【正文】 l Education ECNU Department of Special Education ECNU Statistics of Education Statistics of Education Statistics of Education Statistics of Education Statistics of Education 因為累積頻數(shù)和累積百分比圖形都成“ S”形，所以統(tǒng)稱為“ S”型曲線 。 S型曲線特殊應(yīng)用是： 假如給出橫軸上一個分值，我們可以找出其百分位置。 Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Statistics of Education Statistics of Education Statistics of Education Statistics of Education Statistics of Education ?將統(tǒng)計資料通俗化、形象化、使人一目了然、易于接收。 ?有利于統(tǒng)計資料的比較對照，有助于科學(xué)分析研究。 ?根據(jù)資料的性質(zhì)和分析的目的，正確選擇適合的圖形。 ?要寫明圖的標題和圖號，文字明確扼要，寫在圖的正下方。 ?圖內(nèi)應(yīng)寫出所依據(jù)的數(shù)字，如未標明數(shù)字則應(yīng)附以統(tǒng)計表或文字說明。 ?圖內(nèi)資料配置一般應(yīng)從左到右。 ?圖中如有必須解釋的地方，可用圖注加以說明。 統(tǒng)計圖的功用 繪制統(tǒng)計圖的規(guī)則 Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Statistics of Education Statistics of Education Statistics of Education Statistics of Education Statistics of Education 1．將下例 125名中學(xué)生語文測驗分數(shù)編成累積頻數(shù)，累積百分比分布表，并制成累積頻數(shù)分布圖和累積頻數(shù)分布圖。 分數(shù) － － － － － － 頻數(shù) 2 4 6 15 20 36 分數(shù) － － － － － 總和 頻數(shù) 20 12 6 3 1 125 Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Statistics of Education Statistics of Education Statistics of Education Statistics of Education Statistics of Education 成績 組中值 甲組 乙組 20－ 3 1 25－ 1 14 30－ 6 20 35－ 10 19 40－ 18 21 45－ 21 21 50－ 29 14 55－ 28 13 60－ 40 5 65－ 31 4 70－ 32 2 75－ 19 0 80－ 14 0 85－ 10 0 90－ 4 0 總計 266 134 把下列甲乙兩組學(xué)生化學(xué)成績的分布制在同一直角坐標上，以資比較。 Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Statistics of Education Statistics of Education Statistics of Education Statistics of Education Statistics of Education 第三章 集中量 CENTRAL TENDENCY ?三種主要集中量 THREE MEASURES OF CENTRAL TENDENCY ?集中量的比較 COMPARING MEASURES OF CENTRAL TENDENCY ?對稱分布和偏態(tài)分布 SYMMETRICAL AND SKEWED DISTRIBUTION Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Statistics of Education Statistics of Education Statistics of Education Statistics of Education Statistics of Education 概述 描述性統(tǒng)計 (DESCRIPTIVE STATISTICS) ?概念 研究如何整理實驗或調(diào)查得到的大量數(shù)據(jù) ， 找出這些數(shù)據(jù)的分布特征 。 ?種類 集中量 (如平均數(shù) )、差異量 (如標準差 )、相關(guān)量 (相關(guān)系數(shù) )等。 X??Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Statistics of Education Statistics of Education Statistics of Education Statistics of Education Statistics of Education 集中量的概念及作用 集中量是代表一組數(shù)據(jù)典型水平或集中趨勢的量 。 ?集中量的作用： 利用集中量數(shù)可以對各個總體 (或各個樣本 )進行比較。 利用集中量數(shù)可以研究總體的一般水平在時間上的變化。 利用集中量數(shù)可以分析現(xiàn)象之間的依存關(guān)系。 ?集中量 (CENTRAL TENDENCY)的種類： 平均數(shù) (MEAN) 。 中位數(shù) (MEDIAN) 。 眾數(shù) (MODE) Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Statistics of Education Statistics of Education Statistics of Education Statistics of Education Statistics of Education 概念 算術(shù)平均數(shù)通常稱平均數(shù) ， 統(tǒng)計上簡稱均值或均數(shù) ， 是最重要的集中量數(shù) ， 常用 代表總體平均數(shù) ， 代表樣本平均數(shù) 。 X?2．公式： NXX ?? ( 算術(shù)平均數(shù) = ) 總次數(shù)變量總和其中： =總和 X=各觀察值 N=觀察值的個數(shù) ? 算術(shù)平均數(shù) (MEAN) 算術(shù)平均數(shù)概念 Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Statistics of Education Statistics of Education Statistics of Education Statistics of Education Statistics of Education 1. 原始數(shù)據(jù)計算法 例：某幼兒園大班幼兒 10名，在某次計算練習(xí)中成績分別為9， 6， 8， 9， 7， 6， 8， 9， 7， 7。試計算這些幼兒的計算練習(xí)的平均成績。 NXX ??767798679869 ???????????? X)( 分??X 算術(shù)平均數(shù)計算 解： Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Statistics of Education Statistics of Education Statistics of Education Statistics of Education Statistics of Education 公式： NfxX ?? 其中： 表示各組組中值與頻數(shù)乘積之和 表示頻數(shù)總和 ( =N) ?fx?f ?f2. 頻數(shù)分布表計算法 (組中值計算法 ) Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Statistics of Education Statistics of Education Statistics of Education Statistics of Education Statistics of Education 例：表 48個學(xué)生數(shù)學(xué)分數(shù)算術(shù)平均數(shù)組中值計算 Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Department of Special Education ECNU Statistics of Education Statistics of Education Statistics of Education Statistics of Education Statistics of Education 算術(shù)平均數(shù)的應(yīng)用及其特點 算術(shù)平均數(shù)是最好的集中量數(shù)，因為它具備一個良好的集中量所應(yīng)具備的條件。 (1)優(yōu)點： ○ 反應(yīng)靈敏，一組數(shù)據(jù)中任何一個數(shù)值發(fā)生或大或小的變化，所計算出來的算術(shù)平均數(shù)也會隨之變大變小。 ○嚴密確定。由同一組數(shù)據(jù)計算出來的平均數(shù)是同一個值。 ○計算簡便，只需四則運算。 ○受抽樣變動的影響較小。 ○是計算方差、標準差、相關(guān)系數(shù)以及推斷統(tǒng)計的基礎(chǔ)。 (2) 缺點： ○ 易受兩極端數(shù)值的影響 (只要一個極低值， 就會下降，反之則上升 )。 ○一組數(shù)據(jù)中某個數(shù)值模糊或不確切，就