제6판 2023.06.23

제5판 2021.06.30

중판 2020.09.25

제4판 2019. 1. 15

제3판 2017. 6. 10

중판 2017. 2. 10

중판 2016. 2. 10

제2판 2015. 1. 15

중판 2013. 7. 20.

초판 2013. 1. 20.

지금 세계는 공포 속에서 불안에 떨면서 살아가고 있다. 러시아는 우크라이나를 침공하여 전쟁이 진행 중이고 미국은 중국과 사생결단의 패권경쟁에 여념이 없어 중국 경제는 쇠락의 길로 달려가는 듯하다.

이런 와중에 북한은 미국과 한국을 위협하면서 걸핏하면 미사일을 쏘아대고 있다.

국내적으로는 지금 경제가 엉망으로 치닫고 있다. 중국에 대한 수출이 부진하고 침체 속에서 물가는 올라 이를 잡으려고 미국 따라 금리를 인상하고 있다. 한국 경제는 상당기간 침체의 늪에서 헤어나기 어려울 듯하다.

이러한 내우외환 속에서 기업경영을 담당하는 경영자들은 참으로 고초가 많을 것 같다. 불확실하고 불안정한 환경에서 의사결정하기가 무척 힘들 것이다. 이러한 상태에서도 경영자들은 빠르고 현명한 의사결정에 전념해야 할 것이다. 기업들은 그동안 발전해 오면서 가격(효율), 품질, 스피드, 이노베이션 등을 통해 경쟁해 왔다. 그러나 이제는 4차 산업혁명이 진행하면서 쏟아져나오는 빅데이터를 분석하여 얻는 지식, 정보, 통찰력 등을 통한 데이터 기반 의사결정을 신속하게 하면서 경쟁력을 강화하고 있는 추세이다. 통계학과 데이터 마이닝, 경영과학과 비즈니스 분석론이 각광을 받는 이유가 바로 여기에 있다.

이번 개정판을 손질하는 데 있어서 4차 산업혁명에 관한 내용과 빅데이터가 통계학의 여러 분야에 미치는 영향에 관한 내용을 보완하였다. 통계문제를 푸는 데는 Excel의 활용이 중요하다. 이제는 손 사용 문제풀이 다음에 바로 Excel 활용문제풀이를 연속함으로써 두 가지 방법을 동시에 공부할 수 있도록 하였다.

독자들은 연습문제에 대한 손 사용 방법과 Excel 활용 방법을 출판사 박영사의 HomePage에 접속하여 다운로드 받아 활용하기 바란다. 한편 이 책을 교재로 사용하시는 강사님들은 이러한 해답집 외에 PowerPoint를 사용하여 만든 강의안을 다운로드하여 이용하시기 바란다.

끝으로 본 개정판이 출판되기까지 많은 분들의 배려와 수고가 있었다. 우선 박영사의 안종만 회장님의 협조와 배려에 감사하다는 인사를 전하고자 한다. 또한 시간이 촉박한 가운데도 열정과 노력을 아낌없이 쏟아 부은 편집부의 전채린 차장께 심심한 사의를 표하고자 한다.

2023. 5. 29.

강금식

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

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