【統計學】第三章

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數據的預處理包括哪些內容？

1.數據審核
2.數據篩選
3.數據排序
4.數據透視表

分類數據和順序數據的整理和圖示方法各有哪些？

1.分類數據整理：對於定性數據，使用頻數分布進行描述，還可以進行比例、百分比、比率等級統計量描述。

• 分類數據的圖示
• 條形圖
• 帕累托圖
• 餅圖
• 環形圖

2.順序數據整理： 對於順序數據，除了可以使用以上整理和顯示技術，還可以計算累積頻數和累積頻率(百分比)

• 順序數據的圖示
• 折線圖

數值型數據的分組方法有哪些？簡述組距分組的步驟。

數據分組的主要目的是觀察數據的分布特征。數據經分組后再計算出各組中數據出現的頻數，就形成了一張頻數分布表。
數據分組的方法有單變量值分組和組距分組兩種。

• 確定組數
• 確定各組的組距
• 根據分組整理成頻數分布表

直方圖與條形圖有何區別？

首先，條形圖是用條形的長度表示各類別頻數的多少，其寬度(表示類別)則是固定的；直方圖是用面積表示各組頻數的多少。矩形的高度表示每一組的頻數或頻率，寬度則表示各組的組距，因此其高度與寬度均有意義。
其次，由於分組數據具有連續性，直方圖的各矩形通常是連續排列，而條形圖則是分開排列。
條形圖用於展示分類數據，而直方圖用於展示數值型數據

繪制線圖應注意哪些問題？

繪制線圖時，時間一般繪在橫軸，觀測值在縱軸。一般應該繪成橫軸略大於縱軸的長方形，其長寬比例大致為10:7.
圖形過扁或過於瘦高，不僅不美觀，而且會給人造成視覺上的錯覺，不便於對數據變化的理解。一般情況下，縱軸數據下端應從"0"開始，以便於對數據變化的理解。一般情況下，縱軸數據下端應從"0"時開始，便於比較。如果數據"0"之間的間距過大，可以采取折斷的符號將縱軸折斷。

餅圖和環形圖有什么不同？

餅圖與環形圖類似，但是又有區別。環形圖中間有一個"空洞"，每個樣本用一個環來表示，樣本中的每一部分數據用環中的一段表示。因此環形圖可顯示多個樣本各部分所占的響應比例，從而有利於對構成的比較研究。

莖葉圖和環形圖相比有什么優點？它們的應用場合是什么？

莖葉圖是反映原始數據分布的圖形。它由莖和葉兩部分構成，其圖形是由數字組成的。通過莖葉圖，可以看出數據的分布形狀及數據的離散程度，比如是否對稱，數據是否集中，是否有離群點，等等。
莖葉圖類似於橫置的直方圖，與直方圖對比，莖葉圖既能給出數據的分布狀況，又能給出每一個原始數值，即保留了原始數據的信息。而直方圖雖然能很好的顯示數據的分布，但是不能保留原始的數值。在應用方面，直方圖通常適用於大批量數據，莖葉圖通常適用於小批量數據。
環形圖可顯示多個樣本各部分所占的相應比例，從而有利於對構成的比較研究。

鑒別圖表優劣的准則有哪些？

• 1.一張好圖應當靜心設計，有助於洞察問題的實質。
• 2.一張好圖應當使復雜的觀點得到簡明、確切、高效的闡述。
• 3.一張好圖應當能在最短的時間內以最少的筆墨給讀者提供大量的信息。
• 4.一張好圖應當是多維的。
• 5.一張好圖應當表述數據的真實情況。
  在繪制圖形時，應避免一切不必要的修飾。過於花哨的修飾往往會使人注重圖形本身，而掩蓋了圖形所要表達的信息。圖形產生的視覺效果應與數據所體現的事物特征相一致，否則有可能歪曲數據，給人留下錯誤的印象。

制作統計表應注意哪些問題？

• 首先，要合理安排統計表的結構，比如行標題、列標題、數據資料的位置應安排合理。當然，由於強調的問題不同，行標題和列標題可以互換，但是應使統計表的橫豎長度比例適當，避免出現過高或過寬的表格形式。
• 其次，表頭一般應包括表號、總標題和表中的數據的單位等內容。總標題應簡明確切地概括出統計表的內容，一般需要說明統計數據的時間，地點以及何種數據，即標題內容應滿足3W要求。如果表中的全部數據都是同一個計量單位，可在表的右上角標明。若各變量的計量單位不同，則應放在每個變量后或單列出一列標明。
• 再次，表中的上下兩條橫線一般用粗線，中間的其他線要用細線，這樣使人看起來清除、醒目。通常情況下，統計表的左右兩邊不封口，列標題之間在必要時可用豎線分開，而行標題之間通常不必用橫線隔開。總之表中盡量少用橫豎線。表中的數據一般是右對齊，有小數點時應以小數點對齊，而且小數點的位數應統一。對於沒有數據的表格單元，一般用"-"表示，一張填好的統計表不應出現空白單元格。

錯題集

• 1.樣本或總體中各不同類別數值之間的比值稱為比率
• 2.將比例乘以100得到的數值稱為百分數
• 3.餅圖最適合描述結構性問題
• 4.環形圖適合於比較研究兩個或多個樣本或總體的結構性問題
• 5.最適合描述一組數據分布的圖形是直方圖
• 6.對於大批量的數據，最適合描述分布的圖形是直方圖
• 7.對於小批量的數據，最適合描述分布的圖形是莖葉圖
• 8.對於時間序列數據，用於描述其變化趨勢的圖形通常是箱線圖
• 9.氣泡圖主要用於描述三個變量之間的相關關系
• 10.與直方圖相比莖葉圖保留了原始數據的信息
• 11.莖葉圖不適合描述分類數據
• 12.直方圖與條形圖的區別之一是直方圖的各矩形通常是連續排列的，而條形圖則是分開排列的

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