제1 장 통계학의 이해
1.1 통계학의 의미 ······························································································· 3
1.2 통계학의 분류 ······························································································· 4
1.3 모집단과 표본 ······························································································· 7
1.4 데이터 마이닝 ····························································································· 13
4차 산업혁명 _ 13
빅데이터 _ 15
비즈니스 분석론 _ 16
인공지능 _ 19
데이터 마이닝 _ 20
▶ 연습문제 ········································································································· 22

제2 장 기술통계학Ⅰ：데이터의 정리 및 표현
2.1 데이터의 종류 ····························································································· 27
범주 데이터와 수치 데이터 _ 28
이산 데이터와 연속 데이터 _ 29
단변수 데이터와 다변수 데이터 _ 30

2.2 측정척도의 형태 ························································································· 32
명목척도 _ 32
서열척도 _ 33
구간척도 _ 34
비율척도 _ 34
2.3 도수분포표 ·································································································· 36
기본 개념 _ 36
도수분포표의 그래프 _ 37
2.4 범주 데이터의 정리 ···················································································· 37
도수분포표 _ 37
도수분포표의 그래프 _ 40
2.5 수치 데이터의 정리：이산 데이터 ····························································· 45
도수분포표 _ 45
도수분포표의 그래프 _ 46
2.6 수치 데이터의 정리：연속 데이터 ····························································· 47
도수분포표의 그래프 _ 50
2.7 EXCEL 활용 ································································································ 53
▶ 연습문제 ········································································································· 64

제3장 기술통계학Ⅱ：요약통계량
3.1 중심경향의 측정치 ······················································································ 73
산술평균 _ 74
중앙치 _ 75
최빈치 _ 76
평균, 중앙치, 최빈치의 비교 _ 77
3.2 산포의 측정치 ····························································································· 78
범위 _ 80
중간범위 _ 81
평균절대편차 _ 82
분산과 표준편차 _ 83
Chebyshev의 정리 _ 88
변동계수 _ 90
3.3 상대위치의 측정치 ······················································································ 91
백분위수 _ 92
사분위수 _ 93
Z 값 _ 94
3.4 형태의 측정치 ····························································································· 97
비대칭도 _ 97
첨도 _ 99
3.5 EXCEL 활용 ·······························································································100
▶ 연습문제 ········································································································108
제4장 확률이론
4.1 사상과 표본공간 ························································································113
4.2 집합이론 ····································································································118
집합의 개념 _ 118
집합의 종류 _ 119
4.3 확률의 정의 ·······························································································124
고전적 방법 _ 125
상대도수 방법 _ 125
주관적 방법 _ 127
4.4 확률의 공리 ·······························································································127
4.5 확률의 연산법칙 ························································································129
덧셈법칙 _ 129
조건확률 _ 132
곱셈법칙 _ 140
4.6 Bayes 정리 ································································································142
개념 _ 142
표의 이용 _ 144
4.7 EXCEL 활용 ·······························································································146
▶ 연습문제 ········································································································147

제5장 확률변수와 확률분포
5.1 확률변수 ····································································································155
5.2 확률분포 ····································································································157
이산확률분포 _ 158
연속확률분포 _ 160
5.3 확률함수 ····································································································161
확률질량함수 _ 162
확률밀도함수 _ 164
5.4 확률변수의 기대값과 분산 ·········································································167
기대값의 의미 _ 167
기대값의 특성 _ 168
분산 _ 169
5.5 결합확률분포 ·····························································································173
결합확률분포의 개념 _ 173
조건확률 _ 175
두 변수의 독립성 _ 176
5.6 공분산과 상관계수 ·····················································································177
공분산 _ 177
상관계수 _ 179
5.7 EXCEL 활용 ·······························································································180
▶ 연습문제 ········································································································184

제6장 확률분포Ⅰ：이산확률분포
6.1 베르누이 시행 ····························································································191
6.2 이항분포 ····································································································192
이항 확률질량함수의 이용 _ 193
이항확률표의 이용 _ 195
6.3 이항분포의 형태 ························································································197
6.4 이항분포의 기대값과 분산 ·········································································199
6.5 포아송분포 ·································································································202
개념 _ 202
포아송 확률질량함수의 이용 _ 203
포아송 분포표의 이용 _ 204
6.6 초기하분포 ·································································································206
개념 _ 206
초기하분포의 확률질량함수 _ 207
6.7 EXCEL 활용 ·······························································································209
▶ 연습문제 ········································································································211
제7장 확률분포Ⅱ：연속확률분포
7.1 확률밀도함수 ·····························································································217
7.2 정규분포 ····································································································219
정규분포의 사용 _ 219
정규곡선의 형태 _ 219
정규곡선의 특성 _ 220
7.3 표준정규분포 ·····························································································224
정의 _ 224
표준정규분포표의 이용 _ 230
정규분포의 응용 예 _ 238
7.4 이항분포의 정규근사 ·················································································241
7.5 지수분포 ····································································································243
개념 _ 243
지수분포의 확률 _ 245
7.6 EXCEL 활용 ·······························································································247
▶ 연습문제 ········································································································252
제8장 표본분포
8.1 표본추출 ····································································································259
표본조사의 필요성 _ 259
표본오차와 비표본오차 _ 260
8.2 표본추출 과정 ····························································································262
8.3 표본추출 방법 ····························································································263
확률 추출방법 _ 264
비확률 추출방법 _ 266
8.4 표본분포 ····································································································266
8.5 평균의 표본분포：복원추출 ······································································269
개념 _ 269
평균의 표본분포의 기대값과 분산 _ 273
평균의 표준오차 _ 275
8.6 평균의 표본분포：비복원추출 ··································································277
8.7 중심극한정리 ·····························································································281
표본크기의 영향 _ 281
모집단이 정규분포를 따를 때 _ 282
모집단이 정규분포를 따르지 않을 때 _ 284
8.8 비율의 표본분포 ························································································287
개념 _ 287
비율의 표본분포의 기대값과 표준편차 _ 289
이항분포의 정규근사 _ 292
유한 모집단에서의 표본비율의 표준편차 _ 293
8.9 EXCEL 활용 ·······························································································294
▶ 연습문제 ········································································································298
제9장 통계적 추정：한 모집단
9.1 점추정과 구간추정 ·····················································································305
9.2 추정량의 결정기준 ·····················································································306
불편성 _ 307
효율성 _ 308
일관성 _ 309
충족성 _ 310
9.3 신뢰구간 추정 ····························································································311
개념 _ 311
오차율 _ 313
9.4 모평균의 신뢰구간 ·····················································································314
모표준편차를 아는 경우 _ 314
모표준편차를 모르는 경우：소표본 _ 320
9.5 t 분포 ·········································································································320
모표준편차를 모르는 경우：대표본 _ 327
9.6 모비율의 신뢰구간 ·····················································································329
9.7 표본크기 결정 ····························································································331
모평균 추정 _ 331
모비율 추정 _ 334
9.8 모분산의 신뢰구간 ·····················································································336
χ2 분포의 특성 _ 337
모분산의 신뢰구간 _ 341
9.9 EXCEL 활용 ·······························································································344
▶ 연습문제 ········································································································348
제10장 가설검정：한 모집단
10.1 가설검정 ····································································································355
가설의 의미와 종류 _ 355
가설의 설정 _ 356
가설의 형태 _ 358
가설검정의 오류 _ 360
결정규칙 _ 362
가설검정의 순서 _ 366
10.2 모평균의 가설검정 ·····················································································367
모표준편차를 아는 경우 _ 368
모표준편차를 모르는 경우 _ 378
10.3 모비율의 가설검정 ·····················································································383
10.4 모분산의 가설검정 ·····················································································387
10.5 EXCEL 활용 ·······························································································390
▶ 연습문제 ········································································································395
제11장 통계적 추정과 가설검정：두 모집단
11.1 표본의 독립성과 종속성 ············································································403
11.2 두 표본평균 차이의 표본분포 ····································································404
11.3 두 모평균 차이에 대한 추정과 검정 ··························································406
독립표본 _ 406
대응표본 _ 414
11.4 두 모비율 차이에 대한 추정과 검정 ··························································418
11.5 두 모분산 비율에 대한 추정과 검정 ··························································423
F 분포 _ 423
두 모분산 비율의 추정 _ 427
두 모분산 비율의 검정 _ 428
11.6 EXCEL 활용 ·······························································································431
▶ 연습문제 ········································································································438
제12장 분산분석
12.1 분산분석의 의미 ························································································447
12.2 실험설계의 기본 개념 ················································································448
12.3 분산분석의 기본 원리 ················································································450
12.4 일원배치법：반복 수가 같은 경우 ····························································452
12.5 이원배치법：반복없는 경우 ······································································462
12.6 이원배치법：반복 있는 경우 ·····································································468
12.7 EXCEL 활용 ·······························································································475
▶ 연습문제 ········································································································480
제13장 회귀분석과 상관분석
13.1 회귀분석과 상관분석 ·················································································487
13.2 산포도 ········································································································488
13.3 단순선형회귀모델 ······················································································491
확정적 모델과 확률적 모델 _ 491
모집단 단순회귀모델 _ 492
표본 회귀모델 _ 494
오차항에 대한 가정 _ 496
13.4 최소자승법 ·································································································498
13.5 표본회귀선의 적합도 검정 ·········································································502
13.6 상관분석 ····································································································510
공분산 _ 510
상관계수 _ 512
13.7 표본회귀선의 유의성 검정 ·········································································515
13.8 종속변수 Y 의 추정과 예측 ········································································520
13.9 EXCEL 활용 ·······························································································526
▶ 연습문제 ········································································································534
제14장 다중회귀분석
14.1 다중회귀모델 ·····························································································541
다중선형회귀모델 _ 541
다중회귀모델의 가정 _ 543
14.2 최소자승법 ·································································································544
14.3 다중표본회귀식의 적합도 검정 ·································································546
추정치의 표준오차 _ 546
결정계수 _ 548
14.4 다중회귀모델에 대한 유의성 검정 ·····························································550
F 검정 _ 550
t 검정 _ 552
14.5 종속변수 Y 의 예측 ····················································································555
14.6 범주적 독립변수 ························································································557
▶ 연습문제 ········································································································561
제15장 χ2 검정과 비모수통계학
15.1 모수통계학과 비모수통계학 ······································································569
15.2 모집단 분포의 적합도 검정 ·······································································570
모비율의 검정 _ 571
모집단 분포의 검정 _ 575
15.3 두 변수 간의 독립성 검정 ··········································································580
15.4 EXCEL 활용 ·······························································································584
▶ 연습문제 ········································································································586
부표
A. 이항분포표 ··································································································· 592
B. e-μ의 값 ······································································································· 595
C. 포아송분포표 ······························································································· 596
D. 표준정규분포표 ···························································································· 598
E. 난수표 ··········································································································· 599
F. t 분포표 ········································································································· 600
G. χ2분포표 ······································································································ 601
H. F 분포표 ······································································································· 603
◈ 영문색인 ················································································································ 607
◈ 국문색인 ················································································································ 612

머리말

지금 4차 산업혁명이 한창 진행 중이다. 4차 산업혁명은 제조업에 인공지능, 사물인터넷, 빅데이터 등 정보통신기술(ICT)을 접목하여 이룩하려는 기술혁명이다. 4차 산업혁명의 기본 핵심기술은 인공지능이다. 그런데 인공지능은 빅데이터를 기반으로 학습을 하고 데이터를 기반으로 정보를 제공한다. 따라서 빅데이터는 4차 산업혁명에서 원유와 같은 역할을 수행한다. 정보기술 기기의 발전으로 데이터는 매일 엄청나게 쏟아지고 있다. 이러한 빅데이터는 규모, 다양성, 스피드 등에 있어 과거에 사용되었던 데이터에 비해 엄청나기 때문에 비즈니스 분석론, 데이터 마이닝과 같은 새로운 빅데이터 분석기법이 출현하였다.
전통적인 통계학의 목적은 스몰 표본 데이터를 이용해서 최대한의 정보를 추출하려는 것이었다. 시간과 비용 등으로 말미암아 표본을 추출할 수밖에 없지만 데이터의 수집ㆍ처리ㆍ분석하는데 부담이 커서 최소한의 표본추출에 기반한 분석에 만족하여야만 하였다. 이제 데이터가 부족한 사회에서 넘치는 사회로 바뀌었다. 빅데이터 시대에는 표본 데이터가 아니라 전체 데이터를 가지고 분석할 수 있게 되었다.
본서는 전통적인 통계분석이론을 기본으로 한다. 여기서는 표본크기가 아주 중요하다. 예를 들면, 표본분포, 통계적 추정과 가설검정, 회귀분석에서는 제한된 표본크기를 전제로 이론을 전개한다. 따라서 빅데이터의 존재는 이러한 부문에서의 의사결정에 영향을 미친다.
데이터가 표본분포에서 표준오차에 미치는 영향, 신뢰구간의 폭에 미치는 영향, 가설검정에서 귀무가설의 기각 여부에 미치는 영향, 가설검정에서 p값에 미치는 영향 등에 관한 내용들을 본서에서 새롭게 설명하였다. 한편 데이터 마이닝에서는 회귀분석이 아주 중요한 역할을 하기 때문에 다중회귀모델에 관한 내용도 추가하였다.
일반적으로 통계학은 어렵고 복잡한 과목이라고 여기고 학생들은 기피하려는 경향이 많다. 왜냐하면, 공식도 많고 수식도 많아 계산하는 과정이 복잡하기 때문이다. 따라서 본서는 공부하는 학생 위주로 집필하였다. 개념과 원리는 이해하기 쉽도록 자세히 설명토록 하고 모든 계산 문제에 대해서는 주어진 데이터를 이용해서 손으로 문제를 풀고 또한 Excel을 사용해서 해답을 구하도록 하였다. 따라서 독자들은 도서출판 박영사의 홈페이지에 접속하여 해답을 다운로드 받아 활용하기 바란다.
한편 이 책을 교재로 채택하시는 강사님들을 위해서는 이들 해답집 외에 별도로 PowerPoint를 사용하여 만든 강의안을 준비하였으니 박영사 기획부에 연락하여 구하시기 바랍니다.
끝으로 본 개정판이 출판되기까지는 많은 분들의 배려와 수고가 있었다. 우선 박영사의 안종만 회장님의 협조와 배려에 대해 감사하다는 인사를 전하고자 한다.
또한 시간이 촉박한 가운데도 열정과 노력을 아낌없이 쏟아 부은 편집부의 전채린 과장께 심심한 사의를 표하고자 한다.
2021. 6. 23.
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