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【繁體】數學女孩秘密筆記:統計篇

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【繁體】數學女孩秘密筆記:統計篇

Name: 【繁體】數學女孩秘密筆記:統計篇
Brand: KingStone
SKU: 3136019861
Price: 25.59 USD
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内容簡介

日本数学会出版賞得主結城浩《數學女孩》系列最新力作

結合文系與理系，史上最強的科普輕小說！

揭開統計之謎，品味其中奧妙。

看穿圖表的詭計、找出硬幣問題的真相…

解開題目的痛快瞬間，令人欲罷不能！

主角和由梨、蒂蒂、米爾迦三位少女，

這次挑戰的是統計問題！

如何跳脫『非零即一的詛咒』？

解開問題，就能互相了解嗎？

答案，就藏在女孩們的對話之間。

前言 1

序章 2

第1章圖表的詭計 3

1.1常見的圖表 3

1.2 製作表格 4

1.3 想要看起來增加很多 6

1.4 想要看起來增加更多 7

1.5 想要看起來增加不多 9

1.6 長條圖 10

1.7 改變橫軸 12

1.8 股價走勢圖 13

1.9 其實是下跌 14

1.10 其實是持續上漲 15

1.11 員工人數的比較 16

1.12 比較員工人數的圖表 17

1.13 旗鼓相當的演出 18

1.14 選擇比較對象 19

1.15 市場競爭 20

1.16 比較什麼？ 22

第1章的問題 23

第2章平分均勻的平均數 24

2.1 測驗的結果 25

2.2 代表值 28

2.3 眾數 29

2.4 中位數 31

2.5 直方圖 34

2.6 眾數 38

2.7 代表值攻擊法 39

2.8 變異數 46

第2章的問題 47

第3章標準化分數的意外感 48

3.1 學校的圖書室 48

3.2 平均數與變異數 49

3.3 數學式 52

3.4 變異數的意義 56

3.5 標準化分數 60

3.6 標準化分數的平均 64

3.7 標準化分數的變異數 66

3.8 標準化分數的意義 69

第3章的問題 72

第4章投擲硬幣10次 74

4.1 村木老師的『問題卡片』 74

4.2 『正面出現次數』的平均數 76

4.3 正面出現k次的機率Pk 79

4.4 巴斯卡三角形 82

4.5 二項式定理 84

4.6 『正面出現次數』的標準差 85

第4章的問題 91

第5章擲出硬幣的真相 91

5.1 和的期望值等於期望值的和 92

5.2 期望值的線性性質 93

5.3 二項分布 99

5.4 硬幣真的公正嗎？ 102

5.5 假設檢定 105

5.6柴比雪夫不等式 110

5.7 弱大數法則 116

5.8 重要的S 120

第5章的問題 121

尾聲 125

解答 127

給想要多思考一點的你 144

後記 147

索引 149

各界推薦／推薦序

前師範大數學系教授兼主任洪萬生

內容試閱

今天，表妹由梨身穿牛仔褲、綁著馬尾，又跑到我的房間玩耍。

我：「由梨，妳看起來很高興喔。」

由梨：「嘿嘿，很明顯嗎？」

我：「很明顯。妳一直在奸笑啊。」

由梨：「我哪有奸笑啊，這是微笑好嗎？」

我：「發生什麼好事了嗎？」

由梨：「嘿嘿，沒什麼，就之前的測驗啦。」

我：「啊，妳拿到不錯的成績。」

由梨：「五科中，最後發下來的數學，我拿到100分！」

我：「好厲害！……不過，測驗的滿分是100分嗎？」

由梨：「這樣問好過份！當然是滿分100分啊。這次測驗，其他四科考糟了，數學剛好救了回來。」

我：「數學考100分，提高了平均分數嘛。」

由梨：「對啊。多虧了數學，平均分數提高了5分！」

我：「原來如此，由梨五科的平均分數是80分啊。」

由梨：「嗯嗯嗯嗯！？給我等一下！」

我：「咦？不對嗎？」

由梨：「為什麼哥哥會知道我的平均分數？」

我：「當然知道啊……」

由梨：「你聽誰說的？」

我：「……妳自己說的。」

由梨：「我才沒有說！我只說──
・最後一科數學拿到100分
・多虧數學，平均分數提高了5分
──而已啊！」

我：「稍微算一下就知道了啊。」

由梨：「咦？」

我：「這就像解這樣的問題嘛。」
問題1（計算平均分數）
由梨應考五科各科滿分100分的測驗。
最後一科數學拿到100分。
平均分數因而提高了5分。
試問由梨的五科平均分數為多少？

由梨：「別換成數學問題啦！」

我：「這很容易解喔。」

由梨：「的確……這可以解開。嗚──太大意了！數學100分提高平均分數5分，另外四科分得20分，所以五科的平均分數等於數學的100分減去20分的80分嘛……哇──」

我：「咦？妳是怎麼算的？」

由梨：「嗯？我是把『數學100分』超過『五科平均分數』的分數，『平分給剩餘的四科』。」

我：「平分嗎？」

由梨：「因為另外四科必須各提高5分，所以要從數學分出5 × 4＝20分嘛。因此，五科的平均分數會是數學的100分減去20分。」

我：「啊啊，原來如此。把數學的分數分給另外四科，平均分數提高5分，這樣全部科目的分數就會相同。這的確很好理解。」

由梨：「嘿嘿！」我：「我的解法是這樣：假設數學以外的四科平均分數為x分，則四科總分數為4x分。加上數學的100分後，則五科的總分數會是4x＋100分。然後，因為五科的平均分數比四科的提高5分，所以五科的平均分數為x＋5分。換句話說，五科的總分數會是5（x＋5）分。由這兩種觀點來想五科的總分數，就可以列出一次方程式，求解得x＝75，所以四科的平均分數是75分，而五科的平均分數是80分。」

由梨：「真的耶……不對啦！你怎麼可以這樣若無其事偷算我的成績？好過分。」

我：「抱歉、抱歉。」

由梨：「一不小心就中了數學的詭計！」

我：「這才不是什麼詭計……」
解答1（計算平均分數）
由梨的五科平均分數是80分。

由梨：「真的不能小看平均數……」

我：「平均數是代表值之一嘛。」

由梨：「代表值？」

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