2025年統(tǒng)計(jì)學(xué)專業(yè)期末考試：數(shù)據(jù)分析計(jì)算題庫(kù)深度解析考試時(shí)間：______分鐘總分：______分姓名：______一、數(shù)據(jù)描述與展示要求：計(jì)算以下數(shù)據(jù)的平均值、中位數(shù)、眾數(shù)、標(biāo)準(zhǔn)差和四分位數(shù)，并使用圖表展示數(shù)據(jù)分布。1.計(jì)算以下數(shù)據(jù)的平均值、中位數(shù)、眾數(shù)、標(biāo)準(zhǔn)差和四分位數(shù)。數(shù)據(jù)集：[15,20,22,18,16,21,23,17,19,20,22,18,20,24,17,19,20,23,21,22]2.使用直方圖展示以下數(shù)據(jù)的分布情況。數(shù)據(jù)集：[2,4,5,5,6,7,7,7,7,8,8,9,9,10,10,10,10,11,11,11,11,11,12,12,12,12,13,13,13,14,14,15,15,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,39,40,40,41,41,42,42,43,43,44,44,45,45,46,46,47,47,48,48,49,49,50,50,51,51,52,52,53,53,54,54,55,55,56,56,57,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,66,67,67,68,68,69,69,70,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,78,79,79,80,80,81,81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,94,94,95,95,96,96,97,97,98,98,99,99,100]3.根據(jù)以下數(shù)據(jù)，繪制散點(diǎn)圖并觀察其分布情況。數(shù)據(jù)集A：[1,2,3,4,5,6,7,8,9,10]數(shù)據(jù)集B：[2,3,4,5,6,7,8,9,10,11]4.使用箱線圖展示以下數(shù)據(jù)的分布情況。數(shù)據(jù)集：[5,7,8,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100]5.根據(jù)以下數(shù)據(jù)，繪制直方圖并計(jì)算其概率密度函數(shù)。數(shù)據(jù)集：[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100]6.根據(jù)以下數(shù)據(jù)，繪制餅圖并計(jì)算每個(gè)類別的概率。數(shù)據(jù)集：[10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100]7.使用莖葉圖展示以下數(shù)據(jù)的分布情況。數(shù)據(jù)集：[5,7,8,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100]8.根據(jù)以下數(shù)據(jù)，繪制折線圖并觀察其變化趨勢(shì)。數(shù)據(jù)集：[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100]9.根據(jù)以下數(shù)據(jù)，繪制雷達(dá)圖并分析其分布情況。數(shù)據(jù)集：[10,20,30,40,50,60,70,80,90,100]10.使用散點(diǎn)圖展示以下數(shù)據(jù)的關(guān)聯(lián)性。數(shù)據(jù)集A：[1,2,3,4,5,6,7,8,9,10]數(shù)據(jù)集B：[2,3,4,5,6,7,8,9,10,11]二、假設(shè)檢驗(yàn)要求：對(duì)以下數(shù)據(jù)進(jìn)行分析，進(jìn)行假設(shè)檢驗(yàn)。1.對(duì)以下數(shù)據(jù)進(jìn)行分析，檢驗(yàn)均值是否顯著不等于0。數(shù)據(jù)集：[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100]2.對(duì)以下數(shù)據(jù)進(jìn)行分析，檢驗(yàn)方差是否顯著不等于1。數(shù)據(jù)集：[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100]3.對(duì)以下數(shù)據(jù)進(jìn)行分析，檢驗(yàn)兩個(gè)樣本均值是否存在顯著差異。數(shù)據(jù)集A：[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100]數(shù)據(jù)集B：[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100]4.對(duì)以下數(shù)據(jù)進(jìn)行分析，檢驗(yàn)兩個(gè)樣本方差是否存在顯著差異。數(shù)據(jù)集A：[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100]數(shù)據(jù)集B：[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,四、回歸分析要求：對(duì)以下數(shù)據(jù)進(jìn)行分析，進(jìn)行線性回歸分析，并解釋結(jié)果。1.對(duì)以下數(shù)據(jù)進(jìn)行分析，進(jìn)行線性回歸分析，計(jì)算回歸方程和決定系數(shù)R2。數(shù)據(jù)集：[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]2.根據(jù)以下數(shù)據(jù)，進(jìn)行多項(xiàng)式回歸分析，并解釋結(jié)果。數(shù)據(jù)集：[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]3.根據(jù)以下數(shù)據(jù)，進(jìn)行邏輯回歸分析，并解釋結(jié)果。數(shù)據(jù)集：[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]4.根據(jù)以下數(shù)據(jù)，進(jìn)行非線性回歸分析，并解釋結(jié)果。數(shù)據(jù)集：[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]5.根據(jù)以下數(shù)據(jù)，進(jìn)行嶺回歸分析，并解釋結(jié)果。數(shù)據(jù)集：[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]6.根據(jù)以下數(shù)據(jù)，進(jìn)行Lasso回歸分析，并解釋結(jié)果。數(shù)據(jù)集：[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]五、時(shí)間序列分析要求：對(duì)以下時(shí)間序列數(shù)據(jù)進(jìn)行分析，使用適當(dāng)?shù)姆椒ㄟM(jìn)行預(yù)測(cè)，并解釋結(jié)果。1.根據(jù)以下時(shí)間序列數(shù)據(jù)，使用移動(dòng)平均法進(jìn)行預(yù)測(cè)，并計(jì)算預(yù)測(cè)值。數(shù)據(jù)集：[100,110,120,130,140,150,160,170,180,190,200,210,220,230,240,250,260,270,280,290]2.根據(jù)以下時(shí)間序列數(shù)據(jù)，使用指數(shù)平滑法進(jìn)行預(yù)測(cè)，并計(jì)算預(yù)測(cè)值。數(shù)據(jù)集：[100,110,120,130,140,150,160,170,180,190,200,210,220,230,240,250,260,270,280,290]3.根據(jù)以下時(shí)間序列數(shù)據(jù)，使用自回歸模型進(jìn)行預(yù)測(cè)，并計(jì)算預(yù)測(cè)值。數(shù)據(jù)集：[100,110,120,130,140,150,160,170,180,190,200,210,220,230,240,250,260,270,280,290]4.根據(jù)以下時(shí)間序列數(shù)據(jù)，使用ARIMA模型進(jìn)行預(yù)測(cè)，并計(jì)算預(yù)測(cè)值。數(shù)據(jù)集：[100,110,120,130,140,150,160,170,180,190,200,210,220,230,240,250,260,270,280,290]5.根據(jù)以下時(shí)間序列數(shù)據(jù)，使用季節(jié)性分解法進(jìn)行預(yù)測(cè)，并計(jì)算預(yù)測(cè)值。數(shù)據(jù)集：[100,110,120,130,140,150,160,170,180,190,200,210,220,230,240,250,260,270,280,290]6.根據(jù)以下時(shí)間序列數(shù)據(jù)，使用機(jī)器學(xué)習(xí)模型進(jìn)行預(yù)測(cè)，并計(jì)算預(yù)測(cè)值。數(shù)據(jù)集：[100,110,120,130,140,150,160,170,180,190,200,210,220,230,240,250,260,270,280,290]六、聚類分析要求：對(duì)以下數(shù)據(jù)進(jìn)行聚類分析，使用適當(dāng)?shù)姆椒ㄟM(jìn)行聚類，并解釋結(jié)果。1.根據(jù)以下數(shù)據(jù)，使用K均值聚類方法進(jìn)行聚類，并解釋結(jié)果。數(shù)據(jù)集：[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]2.根據(jù)以下數(shù)據(jù)，使用層次聚類方法進(jìn)行聚類，并解釋結(jié)果。數(shù)據(jù)集：[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]3.根據(jù)以下數(shù)據(jù)，使用DBSCAN聚類方法進(jìn)行聚類，并解釋結(jié)果。數(shù)據(jù)集：[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]4.根據(jù)以下數(shù)據(jù)，使用高斯混合模型進(jìn)行聚類，并解釋結(jié)果。數(shù)據(jù)集：[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]5.根據(jù)以下數(shù)據(jù)，使用譜聚類方法進(jìn)行聚類，并解釋結(jié)果。數(shù)據(jù)集：[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]6.根據(jù)以下數(shù)據(jù)，使用基于密度的聚類方法進(jìn)行聚類，并解釋結(jié)果。數(shù)據(jù)集：[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]本次試卷答案如下：一、數(shù)據(jù)描述與展示1.平均值：20.25中位數(shù)：20眾數(shù)：20標(biāo)準(zhǔn)差：4.472四分位數(shù)：[17,20,22,24]解析思路：首先計(jì)算所有數(shù)據(jù)的和，然后除以數(shù)據(jù)個(gè)數(shù)得到平均值。中位數(shù)是按順序排列后位于中間的數(shù)值。眾數(shù)是出現(xiàn)次數(shù)最多的數(shù)值。標(biāo)準(zhǔn)差是每個(gè)數(shù)值與平均值之差的平方和的平均數(shù)的平方根。四分位數(shù)是數(shù)據(jù)從小到大排列后，將數(shù)據(jù)分為四等分的位置上的數(shù)值。2.數(shù)據(jù)集的直方圖如下：（此處應(yīng)有直方圖）解析思路：根據(jù)數(shù)據(jù)集的數(shù)值范圍和頻數(shù)，繪制直方圖，其中橫軸表示數(shù)據(jù)值，縱軸表示頻數(shù)。3.數(shù)據(jù)集的散點(diǎn)圖如下：（此處應(yīng)有散點(diǎn)圖）解析思路：根據(jù)數(shù)據(jù)集A和B的數(shù)值，繪制散點(diǎn)圖，橫軸表示數(shù)據(jù)集A，縱軸表示數(shù)據(jù)集B。4.數(shù)據(jù)集的箱線圖如下：（此處應(yīng)有箱線圖）解析思路：根據(jù)數(shù)據(jù)集的數(shù)值，繪制箱線圖，其中中位數(shù)用一條線表示，四分位數(shù)用兩條線表示，異常值用點(diǎn)表示。5.數(shù)據(jù)集的概率密度函數(shù)如下：（此處應(yīng)有概率密度函數(shù)圖）解析思路：根據(jù)數(shù)據(jù)集的數(shù)值，計(jì)算每個(gè)數(shù)值的概率密度，繪制概率密度函數(shù)圖。6.數(shù)據(jù)集的餅圖如下：（此處應(yīng)有餅圖）解析思路：根據(jù)數(shù)據(jù)集的數(shù)值，計(jì)算每個(gè)類別的頻率，繪制餅圖，其中每個(gè)扇形表示一個(gè)類別的頻率。二、假設(shè)檢驗(yàn)1.均值不顯著不等于0。解析思路：使用t檢驗(yàn)或z檢驗(yàn)，比較樣本均值與總體均值是否有顯著差異。2.方差不顯著不等于1。解析思路：使用F檢驗(yàn)，比較樣本方差與總體方差是否有顯著差異。3.兩個(gè)樣本均值存在顯著差異。解析思路：使用t檢驗(yàn)或z檢驗(yàn)，比較兩個(gè)樣本的均值是否有顯著差異。4.兩個(gè)樣本方差存在顯著差異。解析思路：使用F檢驗(yàn)，比較兩個(gè)樣本的方差是否有顯著差異。三、回