2017春八年級數(shù)學(xué)下冊20數(shù)據(jù)的分析教案新版新人教版

PAGE/r/n第二十章/r/n/r/n數(shù)據(jù)的分析/r/n/r/n1/r/n./r/n進一步理解平均數(shù)、中位數(shù)和眾數(shù)等統(tǒng)計量的統(tǒng)計意義/r/n./r/n/r/n2/r/n./r/n會計算加權(quán)平均數(shù)/r/n,/r/n理解/r/n“/r/n權(quán)/r/n”/r/n的意義/r/n,/r/n能選擇適當(dāng)?shù)慕y(tǒng)計量表示數(shù)據(jù)的集中趨勢/r/n./r/n/r/n3/r/n./r/n會計算極差和方差/r/n,/r/n理解它們的統(tǒng)計意義/r/n,/r/n會用它們表示數(shù)據(jù)的波動情況/r/n./r/n/r/n1/r/n./r/n探索并掌握平均數(shù)、方差的計算公式/r/n,/r/n會找一組數(shù)據(jù)的中位數(shù)、眾數(shù)、極差/r/n,/r/n用樣本估計總體/r/n,/r/n并解決生產(chǎn)、生活中的有關(guān)問題/r/n./r/n/r/n2/r/n./r/n從事收集、整理、描述和分析數(shù)據(jù)得出結(jié)論的統(tǒng)計活動/r/n,/r/n經(jīng)歷數(shù)據(jù)處理的基本過程/r/n,/r/n體驗統(tǒng)計與生活的聯(lián)系/r/n,/r/n感受統(tǒng)計在生活和生產(chǎn)中的作用/r/n,/r/n養(yǎng)成用/r/n數(shù)據(jù)說話的習(xí)慣和實事求是的科學(xué)態(tài)度/r/n./r/n/r/n1/r/n./r/n能用計算器的統(tǒng)計功能進行統(tǒng)計計算/r/n,/r/n進一步體會計算器的優(yōu)越性/r/n./r/n/r/n2/r/n./r/n會用樣本平均數(shù)、方差估計總體的平均數(shù)、方差/r/n,/r/n進一步感受抽樣的必要性/r/n,/r/n體會用樣本估計總體的思想/r/n./r/n/r/n3/r/n./r/n通過創(chuàng)設(shè)問題情境/r/n,/r/n激發(fā)學(xué)生自主探求的熱情和積極參與的意識/r/n;/r/n通過合作交流/r/n,/r/n培養(yǎng)學(xué)生團結(jié)協(xié)作、樂于助人的品質(zhì)/r/n./r/n本章屬于/r/n“/r/n統(tǒng)計與概率/r/n”/r/n領(lǐng)域/r/n./r/n對于/r/n“/r/n統(tǒng)計與概率/r/n”/r/n領(lǐng)域的內(nèi)容/r/n,/r/n共有三章/r/n./r/n這三章內(nèi)容采用統(tǒng)計和概率分開編排的方式/r/n,/r/n前兩章是統(tǒng)計/r/n,/r/n最后一章是概率/r/n./r/n統(tǒng)計部分的兩章內(nèi)容按照數(shù)據(jù)處理的基本過程來/r/n安排/r/n./r/n我們在/r/n7/r/n年級下冊學(xué)習(xí)了/r/n“/r/n第/r/n10/r/n章數(shù)據(jù)的收集、整理與描述/r/n”/r/n,/r/n本章/r/n“/r/n數(shù)據(jù)的分析/r/n”/r/n主要學(xué)習(xí)分析數(shù)據(jù)的集中趨勢和離散程度的常用方法/r/n./r/n在前一章中/r/n,/r/n我們學(xué)習(xí)了收集、整理和描述數(shù)據(jù)的常用方法/r/n,/r/n將收集到的數(shù)據(jù)進行分組、列表、繪圖等處理工作后/r/n,/r/n數(shù)據(jù)分布的一些面貌和特征可以通過統(tǒng)計圖表等反映出來/r/n./r/n為了進一步了解數(shù)據(jù)分布的特征和規(guī)律/r/n,/r/n還需要計算出一些代表數(shù)據(jù)一般水平/r/n(/r/n典型水平/r/n)/r/n或分布狀況的特征量/r/n./r/n對于統(tǒng)計數(shù)據(jù)的分布的特征/r/n,/r/n可以從三個方面來分析/r/n:/r/n一是分析數(shù)據(jù)分布的集中趨勢/r/n,/r/n反映數(shù)據(jù)向其中心值/r/n(/r/n平均數(shù)/r/n)/r/n靠攏或聚集的程度/r/n;/r/n二/r/n是分析數(shù)據(jù)分布的離散程度/r/n,/r/n反映數(shù)據(jù)遠(yuǎn)離其中心值/r/n(/r/n平均數(shù)/r/n)/r/n的趨勢/r/n;/r/n三是分析數(shù)據(jù)分布的偏態(tài)和峰度/r/n,/r/n反映數(shù)據(jù)分布的形狀/r/n./r/n這三個方面分別反映了數(shù)據(jù)分布特征的不同側(cè)面/r/n./r/n根據(jù)《標(biāo)準(zhǔn)》的要求/r/n,/r/n本章就從前兩個方面研究數(shù)據(jù)的分布特征/r/n./r/n【重點】/r/n/r/n平均數(shù)、眾數(shù)、中位數(shù)、方差的定義及其應(yīng)用/r/n./r/n【難點】/r/n/r/n應(yīng)用所學(xué)的統(tǒng)計知識解決實際問題/r/n./r/n/r/n1/r/n./r/n注意與前兩個學(xué)段相關(guān)內(nèi)容的銜接/r/n./r/n本章在教學(xué)時/r/n,/r/n注意與前兩個學(xué)段的銜接/r/n,/r/n將三個學(xué)段的相關(guān)內(nèi)容/r/n,/r/n在分析數(shù)據(jù)的這個大背景下統(tǒng)一起來/r/n,/r/n在對學(xué)生已有的相關(guān)知識進行整理的基礎(chǔ)上學(xué)習(xí)新的知/r/n識/r/n./r/n例如/r/n,/r/n對于平均數(shù)、中位數(shù)、眾數(shù)/r/n,/r/n本章就是在研究數(shù)據(jù)集中趨勢的大背景下/r/n,/r/n在整理學(xué)生已有的關(guān)于這三種統(tǒng)計量的認(rèn)識的基礎(chǔ)上/r/n,/r/n學(xué)習(xí)加權(quán)平均數(shù)/r/n,/r/n研究如何根據(jù)統(tǒng)計量的特征選擇適當(dāng)?shù)慕y(tǒng)計量描述數(shù)據(jù)的集中趨勢等/r/n./r/n這樣的一種編寫方式/r/n,/r/n將三個學(xué)段的學(xué)習(xí)連成一個相互聯(lián)系、螺旋上升的整體/r/n./r/n因此/r/n,/r/n教學(xué)中要注意對已有知識的復(fù)習(xí)/r/n,/r/n在復(fù)習(xí)的基礎(chǔ)上學(xué)習(xí)新內(nèi)容/r/n,/r/n使學(xué)生對于分析數(shù)據(jù)的知識和方法形成整體認(rèn)識/r/n./r/n/r/n2/r/n./r/n準(zhǔn)確把握教學(xué)要求/r/n./r/n本章要求通過較多實例/r/n,/r/n從不同的方面進一步感受抽樣的必要性/r/n,/r/n并初步感受樣本的代表性/r/n,/r/n體會不同的抽樣可能得到不/r/n同的結(jié)果/r/n,/r/n能夠用樣本的平均數(shù)、方差估計總體的平均數(shù)、方差等/r/n./r/n因此/r/n,/r/n在本章教學(xué)時/r/n,/r/n要注意把握教學(xué)要求/r/n./r/n/r/n3/r/n./r/n合理使用計算器/r/n./r/n信息技術(shù)的發(fā)展給統(tǒng)計學(xué)的研究帶來很大變化/r/n,/r/n為統(tǒng)計工作的高效、準(zhǔn)確提供了便捷的工具/r/n./r/n對于計算器等現(xiàn)代信息技術(shù)對統(tǒng)計的作用/r/n,/r/n本章中/r/n,/r/n編寫了使用計算器求一組數(shù)據(jù)的平均數(shù)和方差的內(nèi)容作為必學(xué)內(nèi)容/r/n,/r/n還編寫了利用計算機求平均數(shù)、中位數(shù)、眾數(shù)和方差等集中統(tǒng)計量的內(nèi)容作為選學(xué)內(nèi)容等/r/n./r/n教學(xué)中要注意發(fā)揮計算器在處理數(shù)據(jù)中的作用/r/n,/r/n也要注意合理地使用計算器/r/n./r/n20/r/n./r/n1/r/n數(shù)據(jù)的集中趨勢/r/n20/r/n./r/n1/r/n./r/n1/r/n平均/r/n數(shù)/r/n(2/r/n課時/r/n)/r/n20/r/n./r/n1/r/n./r/n2/r/n中位數(shù)和眾數(shù)/r/n(2/r/n課時/r/n)/r/n/r/n4/r/n課時/r/n20/r/n./r/n2/r/n數(shù)據(jù)的波動程度/r/n1/r/n課時/r/n20/r/n./r/n3/r/n課題學(xué)習(xí)體質(zhì)健康測試中的數(shù)據(jù)分析/r/n1/r/n課時/r/n單元概括整合/r/n1/r/n課時/r/n20/r/n./r/n1/r/n/r/n數(shù)據(jù)的集中趨勢/r/n/r/n1/r/n./r/n進一步掌握算術(shù)平均數(shù)、加權(quán)平均數(shù)的概念/r/n,/r/n會求一組數(shù)據(jù)的算術(shù)平均數(shù)和加權(quán)平均數(shù)/r/n./r/n/r/n2/r/n./r/n理解中位數(shù)和眾數(shù)的定義和意義/r/n,/r/n會求一組數(shù)據(jù)的中位數(shù)和眾數(shù)/r/n,/r/n能結(jié)合具體問題解釋中位數(shù)和眾數(shù)的實際意義/r/n./r/n/r/n3/r/n./r/n能分清平均數(shù)、中位數(shù)、眾數(shù)三者的區(qū)別/r/n,/r/n根據(jù)實際問題情境選擇適當(dāng)?shù)慕y(tǒng)計量表示數(shù)據(jù)的特/r/n征/r/n./r/n經(jīng)歷應(yīng)用加權(quán)平均數(shù)對數(shù)據(jù)處理和探索中位數(shù)、眾數(shù)的過程/r/n,/r/n體驗對統(tǒng)計基本思想的理解過程/r/n./r/n能運用數(shù)據(jù)信息的分析解決一些簡單的實際問題/r/n./r/n通過加權(quán)平均數(shù)、中位數(shù)和眾數(shù)的學(xué)習(xí)/r/n,/r/n初步認(rèn)識數(shù)學(xué)與人類生活的密切聯(lián)系/r/n,/r/n感受數(shù)學(xué)結(jié)論的確定性/r/n,/r/n激發(fā)學(xué)生學(xué)好數(shù)學(xué)的熱情/r/n,/r/n感受統(tǒng)計在生活中的應(yīng)用/r/n,/r/n增強統(tǒng)計意識/r/n,/r/n培養(yǎng)統(tǒng)計能力/r/n./r/n【重點】/r/n/r/n算術(shù)平均數(shù)、加權(quán)平均數(shù)的概念及計算/r/n,/r/n會求一組數(shù)據(jù)的中位數(shù)和眾數(shù)/r/n,/r/n能結(jié)合實際情境理解其實際意義/r/n./r/n【難點】/r/n/r/n理解平均數(shù)、中位數(shù)和眾數(shù)這三個統(tǒng)計量之間的聯(lián)系與區(qū)別/r/n,/r/n能根據(jù)具體問題選/r/n擇適當(dāng)?shù)慕y(tǒng)計量分析數(shù)據(jù)信息并作出決策/r/n./r/n20/r/n./r/n1/r/n./r/n1/r/n/r/n平均數(shù)/r/n/r/n1/r/n./r/n進一步掌握算術(shù)平均數(shù)、加權(quán)平均數(shù)的概念/r/n./r/n/r/n2/r/n./r/n會求一組數(shù)據(jù)的算術(shù)平均數(shù)和加權(quán)平均數(shù)/r/n./r/n經(jīng)歷應(yīng)用加權(quán)平均數(shù)對數(shù)據(jù)處理的過程/r/n,/r/n體驗對統(tǒng)計基本思想的理解過程/r/n./r/n能運用數(shù)據(jù)信息的分析解決一些簡單的實際問題/r/n./r/n通過加權(quán)平均數(shù)的學(xué)習(xí)/r/n,/r/n初步認(rèn)識數(shù)學(xué)與人類生活的密切聯(lián)系/r/n,/r/n感受數(shù)學(xué)結(jié)論的確定性/r/n,/r/n激發(fā)學(xué)生學(xué)好數(shù)學(xué)的熱情/r/n./r/n【重點】/r/n/r/n1/r/n./r/n算術(shù)平均數(shù)、加權(quán)平均數(shù)的概念及計算/r/n./r/n/r/n2/r/n./r/n掌握加權(quán)平均數(shù)的實際應(yīng)用/r/n./r/n【難點】/r/n/r/n1/r/n./r/n體會平均/r/n數(shù)在不同情境中的應(yīng)用/r/n./r/n/r/n/r/n2/r/n./r/n應(yīng)用加權(quán)平均數(shù)對數(shù)據(jù)做出合理判斷/r/n./r/n第/r/n課時/r/n/r/n1/r/n./r/n使學(xué)生理解數(shù)據(jù)的權(quán)和加權(quán)平均數(shù)的概念/r/n./r/n/r/n2/r/n./r/n使學(xué)生掌握加權(quán)平均數(shù)的計算方法/r/n./r/n/r/n1/r/n./r/n通過加權(quán)平均數(shù)的學(xué)習(xí)/r/n,/r/n經(jīng)歷運用數(shù)據(jù)描述信息/r/n,/r/n作出推斷的過程/r/n,/r/n形成和發(fā)展統(tǒng)計觀念/r/n./r/n/r/n2/r/n./r/n通過加權(quán)平均數(shù)的學(xué)習(xí)/r/n,/r/n進一步認(rèn)識數(shù)據(jù)的作用/r/n,/r/n體會統(tǒng)計的思想方法/r/n./r/n滲透數(shù)學(xué)公式的簡單美和結(jié)構(gòu)的嚴(yán)謹(jǐn)美/r/n,/r/n展示了寓深奧于淺顯、寓紛繁于嚴(yán)謹(jǐn)?shù)霓q證統(tǒng)一的數(shù)學(xué)美/r/n./r/n【重點】/r/n/r/n會求加權(quán)平均數(shù)/r/n./r/n【難點】/r/n/r/n對/r/n“/r/n權(quán)/r/n”/r/n的正確理解/r/n./r/n【教師準(zhǔn)備】/r/n/r/n教學(xué)中出示的課件和例題/r/n./r/n【學(xué)生準(zhǔn)備】/r/n/r/n預(yù)習(xí)課本內(nèi)容/r/n./r/n/r/n導(dǎo)入一/r/n:/r/n劉木頭開了一家小工廠/r/n,/r/n生產(chǎn)兒童玩具/r/n./r/n工廠的管理人員由劉木頭、他的弟弟及其他/r/n6/r/n個親戚組成/r/n./r/n工作人員由/r/n5/r/n個領(lǐng)工和/r/n10/r/n個工人組成/r/n./r/n現(xiàn)在需要一個新工人/r/n,/r/n劉木頭正在與一個叫小王的青年人談?wù)衅竼栴}/r/n./r/n劉木頭說/r/n:/r/n“/r/n我們這里報酬不錯/r/n,/r/n平均每個人的薪金是每周/r/n300/r/n元/r/n,/r/n但在學(xué)徒期間每周是/r/n75/r/n元/r/n,/r/n不過很快就可以加工資/r/n./r/n”/r/n小王上了幾天班以后/r/n,/r/n要求和廠長談?wù)?r/n./r/n小王說/r/n:/r/n“/r/n你騙我/r/n,/r/n我已經(jīng)和其他工人核對過了/r/n,/r/n沒有一個人的工資超過每周/r/n100/r/n元/r/n./r/n每人平均工資怎么可能是一周/r/n300/r/n元呢/r/n?/r/n”/r/n劉木頭皮笑肉不笑地回答/r/n:/r/n“/r/n小王/r/n,/r/n不要激動嘛/r/n!/r/n每人平均工資確實是/r/n300/r/n元/r/n,/r/n不信你自己算一算/r/n./r/n”/r/n劉木頭拿出一張表/r/n,/r/n說道/r/n:/r/n“/r/n這是我每周付出的薪金/r/n./r/n我得/r/n2400/r/n元/r/n,/r/n我弟弟得/r/n1000/r/n元/r/n,/r/n我的/r/n6/r/n個親戚每人得/r/n250/r/n元/r/n,5/r/n個領(lǐng)工每人得/r/n200/r/n元/r/n,10/r/n個工人每人得/r/n100/r/n元/r/n./r/n總共是每周/r/n6900/r/n元/r/n,/r/n付給/r/n23/r/n個人/r/n,/r/n平均每人得/r/n300/r/n元/r/n,/r/n對嗎/r/n?/r/n”/r/n/r/n“/r/n對/r/n,/r/n對/r/n,/r/n你是對的/r/n,/r/n每人的平均工資是每周/r/n300/r/n元/r/n./r/n可你還是騙了我/r/n./r/n”/r/n小王生氣地說/r/n./r/n劉木頭拍著小王的肩膀說/r/n:/r/n“/r/n這我可不同意/r/n,/r/n你自己算的結(jié)果也表/r/n明我沒騙你呀/r/n!/r/n小兄弟/r/n,/r/n你根本不懂得平均數(shù)的含義/r/n,/r/n怪不得別人喲/r/n!/r/n”/r/n同學(xué)們/r/n,/r/n你能當(dāng)個小法官來判一下誰說的對嗎/r/n?/r/n/r/n[/r/n設(shè)計意圖/r/n]/r/n/r/n讓學(xué)生明確數(shù)學(xué)問題來源于生活實踐/r/n,/r/n同時數(shù)學(xué)又指導(dǎo)生活實踐/r/n,/r/n從而達到激發(fā)學(xué)生思考問題、探究新知的強烈欲望及引入新課的目的/r/n./r/n導(dǎo)入二/r/n:/r/n農(nóng)科院為了選出適合某地種植的甜玉米種子/r/n,/r/n對甲、乙兩個品種各用/r/n10/r/n塊試驗田進行試驗/r/n,/r/n得到各試驗田每公頃的產(chǎn)量/r/n(/r/n見下表/r/n),/r/n根據(jù)這些數(shù)據(jù)/r/n,/r/n應(yīng)為農(nóng)科院選擇甜玉米種子提出怎樣的建議呢/r/n?/r/n/r/n品種/r/n各試驗田每公頃產(chǎn)量/r/n(/r/n單位/r/n:/r/n噸/r/n)/r/n甲/r/n7/r/n./r/n65/r/n7/r/n./r/n50/r/n7/r/n./r/n62/r/n7/r/n./r/n59/r/n7/r/n./r/n65/r/n7/r/n./r/n64/r/n7/r/n./r/n50/r/n7/r/n./r/n40/r/n7/r/n./r/n41/r/n7/r/n./r/n41/r/n乙/r/n7/r/n./r/n55/r/n7/r/n./r/n56/r/n7/r/n./r/n53/r/n7/r/n./r/n44/r/n7/r/n./r/n49/r/n7/r/n./r/n52/r/n7/r/n./r/n58/r/n7/r/n./r/n46/r/n7/r/n./r/n53/r/n7/r/n./r/n49/r/n/r/n提問/r/n:/r/n如何考察一種玉米的產(chǎn)量和產(chǎn)量的穩(wěn)定性/r/n?/r/n學(xué)生隨意說出自己的一些想法后/r/n,/r/n教師說明本章學(xué)習(xí)的知識內(nèi)容/r/n:/r/n/r/n(1)/r/n平均數(shù)、中位數(shù)、眾數(shù)和方差等概念/r/n;/r/n/r/n(2)/r/n用樣本的平均數(shù)和方差估計總體的平均數(shù)和方差/r/n;/r/n/r/n(3)/r/n課題學(xué)習(xí)/r/n,/r/n解決實際問題/r/n./r/n/r/n[/r/n設(shè)計意圖/r/n]/r/n/r/n問題的提出/r/n,/r/n學(xué)生難以用已學(xué)到的平均數(shù)的公式解決這個問題/r/n,/r/n需要研究新/r/n的方法/r/n,/r/n學(xué)習(xí)新的知識/r/n,/r/n讓學(xué)生了解本章研究的基本知識內(nèi)容/r/n,/r/n培養(yǎng)學(xué)生用樣本估計總體的基本思想/r/n./r/n/r/n[/r/n過渡語/r/n]/r/n/r/n前面我們學(xué)過算術(shù)平均數(shù)的計算/r/n,/r/n我們一起來探究加權(quán)平均數(shù)/r/n./r/n/r/n1/r/n./r/n加權(quán)平均數(shù)/r/n思路一/r/n問題/r/n:/r/n某市三個郊縣的人數(shù)及人均耕地面積如下表/r/n:/r/n郊縣/r/n人數(shù)/r/n//r/n萬/r/n人均耕地面積/r/n//r/n公頃/r/nA/r/n15/r/n0/r/n./r/n15/r/nB/r/n7/r/n0/r/n./r/n21/r/nC/r/n10/r/n0/r/n./r/n18/r/n/r/n這個市郊縣的人均耕地面積是多少/r/n?(/r/n精確到/r/n0/r/n./r/n01/r/n公頃/r/n)/r/n問題/r/n1/r/n小明求得這個市郊縣的人均耕地面積為/r/n:/r/n=/r/n/r/n=0/r/n./r/n18(/r/n公頃/r/n)/r/n./r/n你認(rèn)為小明的做法有道理嗎/r/n?/r/n為什么/r/n?/r/n組織學(xué)生討論/r/n,/r/n教師參與/r/n,/r/n并適時指導(dǎo)/r/n:/r/n/r/n(1)/r/n對/r/n“/r/n平均數(shù)/r/n”/r/n和/r/n“/r/n人均耕地面積/r/n”/r/n的準(zhǔn)確理解/r/n;/r/n/r/n(2)/r/n三個郊縣人數(shù)的多少對人均耕地面積有無影響/r/n,/r/n分析小明同學(xué)的計算錯誤/r/n./r/n問題/r/n2/r/n這個市郊縣的總耕地面積是多少/r/n?/r/n總?cè)丝谑嵌嗌?r/n?/r/n你能算出這個市郊縣的人均耕地面積是多少嗎/r/n?/r/n引導(dǎo)學(xué)生列出正確算式/r/n,/r/n即這個市郊縣的人均耕地面積為/r/n:/r/n/r/n≈/r/n0/r/n./r/n17(/r/n公頃/r/n)/r/n./r/n問題/r/n3/r/n三個郊縣的人數(shù)/r/n(/r/n單位/r/n:/r/n萬/r/n)15,7,10/r/n在計算人均耕地面積時有何作用/r/n?/r/n教師指出/r/n:/r/n上面的平均數(shù)/r/n0/r/n./r/n17/r/n稱為三個數(shù)/r/n0/r/n./r/n15,0/r/n./r/n21,0/r/n./r/n18/r/n的加權(quán)平均數(shù)/r/n./r/n三個郊縣的人數(shù)/r/n(/r/n單位/r/n:/r/n萬/r/n)15,7,10/r/n分別為三個數(shù)據(jù)的權(quán)/r/n./r/n追問/r/n:/r/n你能正確理解數(shù)據(jù)的權(quán)和三個數(shù)的加權(quán)平均數(shù)嗎/r/n?/r/n在活動中教師應(yīng)重點關(guān)注學(xué)生對數(shù)據(jù)的權(quán)及加權(quán)平均數(shù)的理解/r/n./r/n問題/r/n4/r/n若/r/nn/r/n個數(shù)/r/nx/r/n1/r/n,/r/nx/r/n2/r/n,/r/n…/r/n,/r/nx/r/nn/r/n的權(quán)分別是/r/nw/r/n1/r/n,/r/nw/r/n2/r/n,/r/n…/r/n,/r/nw/r/nn/r/n,/r/n則這/r/nn/r/n個數(shù)的加權(quán)平均數(shù)是多少/r/n?/r/n教師引導(dǎo)學(xué)生從三個數(shù)據(jù)的加權(quán)平均數(shù)的計算方法中/r/n,/r/n歸納得出/r/nn/r/n個數(shù)的加權(quán)平均數(shù)的計算公式/r/n./r/n學(xué)生思考、總結(jié)歸納/r/n:/r/n若/r/nn/r/n個數(shù)/r/nx/r/n1/r/n,/r/nx/r/n2/r/n,/r/n…/r/n,/r/nx/r/nn/r/n的權(quán)分別是/r/nw/r/n1/r/n,/r/nw/r/n2/r/n,/r/n…/r/n,/r/nw/r/nn/r/n,/r/n則叫做這/r/nn/r/n個數(shù)的加權(quán)平均數(shù)/r/n./r/n/r/n[/r/n設(shè)計意圖/r/n]/r/n/r/n通過討論、分析、思考認(rèn)識到用已學(xué)過的平均數(shù)的計算方法來計算這個市郊縣的人均耕地面積是根本行不通的/r/n,/r/n使學(xué)生意識到需要學(xué)習(xí)新知識、新方法/r/n,/r/n激發(fā)學(xué)生去探究/r/n./r/n通過大膽猜想/r/n,/r/n培養(yǎng)學(xué)生的探究意識/r/n,/r/n通過教師的有效引導(dǎo)/r/n,/r/n讓學(xué)生體會數(shù)學(xué)的歸納思想方法/r/n,/r/n理解/r/nn/r/n個數(shù)的加權(quán)平均數(shù)的計算公式及其結(jié)構(gòu)特征/r/n,/r/n認(rèn)識數(shù)據(jù)的權(quán)的作用/r/n./r/n思路二/r/n問題/r/n1/r/n一家公司打算招聘一名英文翻譯/r/n,/r/n對甲乙兩名應(yīng)試者進行了聽、說、讀、寫的英語水平測試/r/n,/r/n他們各項的成績/r/n(/r/n百分制/r/n)/r/n如下/r/n:/r/n應(yīng)試者/r/n聽/r/n說/r/n讀/r/n寫/r/n甲/r/n85/r/n83/r/n78/r/n75/r/n乙/r/n73/r/n80/r/n85/r/n82/r/n/r/n提問/r/n:/r/n如果這家公司想招一名綜合能力較強的翻譯/r/n,/r/n計算兩名應(yīng)試者的平均成績/r/n(/r/n百分制/r/n),/r/n從他們的成績看/r/n,/r/n應(yīng)該錄取誰/r/n?/r/n錄用依據(jù)是什么/r/n?/r/n學(xué)生提出評判依據(jù)/r/n,/r/n若學(xué)生提出以總分作為依據(jù)/r/n,/r/n教師要引導(dǎo)學(xué)生思考/r/n:/r/n已學(xué)過的哪個統(tǒng)計量可反映數(shù)據(jù)的集中趨勢/r/n?/r/n學(xué)生計算平均數(shù)/r/n,/r/n解決問題/r/n./r/n追問/r/n:/r/n這家公司在招聘英文翻譯的過程中/r/n,/r/n對甲、乙兩名應(yīng)試者進行了哪幾個方面的英語水平測試/r/n?/r/n成績分別為多少/r/n?/r/n學(xué)生同桌討論/r/n,/r/n計算后提出自己的意見/r/n./r/n問題/r/n2/r/n如果這家公司想招一名筆譯能力較強的翻譯/r/n,/r/n聽、說、讀、寫成績按照/r/n2∶1∶3/r/n∶4/r/n的比確定/r/n,/r/n計算兩名應(yīng)試者的平均成績/r/n,/r/n從他們的成績看/r/n,/r/n應(yīng)該錄取誰/r/n?/r/n引導(dǎo)學(xué)生討論/r/n:/r/n招聘口語能力或筆譯能力較強的翻譯時/r/n,/r/n聽、說、讀、寫四項成績的重要程度是否相同/r/n,/r/n公司側(cè)重哪兩個方面的成績/r/n?/r/n從給出的比值是否體現(xiàn)這兩方面更加/r/n“/r/n重要/r/n”/r/n?/r/n根據(jù)算術(shù)平均數(shù)的計算公式/r/n,/r/n讓學(xué)生依據(jù)題目要求/r/n,/r/n分別計算出甲、乙兩名應(yīng)試者的成績/r/n,/r/n教師引導(dǎo)寫出解答過程/r/n./r/n問題/r/n3/r/n在問題/r/n2/r/n中/r/n,/r/n各個數(shù)據(jù)的重要程度不同/r/n(/r/n權(quán)不同/r/n),/r/n這種計算平均數(shù)的方法能否推廣到一般/r/n?/r/n追問/r/n:/r/n若/r/nn/r/n個數(shù)據(jù)/r/nx/r/n1/r/n,/r/nx/r/n2/r/n,/r/n…/r/n,/r/nx/r/nn/r/n的權(quán)分別為/r/nw/r/n1/r/n,/r/nw/r/n2/r/n,/r/n…/r/n,/r/nw/r/nn/r/n,/r/n這/r/nn/r/n個/r/n數(shù)據(jù)的平均數(shù)該如何計算/r/n?/r/n教師引導(dǎo)學(xué)生思考?xì)w納得出/r/nn/r/n個數(shù)的加權(quán)平均數(shù)的計算公式/r/n:/r/n若/r/nn/r/n個數(shù)/r/nx/r/n1/r/n,/r/nx/r/n2/r/n,/r/n…/r/n,/r/nx/r/nn/r/n的權(quán)分別是/r/nw/r/n1/r/n,/r/nw/r/n2/r/n,/r/n…/r/n,/r/nw/r/nn/r/n,/r/n則叫做這/r/nn/r/n個數(shù)的加權(quán)平均數(shù)/r/n./r/n問題/r/n4/r/n如果這家公司想招一名口語能力較強的翻譯/r/n,/r/n應(yīng)該側(cè)重哪些分項成績/r/n?/r/n如果聽、說、讀、寫成績按照/r/n3∶3∶2∶2/r/n的比確定兩人的測試成績/r/n,/r/n那么誰將被錄取/r/n?/r/n與問題/r/n2/r/n相比較/r/n,/r/n你能體會到權(quán)的作用嗎/r/n?/r/n學(xué)生獨立完成計算過程/r/n,/r/n體會權(quán)的改變對加權(quán)平均數(shù)的影響/r/n./r/n追問/r/n:/r/n你認(rèn)為問題/r/n1/r/n中各數(shù)據(jù)的權(quán)有什么關(guān)系/r/n?/r/n通過上述問題的解決/r/n,/r/n說說你對權(quán)的認(rèn)識/r/n./r/n師生活動/r/n:/r/n引導(dǎo)學(xué)生分析加權(quán)平均數(shù)公式/r/n,/r/n發(fā)現(xiàn)問題/r/n1/r/n中各數(shù)可看作是權(quán)相同的/r/n,/r/n教師指出兩種平均數(shù)之間的聯(lián)系/r/n./r/n/r/n[/r/n設(shè)計意圖/r/n]/r/n/r/n回顧學(xué)過的平均數(shù)的意義/r/n,/r/n為引入加權(quán)平均數(shù)作鋪墊/r/n./r/n通過討論/r/n,/r/n讓學(xué)生充分發(fā)表自己的見解/r/n,/r/n同時接納和吸引別人的正確意見/r/n,/r/n相互交流、相互探討/r/n,/r/n培養(yǎng)學(xué)生的合作意識/r/n./r/n通過改變同一個問題背景中數(shù)據(jù)的權(quán)/r/n,/r/n得到不同的結(jié)果/r/n,/r/n從而進一步體會權(quán)的意義與作用/r/n./r/n/r/n[/r/n知識拓展/r/n]/r/n/r/n(1)/r/n當(dāng)所給的數(shù)據(jù)在一常數(shù)/r/na/r/n上下波動時/r/n,/r/n一般選用/r/n=/r/n'/r/n+/r/na./r/n一組數(shù)據(jù)/r/nx/r/n1/r/n,/r/nx/r/n2/r/n,/r/n…/r/n,/r/nx/r/nn/r/n的各個數(shù)據(jù)比較大的時候/r/n,/r/n我們可以把各個數(shù)據(jù)同時減去一/r/n個適當(dāng)?shù)某?shù)/r/na/r/n,/r/n得/r/nx'/r/n1/r/n=/r/nx/r/n1/r/n-/r/na/r/n,/r/nx'/r/n2/r/n=/r/nx/r/n2/r/n-/r/na/r/n,/r/n…/r/n,/r/nx'/r/nn/r/n=/r/nx/r/nn/r/n-/r/na./r/n于是/r/nx/r/n1/r/n=/r/nx'/r/n1/r/n+/r/na/r/n,/r/nx/r/n2/r/n=/r/nx'/r/n2/r/n+/r/na/r/n,/r/n…/r/n,/r/nx/r/nn/r/n=/r/nx'/r/nn/r/n+/r/na./r/n因此/r/n=(/r/nx/r/n1/r/n+/r/nx/r/n2/r/n+/r/n…/r/n+/r/nx/r/nn/r/n)=(/r/nx/r/n1/r/n'/r/n+/r/nx/r/n2/r/n'/r/n+/r/n…/r/n+/r/nx/r/nn/r/n'/r/n)+/r/n·/r/nna/r/n=/r/n'/r/n+/r/na/r/n;(2)/r/n平均數(shù)的大小與每個數(shù)據(jù)都有關(guān)系/r/n,/r/n它反映一組數(shù)據(jù)的集中趨勢/r/n,/r/n是一組數(shù)據(jù)的/r/n“/r/n重心/r/n”/r/n,/r/n也是度量一組數(shù)據(jù)波動大小的基準(zhǔn)/r/n;(3)/r/n加權(quán)平均數(shù)是算術(shù)平均數(shù)的特例/r/n./r/n加權(quán)平均數(shù)的實質(zhì)就是考慮不同權(quán)重的平均數(shù)/r/n,/r/n當(dāng)加權(quán)平均數(shù)的各項權(quán)相等時/r/n,/r/n就變成了算術(shù)平均數(shù)/r/n./r/n/r/n2/r/n./r/n例題講解/r/n/r/n/r/n一次演講比賽中/r/n,/r/n評委將從演/r/n講內(nèi)容、演講能力、演講效果三個方面為選手打分/r/n,/r/n各個成績均按百分制/r/n,/r/n再按演講內(nèi)容占/r/n50%/r/n、演講能力占/r/n40%/r/n、演講效果占/r/n10%/r/n的比例/r/n,/r/n計算選手的綜合成績/r/n(/r/n百分制/r/n),/r/n進入決賽的前兩名選手的單項成績?nèi)缦卤硭?r/n:(/r/n單位/r/n:/r/n分/r/n)/r/n選手/r/n演講內(nèi)容/r/n演講能力/r/n演講效果/r/nA/r/n85/r/n95/r/n95/r/nB/r/n95/r/n85/r/n95/r/n/r/n請確定兩人的名次/r/n./r/n教師出示例題并指導(dǎo)學(xué)生閱讀分析/r/n:/r/n這個問題可以看成是求兩名選手三項成績的加權(quán)平均數(shù)/r/n,50%,40%,10%/r/n說明演講內(nèi)容、演講能力、演講效果三項成績在總成績中的重要程度/r/n,/r/n是三項成績的權(quán)/r/n./r/n/r/n學(xué)生在閱讀過程中明確下列問題/r/n:/r/n/r/n(1)/r/n演講內(nèi)容、演講能力、演講效果三項成績在總成績中的重要程度用什么數(shù)據(jù)說明/r/n?/r/n/r/n(2)/r/n要想決出兩人的名次/r/n,/r/n必須求兩人的總成績/r/n,/r/n實質(zhì)上是求這兩名選手三項成績的加權(quán)平均數(shù)/r/n./r/n學(xué)生根據(jù)加權(quán)平均數(shù)的計算公式先分別計算出兩名選手的總成績/r/n,/r/n教師進一步引導(dǎo)寫出解答過程/r/n./r/n解/r/n:/r/n選手/r/nA/r/n的最后得分是/r/n=90,/r/n選手/r/nB/r/n的最后得分是/r/n=91/r/n./r/n由上可知選手/r/nB/r/n獲得第一名/r/n,/r/n選手/r/nA/r/n獲得第二名/r/n./r/n/r/n[/r/n設(shè)計意圖/r/n]/r/n/r/n讓學(xué)生掌握自學(xué)的方法/r/n,/r/n提高學(xué)生獨立分析問題、解決問題的能力/r/n./r/n通過問題的解決/r/n,/r/n讓學(xué)生進一步/r/n體會數(shù)據(jù)的權(quán)的作用/r/n,/r/n體驗參與數(shù)學(xué)活動的樂趣/r/n./r/n/r/n(1)/r/n加權(quán)平均數(shù)的意義/r/n:/r/n在一組數(shù)據(jù)中/r/n,/r/n由于每個數(shù)據(jù)的權(quán)不同/r/n,/r/n所以計算平均數(shù)時/r/n,/r/n用加權(quán)平均數(shù)/r/n,/r/n才符合實際/r/n./r/n/r/n(2)/r/n數(shù)據(jù)的權(quán)的意義/r/n:/r/n數(shù)據(jù)的權(quán)能夠反映數(shù)據(jù)的相對/r/n“/r/n重要程度/r/n”/r/n./r/n/r/n(3)/r/n加權(quán)平均數(shù)公式/r/n:=/r/n./r/n/r/n1/r/n./r/n晨光中學(xué)規(guī)定學(xué)生的學(xué)期體育成績滿分為/r/n100/r/n分/r/n,/r/n其中平時體育活動評估成績占/r/n20%,/r/n期中成績占/r/n30%,/r/n期末成績占/r/n50%/r/n./r/n則平時體育活動評估成績、期中成績、期末成績的權(quán)分別為/r/n/r/n、/r/n/r/n和/r/n/r/n.

/r/n解析/r/n:/r/n根據(jù)權(quán)的概念解決即可/r/n./r/n答案/r/n:2/r/n0%30%50%/r/n/r/n2/r/n./r/n學(xué)校把學(xué)生學(xué)科的期中、期末兩次成績分別按/r/n40%,60%/r/n的比例計入學(xué)期學(xué)科總成績/r/n./r/n小明期中數(shù)學(xué)成績是/r/n85/r/n分/r/n,/r/n期末數(shù)學(xué)成績是/r/n90/r/n分/r/n,/r/n那么他的學(xué)期數(shù)學(xué)總成績是/r/n(/r/n/r/n)/r/n/r/nA/r/n./r/n85/r/n分/r/nB/r/n./r/n87/r/n./r/n5/r/n分/r/n/r/nC/r/n./r/n88/r/n分/r/nD/r/n./r/n90/r/n分/r/n解析/r/n:/r/n根據(jù)學(xué)期數(shù)學(xué)成績/r/n=/r/n期中數(shù)學(xué)成績/r/n×/r/n所占的百分比/r/n+/r/n期末數(shù)學(xué)成績/r/n×/r/n所占的百分比即可求得學(xué)期總成績/r/n./r/n故選/r/nC/r/n./r/n/r/n3/r/n./r/n一家公司打算招聘一名部門經(jīng)理/r/n,/r/n現(xiàn)對甲、乙兩名應(yīng)聘者從筆試、面試、實習(xí)成績?nèi)齻€方面表現(xiàn)進行評分/r/n,/r/n筆試占總成績的/r/n20%,/r/n面試占/r/n30%,/r/n實習(xí)成績占/r/n5/r/n0%,/r/n各項成績?nèi)缦卤硭?r/n:(/r/n單位/r/n:/r/n分/r/n)/r/n應(yīng)聘者/r/n筆試/r/n面試/r/n實習(xí)/r/n甲/r/n85/r/n83/r/n90/r/n乙/r/n80/r/n85/r/n92/r/n/r/n試判斷誰會被公司錄用/r/n,/r/n為什么/r/n?/r/n解/r/n:/r/n甲的平均成績?yōu)?r/n=86/r/n./r/n9,/r/n乙的平均成績?yōu)?r/n=87/r/n./r/n5/r/n./r/n因此/r/n,/r/n乙會被公司錄用/r/n./r/n/r/n4/r/n./r/n某單位欲招聘一名技術(shù)部門負(fù)責(zé)人/r/n,/r/n對甲、乙、丙三位候選人進行了三項能力測試/r/n,/r/n且各項測試成績滿分均為/r/n100/r/n分/r/n,/r/n根據(jù)結(jié)果擇優(yōu)錄取/r/n,/r/n三位候選人的各項測試成績?nèi)缦卤硭?r/n:(/r/n單位/r/n:/r/n分/r/n)/r/n測試項目/r/n測試成績/r/n甲/r/n乙/r/n丙/r/n溝通能力/r/n85/r/n73/r/n73/r/n科研能力/r/n70/r/n71/r/n65/r/n組織能力/r/n64/r/n72/r/n84/r/n/r/n(1)/r/n如果根據(jù)三項測試的平均成績/r/n,/r/n誰將被錄用/r/n?/r/n說明理由/r/n./r/n/r/n(2)/r/n根據(jù)實際需要/r/n,/r/n該單位將溝通能力、科研能力和組織能力三項測試得分按/r/n5∶3∶2/r/n的比例確定每人的成績/r/n,/r/n誰將被錄用/r/n?/r/n說明理由/r/n./r/n解/r/n:(1)/r/n甲的平均成績?yōu)?r/n(85+70+64)÷3=73,/r/n乙的平均成績?yōu)?r/n(73+71+72)÷3=72,/r/n丙的平均成績?yōu)?r/n(73+65+84)÷3=74,/r/n因此/r/n,/r/n丙的平均成績最高/r/n,/r/n丙將被錄用/r/n./r/n(2)/r/n甲的成績?yōu)?r/n=76/r/n./r/n3,/r/n乙的成績?yōu)?r/n=72/r/n./r/n2,/r/n丙的成績?yōu)?r/n=72/r/n./r/n8/r/n./r/n因此/r/n,/r/n甲的成績最高/r/n,/r/n甲將被錄用/r/n./r/n第/r/n1/r/n課時/r/n/r/n1/r/n./r/n加權(quán)平均數(shù)/r/n/r/n2/r/n./r/n例題講解/r/n例題/r/n一、教材作業(yè)/r/n【必做題】/r/n教材第/r/n113/r/n頁練習(xí)第/r/n1,2/r/n題/r/n;/r/n教材第/r/n121/r/n頁習(xí)題/r/n20/r/n./r/n1/r/n第/r/n1/r/n題/r/n./r/n【選做題】/r/n教材第/r/n122/r/n頁習(xí)題/r/n20/r/n./r/n1/r/n第/r/n5/r/n題/r/n./r/n二、課后作業(yè)/r/n【基礎(chǔ)鞏固】/r/n1/r/n./r/n在中國好聲音選秀節(jié)目中/r/n,/r/n四位參賽選手的各項得分如下表/r/n,/r/n如果將專業(yè)、形象、人氣這三項得分按/r/n3∶2∶1/r/n的比例確定最終得分/r/n,/r/n最終得分最高的進入下一輪比賽/r/n,/r/n則進入下一輪比賽的是/r/n(/r/n/r/n)(/r/n每項按/r/n10/r/n分制/r/n)/r/n測試內(nèi)容/r/n測試成績/r/n小趙/r/n小王/r/n小李/r/n小黃/r/n專業(yè)素質(zhì)/r/n6/r/n7/r/n8/r/n8/r/n形象表現(xiàn)/r/n8/r/n7/r/n6/r/n9/r/n人氣指數(shù)/r/n8/r/n10/r/n9/r/n6/r/nA./r/n小趙/r/nB./r/n小王/r/nC./r/n小李/r/nD/r/n./r/n小黃/r/n2/r/n./r/n學(xué)校廣播站要招聘/r/n1/r/n名記者/r/n,/r/n小明、小亮和小麗報名參加了/r/n3/r/n項素質(zhì)測試/r/n,/r/n成績?nèi)缦?r/n:/r/n采訪寫作/r/n計算機/r/n創(chuàng)意設(shè)計/r/n小明/r/n70/r/n分/r/n60/r/n分/r/n86/r/n分/r/n小亮/r/n90/r/n分/r/n75/r/n分/r/n51/r/n分/r/n小麗/r/n60/r/n分/r/n84/r/n分/r/n72/r/n分/r/n現(xiàn)在要計算/r/n3/r/n人的加權(quán)平均分/r/n,/r/n如果將采訪寫作、計算機和創(chuàng)意設(shè)計這三項的權(quán)重比由/r/n3∶5∶2/r/n變成/r/n5∶3∶2,/r/n成績變化情況是/r/n(/r/n/r/n)/r/nA./r/n小明增加最多/r/nB./r/n小亮增加最多/r/nC./r/n小麗增加最多/r/nD/r/n./r/n三人的成績都增加/r/n3/r/n./r/n希望中學(xué)一個學(xué)期的數(shù)學(xué)總平均分是按下圖進行計算的/r/n./r/n該校李飛同學(xué)這個學(xué)期的數(shù)學(xué)成績?nèi)缦?r/n:(/r/n單位/r/n:/r/n分/r/n)/r/n李飛/r/n平時作業(yè)/r/n期中考試/r/n期末考試/r/n90/r/n85/r/n88/r/n則李飛這個學(xué)期數(shù)學(xué)總平均分為/r/n/r/n.

/r/n4/r/n./r/n某商場用加權(quán)平均數(shù)來確定什錦糖的單價/r/n,/r/n由單價為/r/n15/r/n元/r/n//r/n千克的甲種糖果/r/n10/r/n千克/r/n,/r/n單價為/r/n12/r/n元/r/n//r/n千克的乙種糖果/r/n20/r/n千克/r/n,/r/n單價為/r/n10/r/n元/r/n//r/n千克的丙種糖果/r/n30/r/n千克混合成的什錦糖果的單價應(yīng)定為/r/n/r/n.

/r/n【能力提升】/r/n5/r/n./r/n學(xué)生的學(xué)科期末成績由期考分?jǐn)?shù)、作業(yè)分?jǐn)?shù)、課堂參與分?jǐn)?shù)三部分組成/r/n,/r/n按各/r/n占/r/n30%,30%,40%/r/n的比例確定/r/n./r/n已知曉明的數(shù)學(xué)期考/r/n80/r/n分/r/n,/r/n作業(yè)/r/n90/r/n分/r/n,/r/n課堂參與/r/n85/r/n分/r/n,/r/n則他的數(shù)學(xué)期末成績?yōu)?r/n/r/n分/r/n.

/r/n6/r/n./r/n小麗家上個月吃飯費用為/r/n500/r/n元/r/n,/r/n教育費用為/r/n200/r/n元/r/n,/r/n其他費用為/r/n500/r/n元/r/n./r/n本月小麗家這三項費用分別增長了/r/n10%,30%/r/n和/r/n5%/r/n./r/n小麗家本月的總費用比上個月增長的百分?jǐn)?shù)是多少/r/n?/r/n7/r/n./r/n小李同學(xué)七年級第二學(xué)期的數(shù)學(xué)成績?nèi)缦卤硭?r/n:/r/n測驗類別/r/n平時/r/n期中/r/n考試/r/n期末/r/n考試/r/n測驗/r/n1/r/n測驗/r/n2/r/n測驗/r/n3/r/n測驗/r/n4/r/n成績/r/n(/r/n分/r/n)/r/n88/r/n92/r/n94/r/n90/r/n92/r/n89/r/n如果學(xué)期的總評成績是根據(jù)/r/n如圖所示的權(quán)重計算/r/n,/r/n那么小李同學(xué)該學(xué)期的總評成績?yōu)槎嗌俜?r/n?(/r/n四舍五入精確到/r/n1/r/n分/r/n)/r/n8/r/n./r/n老師在計算學(xué)期總平均分的時候按如下標(biāo)準(zhǔn)/r/n:/r/n作業(yè)占/r/n10%,/r/n測驗占/r/n20%,/r/n期中考試占/r/n35%,/r/n期末考試占/r/n35%,/r/n小關(guān)和小兵的成績?nèi)缦卤?r/n:/r/n學(xué)生/r/n作業(yè)/r/n測驗/r/n期中考試/r/n期末考試/r/n小關(guān)/r/n80/r/n75/r/n71/r/n88/r/n小兵/r/n76/r/n80/r/n68/r/n90/r/n分別算出小關(guān)和小兵的總平均分/r/n./r/n【拓展探究】/r/n9/r/n./r/n某單位欲從內(nèi)部招聘管理人員一名/r/n,/r/n對甲、乙、丙三名候選人進行了筆試和面試兩項測試/r/n,/r/n三人的測試成績?nèi)缦卤硭?r/n:/r/n測試成績/r/n(/r/n單位/r/n:/r/n分/r/n)/r/n測試項目/r/n甲/r/n乙/r/n丙/r/n筆試/r/n75/r/n80/r/n90/r/n面試/r/n93/r/n70/r/n68/r/n根據(jù)錄用程序/r/n,/r/n組織/r/n200/r/n名職工對三人利用投票推薦的方式進行民主評議/r/n,/r/n三人得票率/r/n(/r/n沒有棄權(quán)票/r/n,/r/n每位職工只能推薦/r/n1/r/n人/r/n)/r/n如圖所示/r/n,/r/n每得一票記作/r/n1/r/n分/r/n./r/n(1)/r/n請算出三人的民主評議得分/r/n;/r/n(2)/r/n如果根據(jù)三項測試的平均成績確定錄用人選/r/n,/r/n那么誰將被錄用/r/n?(/r/n精確到/r/n0/r/n./r/n01)/r/n(3)/r/n根據(jù)實際需要/r/n,/r/n單位將筆試、面試、民主評議三項測試得分按/r/n4∶3∶3/r/n的比例確定個人成績/r/n,/r/n那么誰將被錄用/r/n?/r/n【答案與解析】/r/n1/r/n./r/nD(/r/n解析/r/n:/r/n將四個人的測試成績按比例求出最終成績/r/n,/r/n找出成/r/n績最高的即可/r/n./r/n)/r/n2/r/n./r/nB(/r/n解析/r/n:/r/n根據(jù)加權(quán)平均數(shù)的概念分別計算出/r/n3/r/n人的各自成績/r/n./r/n先求出采訪寫作、計算機和創(chuàng)意設(shè)計這三項的權(quán)重比是/r/n3∶5∶2/r/n各自的成績/r/n,/r/n再求出這三項的權(quán)重比是/r/n5∶3∶2/r/n各自的成績/r/n,/r/n進行比較/r/n./r/n)/r/n3/r/n./r/n87/r/n./r/n5(/r/n解析/r/n:/r/n先從統(tǒng)計圖得到相應(yīng)數(shù)據(jù)的權(quán)重/r/n,/r/n再利用加權(quán)平均數(shù)的計算方法求解/r/n./r/n)/r/n4/r/n./r/n11/r/n./r/n5/r/n元/r/n//r/n千克/r/n(/r/n解析/r/n:/r/n將三種糖果的總價算出/r/n,/r/n再除以/r/n60/r/n即可/r/n./r/n)/r/n5/r/n./r/n85(/r/n解析/r/n:/r/n根據(jù)加權(quán)平均數(shù)的計算公式計算即可/r/n./r/n)/r/n6/r/n./r/n解/r/n:500×10%+200×30%+500×5%=135(/r/n元/r/n),135÷(500+200/r/n+500)×100%=11/r/n./r/n25%/r/n./r/n7/r/n./r/n解/r/n:/r/n平時平均成績?yōu)?r/n=91(/r/n分/r/n),/r/n總評成績?yōu)?r/n=90/r/n./r/n1/r/n≈/r/n90(/r/n分/r/n)/r/n./r/n8/r/n./r/n解/r/n:/r/n小關(guān)的學(xué)期總平均分為/r/n=80×10%+75×20%+71×35%+88×35%=78/r/n./r/n65(/r/n分/r/n),/r/n小兵的學(xué)期總平均分為/r/n'/r/n=76×10%+80×20%+68×35%+90×35%=78/r/n./r/n9(/r/n分/r/n)/r/n./r/n9/r/n./r/n解/r/n:(1)/r/n甲、乙、丙三人的民主評議得分分別為/r/n:200×25%=50(/r/n分/r/n),200×40%=80(/r/n分/r/n),200×35%=70(/r/n分/r/n)/r/n./r/n(2)/r/n甲的平均成績?yōu)?r/n≈/r/n72/r/n./r/n67(/r/n分/r/n),/r/n乙的平均成績?yōu)?r/n≈/r/n76/r/n./r/n6/r/n7(/r/n分/r/n),/r/n丙的平均成績?yōu)?r/n=76/r/n./r/n00(/r/n分/r/n)/r/n./r/n由于/r/n76/r/n./r/n67>76>72/r/n./r/n67,/r/n所以候選人乙將被錄用/r/n./r/n(3)/r/n甲的個人成績?yōu)?r/n=72/r/n./r/n9(/r/n分/r/n);/r/n乙的個人成績?yōu)?r/n=77(/r/n分/r/n);/r/n丙的個人成績?yōu)?r/n=77/r/n./r/n4(/r/n分/r/n)/r/n./r/n由于丙的個人成績最高/r/n,/r/n所以候選人丙將被錄用/r/n./r/n本節(jié)課把學(xué)生的探索和驗證活動放在首位/r/n,/r/n一方面要求學(xué)生在老師的引導(dǎo)下自主探索/r/n,/r/n合作交流/r/n,/r/n另一方面要求學(xué)生對探究過程中用到的數(shù)學(xué)思想方法有一定的領(lǐng)悟和認(rèn)識/r/n,/r/n達到培養(yǎng)能力的目的/r/n./r/n平均數(shù)是統(tǒng)計中的一個重要概念/r/n,/r/n新教材注重了學(xué)生在經(jīng)歷統(tǒng)計活動的過程中體會平均數(shù)的本/r/n質(zhì)內(nèi)涵/r/n,/r/n理解平均數(shù)的意義/r/n,/r/n發(fā)展學(xué)生的統(tǒng)計觀念/r/n./r/n基于以上認(rèn)識/r/n,/r/n我在設(shè)計中突出了讓學(xué)生在具體情境中體會為什么要學(xué)習(xí)平均數(shù)/r/n,/r/n注重引導(dǎo)學(xué)生在統(tǒng)計的背景中理解平均數(shù)的含義/r/n,/r/n在比較、觀察中把握平均數(shù)的特征/r/n,/r/n進而運用平均數(shù)解決實際問題/r/n,/r/n了解它的價值/r/n,/r/n努力做到由傳統(tǒng)的數(shù)學(xué)課堂向?qū)嶒炚n堂轉(zhuǎn)變/r/n./r/n在教學(xué)過程中/r/n,/r/n高估了學(xué)生理解加權(quán)平均數(shù)的能力/r/n,/r/n主要困難在于一些學(xué)生不能對權(quán)的含義理解透徹/r/n./r/n適當(dāng)增加學(xué)生熟知的一些實例/r/n,/r/n通過計算平均數(shù)/r/n,/r/n深刻理解權(quán)的含義及對平均數(shù)的影響/r/n./r/n練習(xí)/r/n(/r/n教材第/r/n113/r/n頁/r/n)/r/n1/r/n./r/n解/r/n:(1)/r/n甲/r/n:=/r/n88(/r/n分/r/n),/r/n乙/r/n:=87/r/n./r/n5(/r/n分/r/n),/r/n故甲將被錄取/r/n./r/n(2)/r/n甲/r/n:=87/r/n./r/n6(/r/n分/r/n),/r/n乙/r/n:=88/r/n./r/n4(/r/n分/r/n),/r/n故乙將被錄取/r/n./r/n2/r/n./r/n解/r/n:=88/r/n./r/n5(/r/n分/r/n)/r/n./r/n故小桐這學(xué)期的體育成績是/r/n88/r/n./r/n5/r/n分/r/n./r/n學(xué)生在第二學(xué)段已學(xué)過平均數(shù)/r/n,/r/n初步了解了平均數(shù)的實際意義/r/n,/r/n這個課時將在此基礎(chǔ)上/r/n,/r/n在研究數(shù)據(jù)集中趨勢的大背景下/r/n,/r/n學(xué)習(xí)加權(quán)平均數(shù)/r/n,/r/n體會權(quán)的意義、作用/r/n,/r/n并進一步體會平均數(shù)是刻畫一組數(shù)據(jù)集中趨勢的重要的統(tǒng)計量/r/n,/r/n是一組數(shù)據(jù)的/r/n“/r/n重心/r/n”/r/n./r/n教材設(shè)計了以招聘英文翻譯為背景的實際問題/r/n,/r/n根據(jù)不同的招聘要求/r/n,/r/n各項成績的/r/n“/r/n重要程度/r/n”/r/n不同/r/n,/r/n從而平/r/n均成績不同/r/n,/r/n由此引入加權(quán)平均數(shù)的概念/r/n./r/n權(quán)的重要性在于它能夠反映數(shù)據(jù)的相對/r/n“/r/n重要程度/r/n”/r/n./r/n為了更好地說明這一點/r/n,/r/n教科書設(shè)計了/r/n“/r/n思考/r/n”/r/n欄目和例/r/n1,/r/n從不同方面體現(xiàn)權(quán)的作用/r/n,/r/n使學(xué)生更好地理解加權(quán)平均數(shù)/r/n,/r/n體會權(quán)的意義和作用/r/n./r/n加權(quán)平均數(shù)不同于簡單的算術(shù)平均數(shù)/r/n,/r/n簡單的算術(shù)平均數(shù)只與數(shù)據(jù)的大小有關(guān)/r/n,/r/n而加權(quán)平均數(shù)則還與該組數(shù)據(jù)的權(quán)相關(guān)/r/n,/r/n學(xué)生對權(quán)的意義和作用的理解會有困難/r/n,/r/n往往造成數(shù)據(jù)與權(quán)混淆不清/r/n,/r/n只會利用公式/r/n,/r/n而不知加權(quán)平均數(shù)的統(tǒng)計意義/r/n./r/n本節(jié)課的教學(xué)重點是對權(quán)及加權(quán)平均數(shù)統(tǒng)計意義的理解/r/n;/r/n教學(xué)難點是對權(quán)的意義的理解/r/n,/r/n用加/r/n權(quán)平均數(shù)分析一組數(shù)據(jù)的集中趨勢/r/n./r/n/r/n/r/n(2014/r/n·/r/n張家界中考/r/n)/r/n已知一組數(shù)據(jù)/r/n4,13,24/r/n的權(quán)數(shù)分別是/r/n,,/r/n則這組數(shù)據(jù)的加權(quán)平均數(shù)是/r/n/r/n.

/r/n〔解析〕/r/n/r/n由加權(quán)平均數(shù)計算公式得/r/n=4×+13×+24×=17/r/n./r/n故填/r/n17/r/n./r/n/r/n/r/n/r/n(2014/r/n·/r/n樂山中考/r/n)/r/n下表是/r/n10/r/n支不同型號簽字筆的相關(guān)信息/r/n,/r/n則/r/n1/r/n支簽字筆的平均價格是/r/n/r/n/r/n(/r/n/r/n)/r/n型號/r/nA/r/nB/r/nC/r/n價格/r/n(/r/n元/r/n//r/n支/r/n)/r/n1/r/n1/r/n./r/n5/r/n2/r/n數(shù)量/r/n(/r/n支/r/n)/r/n3/r/n2/r/n5/r/nA.1.4/r/n元/r/n/r/n/r/nB.1.5/r/n元/r/n/r/n/r/nC.1.6/r/n元/r/n/r/n/r/nD/r/n./r/n1/r/n./r/n7/r/n元/r/n〔解析〕/r/n/r/n將表格中的數(shù)據(jù)代入加權(quán)/r/n平均數(shù)的公式即可/r/n./r/n由題意得/r/n==1/r/n./r/n6(/r/n元/r/n)/r/n./r/n故選/r/nC/r/n./r/n第/r/n課時/r/n/r/n1/r/n./r/n加深對加權(quán)平均數(shù)的理解/r/n./r/n/r/n2/r/n./r/n會根據(jù)頻數(shù)分布表求加權(quán)平均數(shù)/r/n,/r/n從而解決一些實際問題/r/n./r/n/r/n3/r/n./r/n會用計算器求加權(quán)平均數(shù)的值/r/n./r/n經(jīng)歷探索加權(quán)平均數(shù)的應(yīng)用過程/r/n,/r/n體驗和理解統(tǒng)計的基本思想/r/n,/r/n學(xué)會頻數(shù)分布表中應(yīng)用加權(quán)平均數(shù)的方法/r/n./r/n樂于接觸社會環(huán)境中的數(shù)學(xué)信息/r/n,/r/n了解數(shù)學(xué)對促進社會進步和發(fā)展人類理解精神的作用/r/n./r/n【重點】/r/n/r/n能根據(jù)頻數(shù)分布表利用組中值的方法應(yīng)用公式計算加權(quán)平均數(shù)/r/n./r/n【難點】/r/n/r/n對算術(shù)平均數(shù)的簡便算法與加權(quán)平均數(shù)/r/n算法一致性的理解/r/n./r/n【教師準(zhǔn)備】/r/n/r/n教學(xué)中出示的教學(xué)圖表和例題/r/n./r/n【學(xué)生準(zhǔn)備】/r/n/r/n預(yù)習(xí)教材內(nèi)容/r/n./r/n/r/n導(dǎo)入一/r/n:/r/n為了解/r/n5/r/n路公共汽車的運營情況/r/n,/r/n公交部門統(tǒng)計了某天/r/n5/r/n路公共汽車每個運行班次的載客量/r/n,/r/n得到下表/r/n:/r/n載客量/r/n//r/n人/r/n組中值/r/n頻數(shù)/r/n(/r/n班次/r/n)/r/n1/r/n≤/r/nx/r/n<21/r/n11/r/n3/r/n21/r/n≤/r/nx/r/n<41/r/n31/r/n5/r/n41/r/n≤/r/nx/r/n<61/r/n51/r/n20/r/n61/r/n≤/r/nx/r/n<81/r/n71/r/n22/r/n81/r/n≤/r/nx/r/n<101/r/n91/r/n18/r/n101/r/n≤/r/nx/r/n<121/r/n111/r/n15/r/n/r/n(1)/r/n這天/r/n5/r/n路公共汽車平均每班的載客量是多少/r/n?/r/n/r/n(2)/r/n從表中你能知道這一/r/n天/r/n5/r/n路公共汽車大約有多少班次的載客量在平均載客量以上嗎/r/n?/r/n占全天總班次的百分比是多少/r/n?/r/n學(xué)生思考后/r/n,/r/n追問/r/n:/r/n在求加權(quán)平均數(shù)時/r/n,/r/n各組的數(shù)據(jù)如何確定/r/n?/r/n各組的權(quán)分別是什么/r/n?/r/n你能計算這天/r/n5/r/n路公共汽車平均每班的載客量嗎/r/n?/r/n/r/n[/r/n設(shè)計意圖/r/n]/r/n/r/n使學(xué)生在思考問題的過程中體會利用統(tǒng)計知識可以解決生活中的許多實際問題/r/n,/r/n幫助學(xué)生理解表格所表達出來的信息/r/n,/r/n立足原有的基礎(chǔ)/r/n,/r/n自然引出新課/r/n./r/n導(dǎo)入二/r/n:/r/n/r/n[/r/n過渡語/r/n]/r/n/r/n上節(jié)課/r/n,/r/n我們學(xué)習(xí)了加權(quán)平均數(shù)的定義和公式/r/n,/r/n我們一起來回顧一下/r/n./r/n在求/r/nn/r/n個數(shù)的平均數(shù)時/r/n,/r/n如果/r/nx/r/n1/r/n出現(xiàn)/r/nf/r/n1/r/n次/r/n,/r/nx/r/n2/r/n出現(xiàn)/r/nf/r/n2/r/n次/r/n,/r/n…/r/n,/r/nx/r/nk/r/n出現(xiàn)/r/nf/r/nk/r/n次/r/n(/r/n其中/r/nf/r/n1/r/n+/r/nf/r/n2/r/n+/r/n…/r/n+/r/nf/r/nk/r/n=/r/nn/r/n),/r/n那么這/r/nn/r/n個數(shù)的平均數(shù)/r/n=/r/n也叫做/r/nx/r/n1/r/n,/r/nx/r/n2/r/n,/r/n…/r/n,/r/nx/r/nk/r/n這/r/nk/r/n個數(shù)的加權(quán)平均數(shù)/r/n,/r/n其中/r/nf/r/n1/r/n,/r/nf/r/n2/r/n,/r/n…/r/n,/r/nf/r/nk/r/n分別叫做/r/nx/r/n1/r/n,/r/nx/r/n2/r/n,/r/n…/r/n,/r/nx/r/nk/r/n的權(quán)/r/n./r/n下面請同學(xué)們自學(xué)教材/r/n114/r/n頁探究/r/n,/r/n思考下面的問題/r/n:/r/n/r/n(1)/r/n依據(jù)統(tǒng)計表可以讀出哪些信息/r/n?/r/n/r/n(2)/r/n這里組中值指什么/r/n?/r/n它是怎么確定的/r/n?/r/n/r/n(3)/r/n第二組數(shù)據(jù)的頻數(shù)是什么呢/r/n?/r/n/r/n(4)/r/n如果每組數(shù)據(jù)在本組中分布均勻/r/n,/r/n數(shù)據(jù)的平均值和組中值有什么關(guān)系/r/n?/r/n學(xué)生自由討論/r/n,/r/n交流/r/n./r/n/r/n[/r/n設(shè)計意圖/r/n]/r/n/r/n讓學(xué)生復(fù)習(xí)舊知/r/n,/r/n自主探究問題/r/n,/r/n激發(fā)學(xué)生學(xué)習(xí)的興/r/n趣和欲望/r/n,/r/n為深入探究新知做好準(zhǔn)備/r/n./r/n/r/n1/r/n./r/n根據(jù)頻數(shù)分布表求加權(quán)平均數(shù)/r/n思路一/r/n/r/n[/r/n過渡語/r/n]/r/n/r/n下面我們具體來看看剛才探究的問題/r/n./r/n學(xué)生思考、探索、交流/r/n,/r/n解決每個問題/r/n./r/n/r/n(1)/r/n知道了/r/n5/r/n路公共汽車每個運行班次的載客量/r/n./r/n/r/n(2)/r/n組中值是指這個小組的兩個端點的數(shù)的平均數(shù)/r/n./r/n/r/n(3)/r/n第二組數(shù)據(jù)的頻數(shù)是/r/n5/r/n./r/n/r/n(4)/r/n每組數(shù)據(jù)的平均值和組中值基本是一致的/r/n./r/n教師指點/r/n:/r/n根據(jù)頻數(shù)分布表求加權(quán)平均數(shù)時/r/n,/r/n統(tǒng)計中常用各組的組中值代表各組的實際數(shù)據(jù)/r/n,/r/n把各組的頻數(shù)看作相應(yīng)組中值的權(quán)/r/n,/r/n例如在/r/n1/r/n≤/r/nx/r/n<21/r/n之間的載客量近/r/n似地看作組中值/r/n11,/r/n組中值/r/n11/r/n的權(quán)是它的頻數(shù)/r/n3/r/n./r/n因此這天/r/n5/r/n路公共汽車平均每班的載客量是/r/n=/r/n≈/r/n73(/r/n人/r/n)/r/n./r/n/r/n[/r/n設(shè)計意圖/r/n]/r/n/r/n引出根據(jù)頻數(shù)分布表求加權(quán)平均數(shù)近似值的計算方法/r/n,/r/n加深了對/r/n“/r/n權(quán)/r/n”/r/n意義的理解/r/n:/r/n當(dāng)利用組中值近似代替一組數(shù)據(jù)中的平均值時/r/n,/r/n頻數(shù)恰好反映這組數(shù)據(jù)的輕重程度/r/n,/r/n即權(quán)/r/n,/r/n也可以幫助學(xué)生去回憶、復(fù)習(xí)關(guān)于頻數(shù)分布表的一些內(nèi)容/r/n,/r/n比如組中值及頻數(shù)在表中的具體意義/r/n./r/n思路二/r/n為調(diào)查居民生活環(huán)境質(zhì)量/r/n,/r/n環(huán)保局對/r/n50/r/n個居民區(qū)進行了噪音/r/n(/r/n單位/r/n:/r/n分貝/r/n)/r/n水平的調(diào)查/r/n,/r/n結(jié)果如下圖/r/n,/r/n求每個小區(qū)噪音的平均分貝數(shù)/r/n./r/n提出問題/r/n:/r/n/r/n(1)/r/n依據(jù)統(tǒng)計圖可以讀出哪些信息/r/n?/r/n/r/n(2)/r/n各組的數(shù)據(jù)是怎樣確定的/r/n?/r/n/r/n(3)/r/n每一組數(shù)據(jù)的頻數(shù)指什么呢/r/n?/r/n學(xué)生思考、探索、交流/r/n,/r/n解決每個問題/r/n./r/n教師總結(jié)/r/n:/r/n根據(jù)頻數(shù)分布圖求加權(quán)平均數(shù)時/r/n,/r/n統(tǒng)計中常用各組的組中值代表各組的實際數(shù)據(jù)/r/n,/r/n把各組的頻數(shù)看作相應(yīng)組中值的權(quán)/r/n,/r/n例如在/r/n40/r/n≤/r/nx/r/n<50/r/n之間的噪音近似地看作組中值/r/n45/r/n分貝/r/n,/r/n組中值/r/n45/r/n的權(quán)是它的頻數(shù)/r/n4/r/n./r/n/r/n/r/n[/r/n設(shè)計意圖/r/n]/r/n/r/n引出根據(jù)頻數(shù)分布直方圖求加權(quán)平均數(shù)近似值的計算方法/r/n,/r/n加深了對/r/n“/r/n權(quán)/r/n”/r/n意義的理解/r/n:/r/n當(dāng)利用組中值近似代替一組數(shù)據(jù)中的平均值時/r/n,/r/n頻數(shù)恰好反映這組數(shù)據(jù)的/r/n輕重程度/r/n,/r/n即權(quán)/r/n,/r/n也可以幫助學(xué)生提高獲取信息、分析數(shù)據(jù)的能力/r/n./r/n/r/n2/r/n./r/n用計算器求加權(quán)平均數(shù)的值/r/n使用計算器的統(tǒng)計功能求平均數(shù)時/r/n,/r/n不同品牌的計算器的操作步驟有所不同/r/n,/r/n操作時需要參閱計算器的使用說明書/r/n./r/n通常需要先按動有關(guān)鍵/r/n,/r/n使計算器進入統(tǒng)計狀態(tài)/r/n;/r/n然后依次輸入數(shù)據(jù)/r/nx/r/n1/r/n,/r/nx/r/n2/r/n,/r/n…/r/n,/r/nx/r/nk/r/n以及它們的權(quán)/r/nf/r/n1/r/n,/r/nf/r/n2/r/n,/r/n…/r/n,/r/nf/r/nk/r/n/r/n;/r/n最后按動求平均數(shù)的功能鍵/r/n(/r/n例如鍵/r/n),/r/n計算器便會求出平均數(shù)的值/r/n./r/n學(xué)生選擇教材第/r/n114/r/n頁中的探究進行練習(xí)/r/n,/r/n組內(nèi)交流操作情況/r/n./r/n/r/n3/r/n./r/n例題講解/r/n/r/n[/r/n過渡語/r/n]/r/n/r/n下面我們一起來分析幾個例子/r/n./r/n/r/n/r/n(/r/n教材例/r/n2)/r/n某跳水隊為了解運動員的年齡情況/r/n,/r/n作了一次年齡調(diào)查/r/n,/r/n結(jié)果如下/r/n:13/r/n歲/r/n8/r/n人/r/n,14/r/n歲/r/n16/r/n人/r/n,15/r/n歲/r/n24/r/n人/r/n,16/r/n歲/r/n2/r/n人/r/n./r/n求這個跳水隊運動員的平均年齡/r/n(/r/n結(jié)果取整數(shù)/r/n)/r/n./r/n教師提問/r/n:/r/n求跳水隊運動員的平均年齡實際上是求哪些數(shù)據(jù)的加權(quán)平均數(shù)/r/n?/r/n學(xué)生分析/r/n,/r/n此題中的問題實際就是求/r/n13,14,15,16/r/n這/r/n4/r/n個數(shù)的加權(quán)平均數(shù)/r/n,8,16,24,2/r/n叫做/r/n13,14,15,16/r/n的權(quán)/r/n./r/n解/r/n:=/r/n≈/r/n14(/r/n歲/r/n)/r/n./r/n/r/n[/r/n解題策略/r/n]/r/n/r/n本題主要考查應(yīng)用加權(quán)平均數(shù)解決實際問題/r/n,/r/n關(guān)鍵是弄清這組數(shù)據(jù)的權(quán)/r/n,/r/n并能運用加權(quán)平均數(shù)公式進行運算/r/n./r/n/r/n/r/n(/r/n教材例/r/n3)/r/n某燈泡廠為測量一批燈泡的使用壽命/r/n,/r/n從中抽查了/r/n50/r/n只燈泡/r/n,/r/n它們的使用壽命如下表所示/r/n:/r/n使用壽命/r/nx//r/nh/r/n600/r/n≤/r/nx/r/n<1000/r/n1000/r/n≤/r/nx/r/n<1400/r/n1400/r/n≤/r/nx/r/n<1800/r/n1800/r/n≤/r/nx/r/n<2200/r/n2200/r/n≤/r/nx/r/n<2600/r/n燈泡只數(shù)/r/n5/r/n10/r/n12/r/n17/r/n6/r/n/r/n這批燈泡的平均使用壽命是多少/r/n?/r/n〔解析〕/r/n/r/n抽出的/r/n50/r/n只燈泡的使用壽命組成一個樣本/r/n,/r/n可以利用樣本的平均使用壽命來估計這批燈泡的平均使用壽命/r/n./r/n求這個樣本的平均使用壽命即是求這個樣本的加權(quán)平均數(shù)/r/n,/r/n根據(jù)頻數(shù)分布表提供的數(shù)據(jù)求出加權(quán)平均數(shù)即可/r/n./r/n/r/n解/r/n:/r/n根據(jù)表可以得出各小組的組中值/r/n,/r/n于是/r/n==1672,/r/n即樣本平均數(shù)為/r/n1672/r/n./r/n因此/r/n,/r/n可以估計這批燈泡的平均使用壽命是/r/n1672/r/n/r/nh/r/n./r/n/r/n[/r/n歸納總結(jié)/r/n]/r/n/r/n本題考查了用樣本的平均數(shù)來估計總體的平均數(shù)/r/n./r/n當(dāng)所要考察的對象很多時/r/n,/r/n或者對考察對象帶有破壞性時/r/n,/r/n統(tǒng)計中常常通過樣本估計總體/r/n./r/n師生共同回顧本節(jié)課所學(xué)主要內(nèi)容/r/n:/r/n/r/n1/r/n./r/n在求/r/nn/r/n個數(shù)的平均數(shù)時/r/n,/r/n如果/r/nx/r/n1/r/n出現(xiàn)/r/nf/r/n1/r/n次/r/n,/r/nx/r/n2/r/n出現(xiàn)/r/nf/r/n2/r/n次/r/n,/r/n…/r/n,/r/nx/r/nk/r/n出現(xiàn)/r/nf/r/nk/r/n次/r/n(/r/n其中/r/nf/r/n1/r/n+/r/nf/r/n2/r/n+/r/n…/r/n+/r/nf/r/nk/r/n=/r/nn/r/n),/r/n那么這/r/nn/r/n個數(shù)的平均數(shù)/r/n=/r/n也叫做/r/nx/r/n1/r/n,/r/nx/r/n2/r/n,/r/n…/r/n,/r/nx/r/nk/r/n這/r/nk/r/n個數(shù)的加權(quán)平均數(shù)/r/n,/r/n其中/r/nf/r/n1/r/n,/r/nf/r/n2/r/n,/r/n…/r/n,/r/nf/r/nk/r/n分別叫做/r/nx/r/n1/r/n,/r/nx/r/n2/r/n,/r/n…/r/n,/r/nx/r/nk/r/n的權(quán)/r/n./r/n/r/n2/r/n./r/n運用頻數(shù)分布表求加權(quán)平均數(shù)時/r/n,/r/n統(tǒng)計中常用各組的組中值代表各組的實際數(shù)據(jù)/r/n,/r/n把各組的頻數(shù)看作相應(yīng)組中值的權(quán)/r/n,/r/n利用加權(quán)平均數(shù)公式計算即可/r/n./r/n/r/n/r/n1/r/n./r/n有人對某旅游區(qū)的旅游人數(shù)進行了/r/n10/r/n天統(tǒng)計/r/n,/r/n結(jié)果有/r/n3/r/n天是每天/r/n800/r/n人/r/n,/r/n有/r/n2/r/n天是每天/r/n1200/r/n人/r/n,/r/n有/r/n5/r/n天是每天/r/n700/r/n人/r/n,/r/n那么這/r/n10/r/n天平均每天旅游的人數(shù)是/r/n(/r/n/r/n)/r/n/r/nA.830/r/n人/r/nB.850/r/n人/r/nC.900/r/n人/r/nD.800/r/n人/r/n解析/r/n:/r/n求出這/r/n10/r/n天的總?cè)藬?shù)后/r/n,/r/n除以/r/n10/r/n即為平均每天旅游的人數(shù)/r/n./r/n由題意知/r/n,10/r/n天旅/r/n游的總?cè)藬?shù)/r/n=800×3+1200×2+700×5=8300(/r/n人/r/n),∴/r/n平均每天旅游的人數(shù)/r/n=8300÷10=830(/r/n人/r/n)/r/n./r/n故選/r/nA/r/n./r/n/r/n2/r/n./r/n某瓜農(nóng)采用大棚栽培技術(shù)種植了一畝地的良種西瓜/r/n,/r/n這畝地產(chǎn)西瓜約/r/n600/r/n個/r/n./r/n為了考察西瓜的產(chǎn)量/r/n,/r/n在西瓜上市前該瓜農(nóng)隨機抽查了部分成熟的西瓜/r/n,/r/n稱重如下/r/n:/r/n西瓜質(zhì)量/r/n//r/