뗚32뻭ꆡ뗚3웚놱뺩쳥폽듳톧톧놨ꆡ쓪3퓂뛔쏨쫶탔춳볆솿뗄욫뛈뫍럥뛈펦폃뗄퇐뺿닌훒붨(컂훝듳톧쳥폽톧풺,헣붭컂훝ꆡ325035)햪ꆡ튪:춨맽쪵퇩램ꆢ쫽샭춳볆램뫍퓋폃헽첬럖늼풭샭뛔쏨쫶춳볆솿훐뗄욫뛈뫍럥뛈횵뗄펦폃뷸탐첽쯷탔퇐뺿,훆ퟷ늻춬퇹놾쫽욫뛈뫍럥뛈횵뗄훃탅쟸볤,캪에뛏쫽횵쇏뗄럖늼쳘헷,헽좷냑컕톡퓱쏨쫶탔춳볆솿쳡릩뿆톧뗄샭싛틀뻝ꆣ맘볼듊:욫뛈;럥뛈;쪵퇩;쯦믺돩퇹;첽쯷훐춼럖샠뫅:G80-32ꆡꆡ컄쿗뇪쪶싫:Aꆡꆡ컄헂뇠뫅:1007-3612(2009)03-0075-02OntheApplicationofDeviationandKurtosisinDescriptiveStatisticsCAIZhong2jian(CollegeofSports,WenzhouUniversity,Wenzhou325035,ZhejiangChina)Abstract:Thepaperconductsanexplorationontheapplicationofdeviationandkurtosisindescriptivestatisticsbyexperi2ment,mathematicalstatisticsandnormaldistributionprinciples,,:deviation;kurtosis;experiment;randomsampling;explorationꆡꆡ쏨쫶춳볆뗄죎컱뻍쫇쏨쫶쯦믺뇤솿뗄춳볆맦싉탔ꆣ튪췪ퟩ뗃떽1000룶욫뛈뫍럥뛈횵,퓙볆쯣욫뛈뫍럥뛈뗄욽뻹횵헻뗘쏨쫶쯦믺뇤솿뗄춳볆쳘탔탨튪럖늼몯쫽ꆣ떫퓚쪵볊컊쳢폫뇪ힼ닮ꆣ좻뫳룹뻝헽첬럖늼풭샭ퟶ돶룷퇹놾ퟩ95%ꆢ99%훐,쟳쯦믺뇤솿뗄럖늼몯쫽늢늻쫇튻볾죝틗뗄쫂,쇭튻랽쏦뛔뗄욫뛈뫍럥뛈뗄폐킧쟸볤ꆣ폚튻킩컊쳢튲늻탨튪좥좫쏦뾼달쯦믺뇤솿뗄뇤뮯맦싉,뛸횻ꆡ럖컶램ꆡ룹뻝룷퇹놾ퟩ욫뛈뫍럥뛈뗄폐킧쟸볤횵뛔쏨탨횪뗀쯦믺뇤솿뗄쒳킩쳘헷ꆣ죧뫎헽좷쪹폃쏨쫶춳볆훐뗄벯쫶탔춳볆훐뗄벯훐캻훃솿쫽춳볆솿(쯣쫵욽뻹횵ꆢ훐캻쫽ꆢ훚훐캻훃솿쫽횸뇪(쯣쫵욽뻹쫽ꆢ훐캻쫽뫍훚쫽[1]),쫇쒿잰펦폃쫽)뷸탐쟸뇰펦폃럖컶ꆣ맽돌훐뷏캪쓑냑컕뗄컊쳢,틲캪늻춬럖늼탎첬,펦톡퓱늻춬뗄춳볆솿횸뇪살쏨쫶쫽횵쇏뗄믹놾쳘헷ꆣ퓚쪵볊펦폃훐듳뛠2ꆡ뷡맻폫럖컶쫽죋쫇퓋폃튵횪쪶뫍틔췹뺭퇩톡퓱쯣쫵욽뻹쫽뷸탐쏨쫶,뷌뿎쫩훐쳡벰쯣쫵욽뻹쫽뗄펦폃펦퓚헽첬럖늼믲뷓뷼헽첬럖ꆡ욫뛈뫍럥뛈볆쯣릫쪽벰럖컶ꇆn늼뗄쳵볾쿂ꆣ헽첬럖늼뗄에뛏랽램ퟮ뫃쫇쪹폃헽첬탔볬퇩믲3(x)샻폃럥뛈뫍욫뛈살에뛏쫇럱럾듓헽첬럖늼ꆣ퓚쳥폽뿆퇐훐욫뛈ꆡi-x/ni=1Sk=3,s뫜뛠퇐뺿쫜떽퇹놾쫽뗄쿞훆컞램뷸탐헽첬탔볬퇩,뛸뷌뿎쫩ꇆn4(x짏뛔욫뛈뫍럥뛈횵튪쟳맽룟(벴욫뛈뫍럥뛈횵뗈폚0캪뇪ힼ럥뛈ꆡi-x)/nUi=1u=4-3헽첬럖늼s),퓚쪵볊훐퓋폃쫇폐삧쓑뗄,틲듋,놾컄룹뻝뇪ힼ헽볆쯣릫쪽뿉틔뾴돶,욫뛈뻍쫇퇹놾욫킱뛈뗄맀볆횵,럥뛈첬럖늼풭샭[2],뛔욫뛈뫍럥뛈횵뷸탐쒣쓢쪵퇩,볆쯣늻춬퇹놾풼뗈폚퇹놾럥횵복좥3ꆣ틲듋,죴튻ퟩ맛달쫽뻝뗄욫뛈ꆢ럥뛈쫽뗄헽첬럖늼쿂뗄욫뛈뫍럥뛈횵뗄욽뻹쫽ꆢ뇪ힼ닮,늢훆ퟷ돉뚼뷓뷼폚0,퓲뿉틔죏캪헢ퟩ쫽뻝쫇살ퟔ헽첬럖늼ퟜ쳥ꆣ죴웤늻춬퇹놾쫽뗄욫뛈뫍럥뛈횵뗄뿉탅럖늼쟸볤,틔듋쟸볤살에욫뛈캪헽,퓲뇭쪾폫뇪ힼ헽첬럖늼쿠뇈,웤럥뛈욫쿲뷏킡쫽횵뛏늻춬퇹놾쫽뗄쫽횵쇏뗄럖늼쟩뿶,톡퓱뫏쫊뗄춳볆솿살랽;욫뛈캪뢺,퓲뇭쪾폫뇪ힼ헽첬럖늼쿠뇈,웤럥욫쿲뷏듳쫽횵쏨쫶쫽횵쇏뗄믹놾쳘헷쫇뻟폐쪵볊틢틥뗄ꆣ랽;죴웤럥뛈캪헽,퓲뇭쪾폫뇪ힼ헽첬럖늼쿠뇈,웤럖늼쿠뛔볢죱,럥뛈캪뢺,퓲뇭쪾폫뇪ힼ헽첬럖늼쿠뇈,웤럖늼쿠뛔욽첹ꆣ1ꆡ퇐뺿랽램ꆡ쪵퇩뷡맻럖컶ꆡ춳볆톧뗄튻룶훷튪죎컱쫇퇐뺿ퟜ쳥뫍1퇹놾횮볤뗄맘쾵ꆣ헢훖맘쾵뿉틔듓솽룶랽쿲뷸탐퇐뺿:뗚튻.1ꆡ쪵퇩램ꆡ퇹놾쫽럖10ꆢ20ꆢꆭ100ꆢ500ꆢ1000룶릲12ퟩ,폃EXCEL럖컶릤뻟훐뗄쯦믺쫽랢짺웷내헽첬뻹횵캪0룶랽쿲쫇듓ퟜ쳥떽퇹놾뗄랽쿲,웤쒿뗄쫇튪퇐뺿듓ퟜ쳥훐돩,뇪ힼ닮캪1뗄돩좡퇹놾룷ퟩ1000샽쫽ꆣ돶뗄쯹폐뿉쓜퇹놾춳볆솿뗄럖늼벰웤폫풭ퟜ쳥뗄맘쾵;뗚뛾1룶랽쿲쫇듓퇹놾떽ퟜ쳥뗄랽쿲,벴듓ퟜ쳥훐쯦믺돩좡퇹놾,늢.2ꆡ춳볆볆쯣램ꆡ볆쯣룷1000샽쫽쎿샽뗄욫뛈뫍럥뛈,룷폃퇹놾뛔ퟜ쳥ퟶ돶췆싛ꆣ놾컄룹뻝춳볆톧훐욽뻹쫽돩퇹럖늼춶룥죕웚:2007-04-10ퟷ헟볲뷩:닌훒붨,뢱뷌쫚,퇐뺿랽쿲쳥폽춳볆톧뫍쳥폽뷌톧ꆣ
ꆤ76ꆤ놱뺩쳥폽듳톧톧놨뗚32뻭뚨샭:1)듓ퟜ쳥훐쯦믺돩돶죝솿캪n뗄튻쟐뿉쓜퇹놾뗄욽뻹폐솽샠횸뇪:튻쫇쏨쫶벯훐쟷쫆뗄횸뇪,폃틔랴펳튻ퟩ쫽뻝뗄쫽뗈폚ퟜ쳥뗄욽뻹쫽;2)듓헽첬ퟜ쳥훐,쯦믺돩좡뗄죝솿캪n욽뻹쮮욽;뛾쫇쏨쫶샫즢돌뛈뗄횸뇪,폃틔랴펳튻ퟩ쫽뻝뗄뇤뗄튻쟐뿉쓜퇹놾욽뻹쫽뗄럖늼튲돊헽첬럖늼;3)쯤좻ퟜ쳥늻틬듳킡ꆣ솽샠횸뇪뗄솪뫏펦폃닅쓜좫쏦쏨쫶튻ퟩ쫽횵뇤솿돊헽첬럖늼,죧맻퇹놾죝솿뷏듳,랴펳ퟜ쳥ꛌ뫍ꛒ뗄퇹놾욽뻹쇏뗄믹놾쳘헷,쏨쫶쫽횵뇤솿쇏욽뻹쮮욽뗄뎣폃횸뇪폐뻹쫽뗄돩퇹럖늼,튲뷓뷼폚헽첬럖늼(뇭1)ꆣ쫽(쯣쫵뻹쫽)ꆢ훐캻쫽뫍훚쫽뗈,뛸쏨쫶쫽횵뇤솿쇏샫즢돌뇭1ꆡ룷ퟩ1000듎쪵퇩뗄욫뛈뫍럥뛈횵뗄욽뻹횵뫍뇪ힼ닮뛈뗄뎣폃횸뇪폐뇪ힼ닮,쯄럖캻쫽볤뻠뫍뇤틬쾵쫽뗈ꆣ퓚쪹퇹놾쫽욫뛈뻹횵럥뛈뻹횵욫뛈뇪ힼ닮럥뛈뇪ힼ닮폃쏨쫶벯훐쟷쫆뗄횸뇪쪱,펦힢틢룷룶횸뇪웤쫊폃랶캧,룹뻝100쪵볊쇏뗄럖늼쟩뿶톡퓱웤ퟮ쓜랴펳쇏믹놾쳘헷뗄횸뇪ꆣ.룹뻝뇪ힼ헽첬럖늼풭샭뛔뇭1훐욫뛈뫍럥뛈횵뗄뇪ힼ닮훆ퟷ돉늻춬퇹놾쫽뗄욫뛈뫍럥뛈횵뗄훃탅쟸볤,볻뇭2,듋쟸볤뿉ퟷ캪쫽횵쇏뗄헽첬탔볬퇩ꆣ붫훃탅쟸볤횵캪뷧횵,뛔쯣쫵욽뻹쫽ꆢ훐캻쫽폫훚쫽죽헟늻춬뗄폃램ퟷ죧쿂움에:볻뇭ꆣ욫뛈<뷧횵(뻸뛔횵)쪱,쮵쏷럖늼캪헽첬,헽첬럖늼쳵볾쿂뗄쯣쫵욽뻹쫽ꆢ훐캻쫽뫍훚쫽죽헟쿠뗈믲믹놾뷓뷼,톡폃죽헟훐죎뫎튻룶춳볆솿뻹쓜랴펳벯훐쮮욽;욫뛈>뷧횵(뻸뛔횵),럥뛈<뷧횵(뻸뛔횵)믲<뢺뷧횵쪱,듋럖늼캪욫첬,럥탍ꆡꆡ듓뇭1훐뿉볻,욫뛈뫍럥뛈횵뷓뷼0,쮵쏷쎿ퟩ틔1000듎캪헽뎣믲욽첹,쮵쏷쫽뻝훐폐쳘듳쫽믲쳘킡쫽,쯣쫵욽뻹쫽쫜쪵퇩믱좡욫뛈뫍럥뛈횵욽뻹쫽살췆뛏ퟜ쳥뗄욫뛈뫍럥뛈횵뗄쳘듳쫽뫍쳘킡쫽펰쿬,훐캻쫽늻쫜웤펰쿬,맊톡폃훐캻쫽뇈뷏쫇폐틢틥뗄;욫뛈뫍럥뛈횵뗄뇪ힼ닮쓜랴펳늻춬퇹놾쫽뗄욫쫊뫏;럥뛈>뷧횵(뻸뛔횵),럥뛈>헽뷧횵쪱,럖늼캪욫첬,럥뛈뫍럥뛈횵뗄샫즢돌뛈ꆣ탍캪볢럥,쮵쏷쫽뻝벯훐퓚쒳쫽짏,톡폃훐캻쫽ꆢ훚쫽랴펳벯ꆡ늻춬퇹놾쫽뗄욫뛈뫍럥뛈횵뗄훃탅쟸볤벰럖컶ꆡ춳볆훐쮮욽뷏캪뫏샭ꆣ쏨쫶횸뇪뗄쪹폃폫럖늼쳘헷폐맘,뛠쫽쟩뿶쿂,뿉틔폃쯣쫵욽뇭3ꆡ욫뛈뫍럥뛈횵폫죽헟(쯣쫵욽뻹쫽ꆢ훐캻쫽ꆢ뻹쫽ꆢ훐캻쫽뫍훚쫽뗄맘쾵살에뛏쒳쇏쫇럱럾듓헽첬럖늼ꆣ훚쫽)뗄맘쾵퓚춳볆샭싛훐,헽첬럖늼쇏뗄쯣쫵욽뻹쫽ꆢ훐캻쫽뫍훚쫽죽춳볆솿욫뛈럥뛈헟횮볤뗄닮횵뗈폚쇣,욫첬럖늼쇏뗄쯣쫵욽뻹쫽ꆢ훐캻쫽뫍쯣쫵욽뻹쫽ꆢ훐캻쫽ꆢ훚쫽<뷧횵(뻸뛔횵)훚쫽죽헟횮볤뗄닮횵늻뗈폚쇣,틲듋,퓚쪵볊릤ퟷ훐횻튪쯣쫵훐캻쫽>뷧횵(뻸뛔횵)<뷧횵(뻸뛔횵)욽뻹쫽ꆢ훐캻쫽뫍훚쫽죽헟횮볤뗄쿠닮늻듳쪱,뿉맀볆룃쇏훐캻쫽>뷧횵(뻸뛔횵)<뢺뷧횵럾듓헽첬럖늼;퓚욵쫽뇭뫍횱랽춼훐,헽첬럖늼뗄쫽횵쇏돊훐캻쫽ꆢ훚쫽>뷧횵(뻸뛔횵)>헽뷧횵뛔돆럖늼,튲쫇뿉폃랽램횮튻ꆣ틔짏뗄럖컶횻쫇욾뺭퇩,쎻폐솿뗄뇪ힼ,퇐뺿헟쓑틔냑컕ꆣ헽첬럖늼뗄에뛏랽램춨뎣쫇쪹3ꆡ뷡ꆡ맻폃헽첬탔볬퇩믲샻폃럥뛈쾵쫽뫍욫뛈쾵쫽살에뛏쫇럱럾듓헽첬럖늼ꆣ퓚쳥폽뿆퇐훐,뫜뛠퇐뺿쫜떽퇹놾쫽뗄쿞훆컞램뷸1)룹뻝춳볆톧훐욽뻹쫽돩퇹럖늼뚨샭,뛔늻춬퇹놾쫽뗄탐헽첬탔볬퇩,뛸뷌뿎쫩짏뛔욫뛈뫍럥뛈횵튪쟳맽룟(벴욫뛈돩퇹쪵퇩볆쯣뗄욫뛈뫍럥횵뗄뿉탅럖늼쟸볤쫇뿉ퟷ캪에뛏늻뫍럥뛈횵뗈폚0캪뇪ힼ헽첬럖늼),퓚쪵볊훐쫇컞램퓋폃뗄춬퇹놾쫽뗄쫽횵쇏뗄럖늼쳘헷ꆣ떱쫽횵쇏볆쯣뗄욫뛈퓚,틲듋훃탅쟸볤쪱,뿉에캪헽첬믲뷓뷼헽첬럖늼,듋쪱,죽룶벯훐캻,룹뻝뇪ힼ헽첬럖늼풭샭뛔뇭1훐욫뛈뫍럥뛈횵뗄뇪ힼ닮훆ퟷ돉늻춬퇹놾쫽뗄욫뛈뫍럥뛈횵뗄훃탅쟸볤훃솿쫽횸뇪믹놾쿠뷼,뿉톡웤훐죎뫎튻룶살쏨쫶쇏뗄믹놾,볻뇭2,듋쟸볤뿉ퟷ캪쫽횵쇏뗄헽첬탔볬퇩ꆣ쳘헷ꆣ뇭2)떱쫽횵쇏볆쯣뗄욫뛈퓚훃탅쟸볤횮췢쪱,럥횵퓚헽2ꆡ늻춬퇹놾쫽뗄욫뛈뫍럥뛈횵뗄훃탅쟸볤(뻸뛔횵)뎣횵횮볤믲럥횵킡폚뢺뷧횵횮췢,쮵쏷욫첬럖늼,럥횵헽뎣믲퇹놾쫽욫첬럥첬99%뿉탅ꆡꆡꆡ95%뿉탅99%뿉탅ꆡꆡꆡ욽첹,듋쪱,쫽횵쇏훐폐뎬듳횵믲뎬킡횵펰쿬뻹횵뷏듳,펦95%뿉탅톡폃훐캻쫽살쏨쫶쫽횵쇏뗄믹놾쳘헷뷏캪뫏샭ꆣ)떱쫽횵쇏볆쯣뗄욫뛈퓚훃탅쟸볤횮췢쪱,럥횵폖듳폚헽뷧횵쪱,쮵쏷욫첬럖늼늢쫇볢럥탍,듋쪱,쫽횵쇏훐폐.뎬듳횵믲뎬킡횵,뛸쟒쒳튻랶캧횵뮹뷏벯훐,톡폃훚쫽살쏨쫶쫽횵쇏뗄믹놾쳘헷뷏캪뫏쫊ꆣ닎뾼컄쿗:[1]췵룕.뚨솿럖컶폫움볛랽램[M].짏몣:뮪뚫쪦랶듳톧돶냦짧,+ꇞ,9:[2]듔뫾욽.쳥폽춳볆[M].놱뺩:룟뗈뷌폽돶냦짧,1998,7:88-94..4ꆡ욫뛈뫍럥뛈횵뗄퓋폃ꆡ쏨쫶쫽횵뇤솿쇏뗄믹놾쳘헷
