–205 194.5–205.5 5206–216 205.5–216.5 4217–227 216.5–227.5 2228-238 227.5–238.5 4239–249 238.5–249.5 1250-260 249.5–260.5 1

7. Astudywasconductedontheamount(indollars)spentongasfor30randompeople.Constructagroupedfrequencydistributionwith5classes.Constructacumulativegroupedfrequency.44 50 45 42 46 34 44 34 39 4143 37 47 37 36 45 47 34 39 3730 40 41 45 45 36 31 39 35 43a. Range

b. ClassWidth

Range=highestvalue–lowestvalue. 50-30=20

𝑐𝑙𝑎𝑠𝑠 𝑤𝑖𝑑𝑡ℎ ≈𝑟𝑎𝑛𝑔𝑒

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑙𝑎𝑠𝑠𝑒𝑠 𝑑𝑒𝑠𝑖𝑟𝑒𝑑

205= 4 → 𝟓

Alwaysrounduptothenext#withthesame#ofplacevaluesasthedata.Sincethedataarewhole#s,werounduptheclasswidthtothenextwhole#.So5isnowourclasswidth.

GasSpending

(Thisistheclassusinglimits)AmountSpent(indollars)

(Thisistheclassusingboundaries)AmountSpent(indollars)

Tally

(Thisisthefrequency)NumberofPeople

30–34 29.5–34.5 IIIII 535–39 34.5–39.5 IIIII-IIII 940–44 39.5–44.5 IIIII-III 845–49 44.5–49.5 IIIII-II 750–54 49.5–54.5 I 1

30

TheclassisAmountSpent(datavaluesrepresenttheamountspentforgas).

Noticethattheonlyseparationbetweentheclassesisonewhole#sincethedatavaluesareinwhole#s.

Alwayshaveatitletoletusknowwhatthefrequencydistributionispresenting.

Thefrequencytellsushowmanydatavaluesareinaclass.Inthiscase,thefrequencytellsushowmanypeoplespentacertainamount(indollars)forgas.

Forinstance,8peoplehavespent$40–44ongas.Orbetween$39.5to$44.5ongas.

GasSpending

(Thisistheclassusingboundaries)AmountSpent(indollars)

(Thisisthecumulativefrequency)

NumberofPeopleLessthan29.5 0Lessthan34.5 5Lessthan39.5 14Lessthan44.5 22Lessthan49.5 29Lessthan54.5 30

Forcumulativefrequencydistribution,wewanttoseethefrequencyforaclassthatislessthanacertainvalue.Fortheclassesweuse“lessthan”(acertainboundary).Forcumulativefrequencydistributions,wewillalwaysusetheclassboundariesforourclasses.

The1stclasswillbelessthanthelowestclassboundary(lessthan29.5).Thecumulativefrequency(c.f.)shouldbe0sincetherearenodatavaluesthatislessthan29.5

Lookingatthegroupedfrequencydistribution,thefirstclasshasalowerlimitof30,sonodataisbelow30,hencelessthan29.5hasc.f.of0.

Thenextclasswillbelessthan34.5(thenextclassboundary).Lookingatthegroupedfrequencydistribution,weseethatthe1stclass30–34hasafrequencyof5.So5isthec.f.forthe2ndclass.Alldatavaluesintheclass30–34islessthan34.5

ForLessthan39.5wehaveac.f.of14.Theclass35–39hasafrequencyof9(all9datavaluesintheclass35–39arelessthan39.5).Theclass30–34hasafrequencyof5(all5datavaluesinthisclassislessthan39.5).5+9=14.Wecontinueuntilweendupwithc.f.of30forthelastclass(thisalsotellsusthetotalfrequency).Noticethatthelastclassusedthehighestclassboundary54.5for“Lessthan54.5”

8. Thestategastaxincentspergallonfor18statesisgivenbelow.Constructagroupedfrequencydistributionwith5classes.Constructacumulativegroupedfrequency.7.5 16 23.5 17 22 21.5 19 20 27.142 31 14.5 25.9 18 30 31.5 18.5 25.3a. Range

b. ClassWidth

Range=highestvalue–lowestvalue. 42–7.5=34.5

𝑐𝑙𝑎𝑠𝑠 𝑤𝑖𝑑𝑡ℎ ≈𝑟𝑎𝑛𝑔𝑒

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑙𝑎𝑠𝑠𝑒𝑠 𝑑𝑒𝑠𝑖𝑟𝑒𝑑

34.55

= 6.9 → 𝟕.𝟎

Alwaysrounduptothenext#withthesame#ofplacevaluesasthedata.Sincethedatavalueshaveatmostonedecimalplacevalue(tenths),werounduptheclasswidthtothenext#inthetenths.So7isnowourclasswidth.

GasTaxPerGallon

(Thisistheclassusinglimits)GasTax(incents)

(Thisistheclassusingboundaries)GasTax(incents)

Tally

(Thisisthefrequency)NumberofStates

7.5–14.4 7.45–14.45 I 114.5–21.4 14.45–21.45 IIIII-II 721.5–28.4 21.45–28.45 IIIII-I 628.5–35.4 28.45–35.45 III 335.5–42.4 35.45–42.45 I 1

GasTaxPerGallon

(Thisistheclassusingboundaries)AmountSpent(indollars)

(Thisisthecumulativefrequency)NumberofStates

Lessthan7.45 0Lessthan14.45 1Lessthan21.45 8Lessthan28.45 14Lessthan35.45 17Lessthan42.45 18

9. TheBrunswickResearchOrganizationsurveyed50randomlyselectedindividualsandaskedthemtheprimarywaytheyreceivedthedailynews.Theirchoiceswerevianewspaper(N),television(T),radio(R),orInternet(I).Constructacategoricalfrequencydistributionforthedataandinterprettheresults.N N T T T I R R I TI N R R I N N I T NI R T T T T N R R I

10. AsurveywastakenonhowmuchtrustpeopleplaceintheinformationtheyreadontheInternet.Constructacategoricalafrequencydistributionforthedata.A=trustineverythingtheyread,M–trustinmostofwhattheyread,H=trustinaboutone-halfofwhattheyread,S=trustinasmallportionofwhattheyread.M M M A H M S M H MS M M M M A M M A M

WaysofReceivingDailyNews

(Thisistheclass)WayofReceivingNews

Tally

(Thisisthefrequency)NumberofPeople

Newspaper(N) IIIII-II 7Television(T) IIIII-IIII 9Radio(R) IIIII-II 7Internet(I) IIIII-II 7

30

Categoricalfrequencydistributionsdonotneedtohavethetallycolumn.

Totalfrequencyshouldthesame#ofdatavaluesyouhavecollected.

InformationontheInternet–AmountofTrustPlaced

(Thisistheclass)AmountofTrust

Tally

(Thisisthefrequency)NumberofPeople

All(A) III 3Most(M) IIIII-IIIII-III 13Half(H) II 2

SmallPortion(S) II 2