发现中心极限定理骰子
几何画板及绘图内容加载中,请稍等……
①本范例演示了通过多次投掷骰子并计算平均值,观察样本均值分布逐渐接近正态分布的现象;②涉及的核心数学概念为中心极限定理、概率统计、几何平均数;③作图要点提炼自构造摘要,使用了Sample(抽样)、mean(均值)、Take(取值)、stdev(标准差)、Histogram(直方图)、BoxPlot(箱线图)、NormalQuantilePlot(正态分位数图)、Normal(正态分布)、DotPlot(点图)等GeoGebra命令/对象;④适合高中及以上数学学习者,用于理解中心极限定理的实际应用和可视化表现。
GeoGebra 命令及参数
Sample(X, n) → B2mean(B2) → C2Sample(X, n) → B3mean(B3) → C3Sample(X, n) → B4mean(B4) → C4Sample(X, n) → B5mean(B5) → C5Sample(X, n) → B6mean(B6) → C6Sample(X, n) → B7mean(B7) → C7Sample(X, n) → B8mean(B8) → C8Sample(X, n) → B9mean(B9) → C9Sample(X, n) → B10mean(B10) → C10Sample(X, n) → B11mean(B11) → C11Sample(X, n) → B12mean(B12) → C12Sample(X, n) → B13mean(B13) → C13Sample(X, n) → B14mean(B14) → C14Sample(X, n) → B15mean(B15) → C15Sample(X, n) → B16mean(B16) → C16Sample(X, n) → B17mean(B17) → C17Sample(X, n) → B18mean(B18) → C18Sample(X, n) → B19mean(B19) → C19Sample(X, n) → B20mean(B20) → C20Sample(X, n) → B21mean(B21) → C21Sample(X, n) → B22mean(B22) → C22Sample(X, n) → B23mean(B23) → C23Sample(X, n) → B24mean(B24) → C24Sample(X, n) → B25mean(B25) → C25Sample(X, n) → B26mean(B26) → C26Sample(X, n) → B27mean(B27) → C27Sample(X, n) → B28mean(B28) → C28Sample(X, n) → B29mean(B29) → C29Sample(X, n) → B30mean(B30) → C30Sample(X, n) → B31mean(B31) → C31Sample(X, n) → B32mean(B32) → C32Sample(X, n) → B33mean(B33) → C33Sample(X, n) → B34mean(B34) → C34Sample(X, n) → B35mean(B35) → C35Sample(X, n) → B36mean(B36) → C36Sample(X, n) → B37mean(B37) → C37Sample(X, n) → B38mean(B38) → C38Sample(X, n) → B39mean(B39) → C39Sample(X, n) → B40mean(B40) → C40Sample(X, n) → B41mean(B41) → C41Sample(X, n) → B42mean(B42) → C42Sample(X, n) → B43mean(B43) → C43Sample(X, n) → B44mean(B44) → C44Sample(X, n) → B45mean(B45) → C45Sample(X, n) → B46mean(B46) → C46Sample(X, n) → B47mean(B47) → C47Sample(X, n) → B48mean(B48) → C48Sample(X, n) → B49mean(B49) → C49Sample(X, n) → B50mean(B50) → C50Sample(X, n) → B51mean(B51) → C51Sample(X, n) → B52mean(B52) → C52Sample(X, n) → B53mean(B53) → C53Sample(X, n) → B54mean(B54) → C54Sample(X, n) → B55mean(B55) → C55Sample(X, n) → B56mean(B56) → C56Sample(X, n) → B57mean(B57) → C57Sample(X, n) → B58mean(B58) → C58Sample(X, n) → B59mean(B59) → C59Sample(X, n) → B60mean(B60) → C60Sample(X, n) → B61mean(B61) → C61Sample(X, n) → B62mean(B62) → C62Sample(X, n) → B63mean(B63) → C63Sample(X, n) → B64mean(B64) → C64Sample(X, n) → B65mean(B65) → C65Sample(X, n) → B66mean(B66) → C66Sample(X, n) → B67mean(B67) → C67Sample(X, n) → B68mean(B68) → C68Sample(X, n) → B69mean(B69) → C69Sample(X, n) → B70mean(B70) → C70Sample(X, n) → B71mean(B71) → C71Sample(X, n) → B72mean(B72) → C72Sample(X, n) → B73mean(B73) → C73Sample(X, n) → B74mean(B74) → C74Sample(X, n) → B75mean(B75) → C75Sample(X, n) → B76mean(B76) → C76Sample(X, n) → B77mean(B77) → C77Sample(X, n) → B78mean(B78) → C78Sample(X, n) → B79mean(B79) → C79Sample(X, n) → B80mean(B80) → C80Sample(X, n) → B81mean(B81) → C81Sample(X, n) → B82mean(B82) → C82Sample(X, n) → B83mean(B83) → C83Sample(X, n) → B84mean(B84) → C84Sample(X, n) → B85mean(B85) → C85Sample(X, n) → B86mean(B86) → C86Sample(X, n) → B87mean(B87) → C87Sample(X, n) → B88mean(B88) → C88Sample(X, n) → B89mean(B89) → C89Sample(X, n) → B90mean(B90) → C90Sample(X, n) → B91mean(B91) → C91Sample(X, n) → B92mean(B92) → C92Sample(X, n) → B93mean(B93) → C93Sample(X, n) → B94mean(B94) → C94Sample(X, n) → B95mean(B95) → C95Sample(X, n) → B96mean(B96) → C96Sample(X, n) → B97mean(B97) → C97Sample(X, n) → B98mean(B98) → C98Sample(X, n) → B99mean(B99) → C99Sample(X, n) → B100mean(B100) → C100Sample(X, n) → B101mean(B101) → C101Sample(X, n) → B102mean(B102) → C102Sample(X, n) → B103mean(B103) → C103Sample(X, n) → B104mean(B104) → C104Sample(X, n) → B105mean(B105) → C105Sample(X, n) → B106mean(B106) → C106Sample(X, n) → B107mean(B107) → C107Sample(X, n) → B108mean(B108) → C108Sample(X, n) → B109mean(B109) → C109Sample(X, n) → B110mean(B110) → C110Sample(X, n) → B111mean(B111) → C111Sample(X, n) → B112mean(B112) → C112Sample(X, n) → B113mean(B113) → C113Sample(X, n) → B114mean(B114) → C114Sample(X, n) → B115mean(B115) → C115Sample(X, n) → B116mean(B116) → C116Sample(X, n) → B117mean(B117) → C117Sample(X, n) → B118mean(B118) → C118Sample(X, n) → B119mean(B119) → C119Sample(X, n) → B120mean(B120) → C120Sample(X, n) → B121mean(B121) → C121Sample(X, n) → B122mean(B122) → C122Sample(X, n) → B123mean(B123) → C123Sample(X, n) → B124mean(B124) → C124Sample(X, n) → B125mean(B125) → C125Sample(X, n) → B126mean(B126) → C126Sample(X, n) → B127mean(B127) → C127Sample(X, n) → B128mean(B128) → C128Sample(X, n) → B129mean(B129) → C129Sample(X, n) → B130mean(B130) → C130Sample(X, n) → B131mean(B131) → C131Sample(X, n) → B132mean(B132) → C132Sample(X, n) → B133mean(B133) → C133Sample(X, n) → B134mean(B134) → C134Sample(X, n) → B135mean(B135) → C135Sample(X, n) → B136mean(B136) → C136Sample(X, n) → B137mean(B137) → C137Sample(X, n) → B138mean(B138) → C138Sample(X, n) → B139mean(B139) → C139Sample(X, n) → B140mean(B140) → C140Sample(X, n) → B141mean(B141) → C141Sample(X, n) → B142mean(B142) → C142Sample(X, n) → B143mean(B143) → C143Sample(X, n) → B144mean(B144) → C144Sample(X, n) → B145mean(B145) → C145Sample(X, n) → B146mean(B146) → C146Sample(X, n) → B147mean(B147) → C147Sample(X, n) → B148mean(B148) → C148Sample(X, n) → B149mean(B149) → C149Sample(X, n) → B150mean(B150) → C150Sample(X, n) → B151mean(B151) → C151Sample(X, n) → B152mean(B152) → C152Sample(X, n) → B153mean(B153) → C153Sample(X, n) → B154mean(B154) → C154Sample(X, n) → B155mean(B155) → C155Sample(X, n) → B156mean(B156) → C156Sample(X, n) → B157mean(B157) → C157Sample(X, n) → B158mean(B158) → C158Sample(X, n) → B159mean(B159) → C159Sample(X, n) → B160mean(B160) → C160Sample(X, n) → B161mean(B161) → C161Sample(X, n) → B162mean(B162) → C162Sample(X, n) → B163mean(B163) → C163Sample(X, n) → B164mean(B164) → C164Sample(X, n) → B165mean(B165) → C165Sample(X, n) → B166mean(B166) → C166Sample(X, n) → B167mean(B167) → C167Sample(X, n) → B168mean(B168) → C168Sample(X, n) → B169mean(B169) → C169Sample(X, n) → B170mean(B170) → C170Sample(X, n) → B171mean(B171) → C171Sample(X, n) → B172mean(B172) → C172Sample(X, n) → B173mean(B173) → C173Sample(X, n) → B174mean(B174) → C174Sample(X, n) → B175mean(B175) → C175Sample(X, n) → B176mean(B176) → C176Sample(X, n) → B177mean(B177) → C177Sample(X, n) → B178mean(B178) → C178Sample(X, n) → B179mean(B179) → C179Sample(X, n) → B180mean(B180) → C180Sample(X, n) → B181mean(B181) → C181Sample(X, n) → B182mean(B182) → C182Sample(X, n) → B183mean(B183) → C183Sample(X, n) → B184mean(B184) → C184Sample(X, n) → B185mean(B185) → C185Sample(X, n) → B186mean(B186) → C186Sample(X, n) → B187mean(B187) → C187Sample(X, n) → B188mean(B188) → C188Sample(X, n) → B189mean(B189) → C189Sample(X, n) → B190mean(B190) → C190Sample(X, n) → B191mean(B191) → C191Sample(X, n) → B192mean(B192) → C192Sample(X, n) → B193mean(B193) → C193Sample(X, n) → B194mean(B194) → C194Sample(X, n) → B195mean(B195) → C195Sample(X, n) → B196mean(B196) → C196Sample(X, n) → B197mean(B197) → C197Sample(X, n) → B198mean(B198) → C198Sample(X, n) → B199mean(B199) → C199Sample(X, n) → B200mean(B200) → C200Sample(X, n) → B201mean(B201) → C201Sample(X, n) → B202mean(B202) → C202Sample(X, n) → B203mean(B203) → C203Sample(X, n) → B204mean(B204) → C204Sample(X, n) → B205mean(B205) → C205Sample(X, n) → B206mean(B206) → C206Sample(X, n) → B207mean(B207) → C207Sample(X, n) → B208mean(B208) → C208Sample(X, n) → B209mean(B209) → C209Sample(X, n) → B210mean(B210) → C210Sample(X, n) → B211mean(B211) → C211Sample(X, n) → B212mean(B212) → C212Sample(X, n) → B213mean(B213) → C213Sample(X, n) → B214mean(B214) → C214Sample(X, n) → B215mean(B215) → C215Sample(X, n) → B216mean(B216) → C216Sample(X, n) → B217mean(B217) → C217Sample(X, n) → B218mean(B218) → C218Sample(X, n) → B219mean(B219) → C219Sample(X, n) → B220mean(B220) → C220Sample(X, n) → B221mean(B221) → C221Sample(X, n) → B222mean(B222) → C222Sample(X, n) → B223mean(B223) → C223Sample(X, n) → B224mean(B224) → C224Sample(X, n) → B225mean(B225) → C225Sample(X, n) → B226mean(B226) → C226Sample(X, n) → B227mean(B227) → C227Sample(X, n) → B228mean(B228) → C228Sample(X, n) → B229mean(B229) → C229Sample(X, n) → B230mean(B230) → C230Sample(X, n) → B231mean(B231) → C231Sample(X, n) → B232mean(B232) → C232Sample(X, n) → B233mean(B233) → C233Sample(X, n) → B234mean(B234) → C234Sample(X, n) → B235mean(B235) → C235Sample(X, n) → B236mean(B236) → C236Sample(X, n) → B237mean(B237) → C237Sample(X, n) → B238mean(B238) → C238Sample(X, n) → B239mean(B239) → C239Sample(X, n) → B240mean(B240) → C240Sample(X, n) → B241mean(B241) → C241Sample(X, n) → B242mean(B242) → C242Sample(X, n) → B243mean(B243) → C243Sample(X, n) → B244mean(B244) → C244Sample(X, n) → B245mean(B245) → C245Sample(X, n) → B246mean(B246) → C246Sample(X, n) → B247mean(B247) → C247Sample(X, n) → B248mean(B248) → C248Sample(X, n) → B249mean(B249) → C249Sample(X, n) → B250mean(B250) → C250Sample(X, n) → B251mean(B251) → C251Sample(X, n) → B252mean(B252) → C252Sample(X, n) → B253mean(B253) → C253Sample(X, n) → B254mean(B254) → C254Sample(X, n) → B255mean(B255) → C255Sample(X, n) → B256mean(B256) → C256Sample(X, n) → B257mean(B257) → C257Sample(X, n) → B258mean(B258) → C258Sample(X, n) → B259mean(B259) → C259Sample(X, n) → B260mean(B260) → C260Sample(X, n) → B261mean(B261) → C261Sample(X, n) → B262mean(B262) → C262Sample(X, n) → B263mean(B263) → C263Sample(X, n) → B264mean(B264) → C264Sample(X, n) → B265mean(B265) → C265Sample(X, n) → B266mean(B266) → C266Sample(X, n) → B267mean(B267) → C267Sample(X, n) → B268mean(B268) → C268Sample(X, n) → B269mean(B269) → C269Sample(X, n) → B270mean(B270) → C270Sample(X, n) → B271mean(B271) → C271Sample(X, n) → B272mean(B272) → C272Sample(X, n) → B273mean(B273) → C273Sample(X, n) → B274mean(B274) → C274Sample(X, n) → B275mean(B275) → C275Sample(X, n) → B276mean(B276) → C276Sample(X, n) → B277mean(B277) → C277Sample(X, n) → B278mean(B278) → C278Sample(X, n) → B279mean(B279) → C279Sample(X, n) → B280mean(B280) → C280Sample(X, n) → B281mean(B281) → C281Sample(X, n) → B282mean(B282) → C282Sample(X, n) → B283mean(B283) → C283Sample(X, n) → B284mean(B284) → C284Sample(X, n) → B285mean(B285) → C285Sample(X, n) → B286mean(B286) → C286Sample(X, n) → B287mean(B287) → C287Sample(X, n) → B288mean(B288) → C288Sample(X, n) → B289mean(B289) → C289Sample(X, n) → B290mean(B290) → C290Sample(X, n) → B291mean(B291) → C291Sample(X, n) → B292mean(B292) → C292Sample(X, n) → B293mean(B293) → C293Sample(X, n) → B294mean(B294) → C294Sample(X, n) → B295mean(B295) → C295Sample(X, n) → B296mean(B296) → C296Sample(X, n) → B297mean(B297) → C297Sample(X, n) → B298mean(B298) → C298Sample(X, n) → B299mean(B299) → C299Sample(X, n) → B300mean(B300) → C300Sample(X, n) → B301mean(B301) → C301Sample(X, n) → B302mean(B302) → C302Sample(X, n) → B303mean(B303) → C303Sample(X, n) → B304mean(B304) → C304Sample(X, n) → B305mean(B305) → C305Sample(X, n) → B306mean(B306) → C306Sample(X, n) → B307mean(B307) → C307Sample(X, n) → B308mean(B308) → C308Sample(X, n) → B309mean(B309) → C309Sample(X, n) → B310mean(B310) → C310Sample(X, n) → B311mean(B311) → C311Sample(X, n) → B312mean(B312) → C312Sample(X, n) → B313mean(B313) → C313Sample(X, n) → B314mean(B314) → C314Sample(X, n) → B315mean(B315) → C315Sample(X, n) → B316mean(B316) → C316Sample(X, n) → B317mean(B317) → C317Sample(X, n) → B318mean(B318) → C318Sample(X, n) → B319mean(B319) → C319Sample(X, n) → B320mean(B320) → C320Sample(X, n) → B321mean(B321) → C321Sample(X, n) → B322mean(B322) → C322Sample(X, n) → B323mean(B323) → C323Sample(X, n) → B324mean(B324) → C324Sample(X, n) → B325mean(B325) → C325Sample(X, n) → B326mean(B326) → C326Sample(X, n) → B327mean(B327) → C327Sample(X, n) → B328mean(B328) → C328Sample(X, n) → B329mean(B329) → C329Sample(X, n) → B330mean(B330) → C330Sample(X, n) → B331mean(B331) → C331Sample(X, n) → B332mean(B332) → C332Sample(X, n) → B333mean(B333) → C333Sample(X, n) → B334mean(B334) → C334Sample(X, n) → B335mean(B335) → C335Sample(X, n) → B336mean(B336) → C336Sample(X, n) → B337mean(B337) → C337Sample(X, n) → B338mean(B338) → C338Sample(X, n) → B339mean(B339) → C339Sample(X, n) → B340mean(B340) → C340Sample(X, n) → B341mean(B341) → C341Sample(X, n) → B342mean(B342) → C342Sample(X, n) → B343mean(B343) → C343Sample(X, n) → B344mean(B344) → C344Sample(X, n) → B345mean(B345) → C345Sample(X, n) → B346mean(B346) → C346Sample(X, n) → B347mean(B347) → C347Sample(X, n) → B348mean(B348) → C348Sample(X, n) → B349mean(B349) → C349Sample(X, n) → B350mean(B350) → C350Sample(X, n) → B351mean(B351) → C351Sample(X, n) → B352mean(B352) → C352Sample(X, n) → B353mean(B353) → C353Sample(X, n) → B354mean(B354) → C354Sample(X, n) → B355mean(B355) → C355Sample(X, n) → B356mean(B356) → C356Sample(X, n) → B357mean(B357) → C357Sample(X, n) → B358mean(B358) → C358Sample(X, n) → B359mean(B359) → C359Sample(X, n) → B360mean(B360) → C360Sample(X, n) → B361mean(B361) → C361Sample(X, n) → B362mean(B362) → C362Sample(X, n) → B363mean(B363) → C363Sample(X, n) → B364mean(B364) → C364Sample(X, n) → B365mean(B365) → C365Sample(X, n) → l1mean(B351) → aTake(C2:C350, 1, t) → m_imean(m_i) → mbarstdev(m_i) → s_mHistogram(Classes[m_i, 1 + round(ld(t))], m_i, true, 1 / t) → hBoxPlot(-0.3, 0.2, m_i, true) → bpNormalQuantilePlot(m_i) → nqpNormal(mean[X], stdev[X] / sqrt(n), x, false) → fDotPlot(m_i, true) → l2
AI 绘图提示语参考
展示中央极限定理,通过多次投掷骰子并计算每次投掷的平均值,观察样本均值分布如何逐渐接近正态分布。用直方图和箱线图可视化样本均值,并用正态分布曲线和点图展示其趋势,帮助理解概率统计和几何均值。
以上提示语为根据原始绘图命令整理而来,仅供参考。