【統計課件】教育統計學-資料下載頁

　　

【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 因為累積頻數和累積百分比圖形都成“ S”形，所以統稱為“ S”型曲線 。 S型曲線特殊應用是： 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 ?將統計資料通俗化、形象化、使人一目了然、易于接收。 ?有利于統計資料的比較對照，有助于科學分析研究。 ?根據資料的性質和分析的目的，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。 ?圖內應寫出所依據的數字，如未標明數字則應附以統計表或文字說明。 ?圖內資料配置一般應從左到右。 ?圖中如有必須解釋的地方，可用圖注加以說明。 統計圖的功用 繪制統計圖的規則 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名中學生語文測驗分數編成累積頻數，累積百分比分布表，并制成累積頻數分布圖和累積頻數分布圖。 分數 － － － － － － 頻數 2 4 6 15 20 36 分數 － － － － － 總和 頻數 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 把下列甲乙兩組學生化學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 描述性統計 (DESCRIPTIVE STATISTICS) ?概念 研究如何整理實驗或調查得到的大量數據 ， 找出這些數據的分布特征 。 ?種類 集中量 (如平均數 )、差異量 (如標準差 )、相關量 (相關系數 )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據典型水平或集中趨勢的量 。 ?集中量的作用： 利用集中量數可以對各個總體 (或各個樣本 )進行比較。 利用集中量數可以研究總體的一般水平在時間上的變化。 利用集中量數可以分析現象之間的依存關系。 ?集中量 (CENTRAL TENDENCY)的種類： 平均數 (MEAN) 。 中位數 (MEDIAN) 。 眾數 (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 算術平均數通常稱平均數 ， 統計上簡稱均值或均數 ， 是最重要的集中量數 ， 常用 代表總體平均數 ， 代表樣本平均數 。 X?2．公式： NXX ?? ( 算術平均數 = ) 總次數變量總和其中： =總和 X=各觀察值 N=觀察值的個數 ? 算術平均數 (MEAN) 算術平均數概念 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. 原始數據計算法 例：某幼兒園大班幼兒 10名，在某次計算練習中成績分別為9， 6， 8， 9， 7， 6， 8， 9， 7， 7。試計算這些幼兒的計算練習的平均成績。 NXX ??767798679869 ???????????? X)( 分??X 算術平均數計算 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乘積之和 表示頻數總和 ( =N) ?fx?f ?f2. 頻數分布表計算法 (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個學生數學分數算術平均數組中值計算 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 算術平均數的應用及其特點 算術平均數是最好的集中量數，因為它具備一個良好的集中量所應具備的條件。 (1)優點： ○ 反應靈敏，一組數據中任何一個數值發生或大或小的變化，所計算出來的算術平均數也會隨之變大變小。 ○嚴密確定。由同一組數據計算出來的平均數是同一個值。 ○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、相關系數以及推斷統計的基礎。 (2) 缺點： ○ 易受兩極端數值的影響 (只要一個極低值， 就會下降，反之則上升 )。 ○一組數據中某個數值模糊或不確切，就