A Resource for Freestanding Mathematics Qualifications


 Drusilla Dorsey
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1 A pie chrt shows how somethig is divided ito prts  it is good wy of showig the proportio (or frctio) of the dt tht is i ech ctegory. To drw pie chrt:. Fid the totl umer of items.. Fid how my degrees represet ech item y dividig 360º y the totl. Put this vlue ito your clcultor s memory so tht you c recll it whe eeded. 3. Clculte the gle for ech ctegory y multiplyig the umer of degrees per item y the umer of items i the ctegory. 4. Check the gles dd up to 360º. 5. Write title to sy wht iformtio the pie chrt gives. 6. Drw circle d divide it ito sectors usig the gles you hve foud. 7. Iclude key to show wht ech sector represets or lel ech sector of the pie chrt. Work through this exmple: A shop sells differet sizes of gloves. The tle shows the percetge of gloves sold i yer tht were ech size. Size Smll Medium Lrge % of gloves sold 4% 40% 35% Extr Lrge % As the vlues re percetges, the totl must e 00% (ut check to mke sure). Ech % will e represeted y: 360 = 3.6º 00 The tle shows how to fid the first gle. Use your clcultor to check this gle, the work out the others. Check tht the totl gle is 360º The pie chrt is show here check tht its gles gree with those you hve foud. Size % of gloves sold Agle (erest º) Smll 4% = 50 Medium 40% Lrge 35% Extr Lrge % Totl 00% Glove sizes sold i shop Note Sometimes roudig the gles leds to totl gle of more or less th 360º. If this hppes, djust the gle of the lrgest sector so tht the totl is correct eg if the totl comes to 36º, tke º wy from the lrgest gle. Smll Medium Lrge Extr Lrge The Nuffield Foudtio
2 Worksheet The tle shows the umer of studets i clss who chieved ech grde. Use this dt to drw pie chrt. Accordig to your chrt which grde hd i the lrgest proportio of studets ii the smllest proportio? Grde Numer of studets Distictio 5 Merit 8 Pss 9 Fil The tle shows the results of survey i which people who moved house were sked to give the mi reso. Use this dt to drw pie chrt. Descrie riefly wht your pie chrt shows. Reso % Needed differet size of house 9 Persol (eg mrrige, divorce) 34 To move to etter re 9 Jorelted reso Other 6 3 The tle gives the popultio of differet regios of the world i 00. Drw pie chrt. Descrie riefly wht your pie chrt shows. Regio Popultio (millios) Asi 37 Afric 83 Europe 76 Lti Americ 57 North Americ 37 Ocei 3 4 The tle elow gives the popultio d re of ech coutry i the UK i 00. c Coutry Are (000 km ) Popultio (millios) Egld Norther Ireld Scotld Wles Use the re dt to drw pie chrt. Use the popultio dt to drw pie chrt. Expli wht your chrts show. The Nuffield Foudtio
3 Whe you wish to drw pie chrts from differet qutities of dt, the size of the pie chrts should reflect the qutities of dt represeted. If the first pie chrt represets totl of items d the secod represets totl of items, the the res of the pies should e proportiol to these totls. This gives: π π r r = so r r so the rdius of the secod pie should e = d r = r times the rdius of the first pie. Work through this exmple: The tle gives the umer of mle d femle officers i differet rks of the police force i Egld d Wles i 00. Rk Numer of Officers Femle Mle Costle Serget Ispector & Higher Rks Totl If pie chrts re used to illustrte this dt, the rdius of the pie chrt for mle officers should e = =. 4 times tht for femle officers The gle for ech femle officer is = 0.058º (to 3sf) 785 Check this o your clcultor the multiply y the umer of femle officers i ech rk to check the gles give i the tle elow. Rk Numer of Officers Femle Mle Costle 38º Serget 3º Ispector & Higher Rks º Totl 360º Complete the tle to give gles for ech rk for mle officers. Drw pie chrts to illustrte the dt rememer tht the rdius of the circle represetig the mle officers should e.4 times tht for the femle officers. The Nuffield Foudtio 3
4 Worksheet The umer of households i Gret Briti icresed from 8.6 millio i 97 to 4.4 millio i 00. The tle elow shows how the percetge of households of differet sizes chged over this period. Household Size Percetge i 97 Percetge i 00 Oe perso 8 9 Two people 3 34 Three people 9 6 Four people 7 4 Five people 8 5 Six or more people 6 Drw pie chrts for 97 d 00 d descrie the similrities d differeces. The tle elow shows the proportio of the mle d femle popultio i the UK of differet mritl sttus i 97 d 000. The mle popultio icresed from 7. to 8.8 millio d the femle popultio from 8.8 to 30. millio over this period. Mritl Sttus Percetge i 97 Percetge i 000 M F M F Sigle Mrried Widowed Divorced 8 9 Drw pie chrts for the mles d femles for ech of 97 d 000. Descrie the similrities d differeces. 3 The tle elow gives estimtes of the ir pollutts from differet sources i the UK i 000. Source Cro Mooxide Sulphur Dioxide Nitroge Oxides Rod Trsport 69% % 4% Idustry & Power 4% 90% 36% Other 7% 9% % Totl (thousd toes) Drw pie chrts for ech pollutt. Write prgrph descriig wht your chrts show. The Nuffield Foudtio 4
5 Techer Notes Uits Foudtio Level, Mkig sese of dt Itermedite Level, Hdlig d iterpretig dt Advced Level, Usig d pplyig sttistics. Skills used i this ctivity: drwig pie chrts y hd (or i Excel) Preprtio Studets eed to kow how to use protrctor to drw gles. Notes Studets studyig Mkig sese of dt eed oly work through the first pges. Studets studyig Hdlig d iterpretig dt re likely to eed to work through ll of this ctivity. Studets studyig Usig d pplyig sttistics will proly lredy kow how to drw simple pie chrts. They my oly eed to work through pges 3 to 5. Agles for pie chrts Pge Pge Size Agle (erest º) Smll = 50 Medium = 44 Lrge = 6 Extr Lrge 3.6 = 40 Totl 360 i Pss Grde Agle ii Fil Distictio 75º Merit 0º Pss 35º Fil 30º Reso Agle Needed differet size of house 68º Persol (eg mrrige, divorce) 3º To move to etter re 3º Jorelted reso 43º Other 94º 3 Regio Agle Asi 7º Afric 48º Europe 43º Lti Americ 3º North Americ 9º Ocei º 4, Coutry Are gles Popultio gles Egld 93º 30º Norther Ireld 0º 0º Scotld 6º 3º Wles 3º 8º The Nuffield Foudtio 5
6 Pge 3 Rk Numer of Officers Femle Mle Costle 38º 74º Serget 3º 57º Ispector & Higher Rks º 9º Totl 360º 360º Rks of femle police officers i Egld d Wles i 00 Costle Serget Ispector & Higher Rks Rks of mle police officers i Egld d Wles i 00 Costle Serget Ispector & Higher Rks r =.4r The Nuffield Foudtio 6
7 Pge 4 Household Size Agles for 97 Agles for 00 Oe perso 65º 04º Two people 5º 3º Three people 68º 58º Four people 6º 50º Five people 9º 8º Six or more people º 7º Mritl Sttus Agles for 97 Agles for 000 M F M F Sigle 86º 68º º 94º Mrried 56º 34º 95º 87º Widowed 4º 54º 4º 47º Divorced 4º 4º 9º 3º r =.5r r =.03r r 3 =.03r r 4 =.05r (very little differece) 3 Source Cro Mooxide Sulphur Dioxide Nitroge Oxides Rod Trsport 49º 4º 5º Idustry & Power 50º 34º 30º Other 6º 3º 79º r = 0.58r, r 3 = 0.60r The Nuffield Foudtio 7
n Using the formula we get a confidence interval of 80±1.64
9.52 The professor of sttistics oticed tht the rks i his course re orlly distributed. He hs lso oticed tht his orig clss verge is 73% with stdrd devitio of 12% o their fil exs. His fteroo clsses verge
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